Thanks for the video! Could you explain the underlying math a little bit more? I really don't understand why we assume exponential growth of the probability to see at least one dupe. Isn't it just the # of playsets times 3,64%? For eight playsets in my 40 card deck, drawing a 5-card starting hand, I draw at least one dupe with a probability of 29,1% (I think). Where does the exponential growth come from, seeing that the cards/playsets are independent from each other.
The best way to visualize this without being confused by numbers is this. Imagine you have a 42 card deck and 14 playsets. We will take the draw of 5 one at a time instead of all at once. To start you draw your first card you have out of 5. We will call it A. (A) draw has to doge itself on its second card. Now we draw card 2 you have to dodge copy of A with 2/41 chance to draw a dupe. Say you dodge and draw card B. Now on your 3rd draw A and B BOTH have to dodge thier respective dupes. Which means now 4/40 percent chance to draw a dupe on draw 3. (10%) Your 3rd card you draw is C. Now your 4th card has you have dodge A,B & C and you have 6/39 chance to draw a dupe. Now the forth card is D. That means your 5th card odds to draw are dupe is 8/38. Which that draw alone is 21% When you take all of these factors together you have about a 33% chance of dupe. You can see how because their was a guaranteed chance of getting a playset card in your hand it now made things exponentially worse. If you drew a non playset card like a 1 of then that card "draw" is safe and won't effect. Therefore the more playsets the deadliest it is. Your 5 card hand will become 4 in about 1 in 3 games if you have 8 playsets I can show this math on discord but this one takes a long time so bring popcorn.
@@JessePerezStrategyGaming Ahh, now I see where the misunderstanding comes from. With exponential growth, you are referring to the number of cards drawn from deck. The number of playsets in the deck itself does not contribute to exponential growth in the probability of duplicates on a starting hand of 5. In fact, the probability per playset decreases slightly due to the cases where you draw two duplicate pairs. So, let's take the example of 40 main deck and 5 hand cards: The probability of having at least one duplicate in hand depending on the number of playsets is: 1 - 3,6% 2 - 7,2% 3 - 10,8% 4 - 14,3% 5 - 17,7% 6 - 21,2% 7 - 24,5% 8 - 27,8% 9 - 31,1% With 8 playsets in my 40-card deck, I therefore draw a dead card in over a quarter of all games, provided I always go first. If I go second, i.e. draw 6 cards, the probabilities look much worse due to the exponential growth depending on the cards drawn that you mentioned: 1 - 5,4% 2 - 10,6% 3 - 15,7% 4 - 20,6% 5 - 25,5% 6 - 30,2% 7 - 34,7% 8 - 39,1% 9 - 43,4% If I draw 6 cards from my 40-card deck, that contains 8 playsets, I will have a dead card in my hand 40% of the time! To summarize, the probability of having duplicates in the starting hand increases exponentially with the number of cards drawn and (almost) linearly with the number of playsets in the deck. The number of playsets in the deck raises the exponential curve to a higher trajectory, so to speak.
@@JessePerezStrategyGaming you are correct about this math. But there's no exponential growth here. Each playset that you add has roughly the same chance of getting you a dupe that the previous one. So there's no reason why you should stop at X playsets or whatever. The cost on them is linear so if you think the 9th is bad, the 1st one is also bad
@@lautaromonsalvo8808 there is exponential growth. I made a video specifically going into great detail on it you can find here. th-cam.com/video/_Ia9pq9F4b0/w-d-xo.html
@@JessePerezStrategyGaming The probability of having at least one duplicate in hand depending on the number of playsets is: 1 - 3,6% 2 - 7,2% 3 - 10,8% 4 - 14,3% 5 - 17,7% 6 - 21,2% 7 - 24,5% 8 - 27,8% 9 - 31,1% Can you see how each playset that you add, increases the chance to dupe by almost the same amount? There's no exponential growth there. Playset 9 is as bad as playset 1, they both increase duping by 3.6%. Any rule where you have to play less than X playsets is nonsense because playsets don't get marginally worse as you add more.
Have you tried different shuffling methods? Like not only riffle shuffling. This used to happen to me and by just shuffling differently it just stopped happening
Ive been looking for someone to make comprehensive deck building videos for years. Finally! I love how you break things down in an analytical sense also.
I am so glad you enjoy the videos! I love doing these mathematical breakdowns i have so much fun with them. Glad there are others to that enjoy numbers like i do. Thank you for watching!
-Ash and wanted have NOT been hit in the tcg -Veiler and imperm are not once per turn, so they are still good to draw multiple of -oversimplifying too much because you are not taking the gameplay of the deck into account. snake eye doesnt care about drawing multiple starters because they often need to discard a card. also drawing wanted/diabelle/bonfire on top of one card combo is how you play through handtraps. they are both starters or extenders and necessary during this handtrap heavy format -prank kids needs kids in the deck to summon them. if you dont have 2 of a type in the deck you cant xyz summon that level (ie if you draw 1 of them and only play 2). also they are good to draw in multiples because you can fuse with the ones in your hand and save bodies on the board. not every deck is based on one card combos. labrynth is another good example. good deck building involves understanding how that specific strategy functions and optimizing that, rather than focusing on a specific magic number of starter/nonengine cards -if you run 12 starters, and play 7 rounds of swiss, about 3 games you will draw no starter. probably not going to top doing that. better to see 2 starters some games than have too many games where you cant play, at least in a tournament all that being said this is a good overview of how ratios will affect your starting hand, and the diminishing returns, especially for those new to deck building; you explained it well. i do agree people focus a bit too much on consistency (like always running 40) and less so on other things, such as how well you can play around hand traps/breakers, what nonengine people are playing at the moment, knowing the weaknesses of other decks in the format and how to counter them etc. these things are more instrumental to the success of top players than consistency alone
Sorry for late reply wanted to make sure I address everything as this was a great comment! Sorry ash is limited in MD and OCG & wanted is limited in MD. It is very hard to remember the exact forbidden limited lists for every card in every format. This point was really just a point of interest and not really a major point i just spontaneously said that because it was on my mind at the time. Apologies for the error nonetheless. I thought I mentioned that the playset rule only applies for cards that are HOPT effects. If i missed that then apologies also. Which is why i didn't have imperm in the original playsets. I do talk about imperm specifically how that is good and doesn't follow the birthday paradox but that was in another video and not this one so i might have gotten that confused but yes non HOPT wont be counted to the playset rule/birthday paradox. I could have went further in depth on prank kids but i didn't want to confuse the audience with what pk did and just was using it for a general example. The math does change if you go in depth with prank kids as they can even preform certain 2/3 card combos, the discard with fansies or the banish and draw 1 with rockies or the +1 with plan at the end of the turn benefit thinning strategies. But so many people would be confused and i made an artistic choice to deliberately leave that out as prank kids was not the point of the video. Ultimately, It seems like it came at the cost of confusing the more well known players and skilled players especially those who are skilled at using prank kids in favor of helping those less versed in prank kids. However, Not drawing a starter though in your round of swiss example doesn't automatically equal a loss. If you have 0 starter that means your 5 card hand is all tech/handtraps which is likely enough to force a simplified gamestate and get you another turn at which point you have a big chance of gettiing your starter topdeck or side engine rolling (adventure/kastira as used in example) All in all great points and I agree. Well written comment and well said! Thank you for watching I appreciate comments like these the most.
@@JessePerezStrategyGaming hey thanks for the thoughtful reply! no need to apologize, it definitely is hard to keep track of the banlists between 3 different formats. also w the imperm thing i see it as less of a correction and more just pointing it out so people in the comments are aware if they didnt see the other video; so no need to apologize there either:) glad to hear this didnt come off as a dig or anything, just wanted to point these things out as i think they’re important details. I take your point that you were just trying to show a clear example of not playing too many normal summons as starters basically. branded comes to mind as a good example of this, some players only play 2 aluber for this reason. perhaps it would help in the videos to have a clarifying statement like “there may be other reasons you choose to play more starters in a deck, like if the cards have other uses, but this is an example of a starting point when deck building to not have too much engine”. or something like that if that makes sense. would help to clarify the snake eyes bit too. glad to see thoughtful discussion from you in the comments as always Jesse. Love the energy and keep up the good work :)
I would like to add to this that some cards are just better to draw than others in many situations and so are way better to draw 2 of than others that are different but are way less impactful.
Swordsoul is a 2-card combo deck, it needs to see a normal summon and a wyrm or swoso card. Traptrix is another deck that breaks the 8 playset rule because by design it can't combo with 1 card.
Yes! swordsoul is a 2 card combo! It has diffrent math you can find here th-cam.com/video/dUB_C53DAt4/w-d-xo.html generally, for 2 card combos, you want to play 20-23 cards to be in that 85% range. Hopefully this helps
This is EXTREMELY well articulated not even for just yugioh but the break down of statistics was pleasing to listen too. I hope to see more video on your channel
For the Snake-eyes cards I'm not sure this is the best exemple Diabellstar is both a starter and an extender (so is bonfire) and this would actually change the math because it's great to see 1 Diabel, 1 wanted or 1 bonfire on top of your first starter (the card has multiple uses) The Prankids exemple is perfect though
@@rhyned Not to mention, if you use Pandemonium you're locked into Prank Kids names, which means you can't always reliably go into those strong game-ending link monsters (Borrelsword, Accesscode, etc.) Often Prank Kids will run over 2 turns, and therefore needs more than of each name (Unless you're running Plan to recycle, since you can't always rely on getting to your one copy of Pranks) Besides, all of the Prank Kids can summon from deck OR hand, so yeah- you'd rather have a hand trap in hand, but they're not bricks in hand... There's a reason why literally every single Prank Kids top ran 3 of all of the names besides MAYBE Rocksies. The math may be there, but math isn't always the answer. Sometimes logic is.
The Prankids example is technically bad, too, because the deck Fusion summons, so it has use for more bodies in the hand, but the way it was described here focusing on the ratio of Normal summons, it works.
@@jonathonyeary509during adventurer format some pk lists ran 2 of each name and 2 place, including elijah green's ycs winning list Although those versions of the deck had 4k damage from the adventurer engine + 2.5k from dpe so pushing for game wasn't an issue, nor was playing a longer game with less pk cards since dpe thrives in simplified gamestates Basically the ratios depend on the format and build of the deck
One of my first decks I built for competitive was a hyper consistent Live Twins. I at first was frustrated with how all my opponents seemed to draw their nonengine against me while I kept flooding with normal summons and extenders until I realized I that i was causing myself this problem.
i too made that mistake with MANY of my decks for the longest time. it wasn't until way later i realized there is so much more a deck should do then try to turbo out 1 thing as close to 100% as possible.
cards that are not once per turn are a great way to bypass the 8 playset rule. Also I wouldn't rune any less than 3 ash blossoms in snake eyes as it fufills the very valuable anti maxx "c" roll that I wouldn't run any less than the allowed 6 of, with maxx "c" being basically an auto win against you if you don't draw a counter. This can also make drawing 2 ash less painful because you ash their maxx "c" and then you ash them on their turn (or vise versa if you are going second).
Running only 12 Starters means you brick 15% of the time which is acceptable casually, but if youre playing competitive then you need your Deck to do its thing more than just 85% of the time. Diminishing returns is real but I don't think it applies
@@kenshi1985br Unless all your starters are normal summons, then that won't happen. Like if you're playing Invoked then you don't play too many normal summons. However there are plenty of starters that are spells and special summons. Also, even in a deck like Prank Kids, imagine not opening a single Prank Kid 1/4 games, because you're afraid of a hypothetical hand trap. That's not good deck building theory. If youre afraid of hand traps then max out on starters, extenders, and cards like crossout/talents to keep playing. Don't just cut your starters
Yeah it's not diminshing returns because while the percentage gain decreases as you get closer to 100%, the value of each percent also increases. 95% consistency (brick 1 in 20 games) is literally twice as consistent as 90% (brick 1 in 10 games) consistency. The increase in consistency is actually linear with the number of starters.
I don't deny there are a lot of players that just simply add everything related 3x or simply max copy everything without any thought like just putting a pile of related cards together when comes to deck building, which usually means bad, and you did have a point on the part on the concept of "better choice". However , the main thing about this ain't as simple as "you got starter you are good", it is about "do you really need those in 3 copies?" or may be even "how many copies of this card do I need?", "will this amount of copies synergies each other or just brick me when all drawn to the hand?". 99% hyper consistency is not necessary means bad, it really depends on will it brick, or just can have other uses when multiple of it drawn to hand. Take snake eye as an example. You got diabellstar, blue snake eye, bonfire into the hand, it is still not a bad hand as you can just thrown a card for diabellstar, summon blue snake eye search for kurikara, bonfire into red or may be other useful things, in the mean time you can even force trade your opponent hand trap if you got so many starters. Snake eye got like so many "starters" , but it is never brick due to how flexible it is to the point your opponent has to force their hand trap into your cards so that you can never get that much of value before it start snowballing. The case become slightly different when comes to prankids. Prankids themselves are bound to consume big slots as it don't actually works by themselves if just play to field without legal targets in the deck, which means you pull 1 prankids to the hand, 1 less you can recruit from the deck because of how prankids works. You got 3 prankids in the hand, which can also be bad if you summon 1 and leave the other 2 doing nothing. However , I want to mention if you have a prankids fusion or equivalent in the hand , multiple prankids become somewhat acceptable instead of a bad brick as you save a normal summon while you got 2 or may be 3 pankids to the field which can leads to big board if play properly. Things can even get complicated if you run rank 3 or/ with adventurer engine as well. you can link 2 into burning abyss dark fairy for a set of adventurer while allowing prankids, to build a bunch, transition into apollousa, and may be with a thunder dragon fusion into boss prankids follow up by a thunder dragon colossus, depending on build and situation, which may leads to more complicated when considerating the copies of the same card in the deck as well. Also , I will want to mention with this amount of generic searcher nowadays, there is more to consider when comes to card drawing. Chicken Game and Upstart is good by paper because it can means a -6 to your deck size, but that is assuming you are able to play it on your turn. If you go second, those cards literally doing nothing on your opponent turn and just stuck there. If your deck aren't blind second oriented, those are actually pretty bad if you go second and want to interrupt your opponent turn 1, especially you pull a hand trap that is good for opponent first turn instead of other things on your going second game. If i play a deck that is running heavy hand traps that is good to disrupt opponent turn 1, I will not want to use this in the place of hand traps that allow me to disrupt opponent play on opponent turn 1. Furthermore, there are spells, it also means that the card that synergy will be different as well. It is more synergy to decks like sky striker, spellbooks or decks running reasoning/monster gate that needs to stack spells on the graveyard which in current card pool they are either underwhelming power or just don't see much synergy with majority of decks as majority of decks are more monster oriented rather than spells. Also, 6 slots of the deck space can be a lot, might be better to include another engine depending on deck type and build as well. Hence, if you want a good consistency, frequent testing on pulling the first 5 cards and see will it brick becomes important when comes to deck building (thank god master duel implement this feature). You can hardly build a decent deck without some sort of testing and filter out those bricks as sometimes things are not that obvious and interrupts from your opponent can make things even complicated when comes to consistency.
You are absolutely correct, there are certain 3 card combos in PK like have 2 kids and a fusion that work for hyperconsistancy. The math for 2 and 3 card combos are different. For 2 card combos you want to run between 20-23 starter/combo cards to get that 85% range. You CAN build your Prank kid deck to facilitate this style of play and this can work as well if you want. For simplicity sake i didn't want to confuse the audience that were not familiar with prank kids and go into the fusions - can banish 1 with rockies to go +1 the discard with fansies etc. So I deliberately left this out as an artistic choice so i wouldn't confuse but you are absolutely right and if this video was an hour I would certaintly touched on your points. Funny enough I did not do did math for 3 card combos yet as it seems like you would need to run so many cards for it to reliably work that I treat it as a bonus and wasn't worth my time to do the math but I might do it in the future if I get more requests for it. I also completely agree with your take on upstart & chicken game. My goal was to say that chicken game should not be taking the place of a handtrap and i hope that point got across. Thank you for this detailed comment, well put and well written. Thank you for watching!
I understand the point about 3x everything bad, but at the same time I want to add that just starting out learning a deck, it's great to see how things interact. Part of my process in learning a new deck is to start by playtesting three of each and scale back as I figure it out. As I start to see I don't want certain cards in hand as often I scale them back: I can search this card reliably, so I only need one or two; et cetera. It simultaneously builds knowledge of the deck and gives insight into numbers of copies.
@@Damini368 People tend to do this for different reasons. There are also player who just bad in deck building claiming the deck suck just because they add every card together like grouping a pile of cards but claim it suck when they brick very hard. Also the same type of player telling others "don't build deck yourself, just copy one and you good".
Anything that draws 1 to replace itself went from awesome Exodia fuel to just bad the day Droll & Lock Bird was released, that's why all these old Exodia FTK enablers are being released off the banlist.
@@autobotstarscream765 exodia been always a meme deck even with igknight FTK build. Lately OCG just got new support for it, but still a question will it be close enough for a competitive deck.
what a coincidence, I've been binging Phoenix Wright Trials & Tribulations and here you are using the OST & making your case for NOT being hyper consistent with so many multiple copies.... I love it!!! Also took this principle with Heroes & my going second build.... you're phenomenal man
I Love the Phoenix Wright series :) such great memories. I would play it together with my friends huddled around my DS in a car. LOL. Glad you caught that OST.
something i remember hearing from johnny li in a true draco sky striker deck profile on cimo's channel was something along the lines of "too many starters and your deck will be consistent but weak, too many extenders and your deck will be powerful but bricky"
One of my biggest challenges as a deck builder is often trying to figure out how much engine I need in my deck, mainly because it often depends on what you're piloting. Most decks want to have plenty of space for non-engine, and the type of non-engine depends on the deck. For example, i've been messing with Shining Sarc lately, and this deck cares a lot about including handtraps and quick-play spells for non-engine since it synergizes with Future Silence. But if you're playing either a mishmash of archetypes or just a ramp or combo deck in general (insert obligatory jab at Branded players), the engine to non-engine ratio isnt always very clear because in some instances, you're basically falling back on either extenders or a secondary engine as opposed to non-engine pieces. I think an excellent example of this is Live Twin Runick Spright. While its not seeing a lot of meta play right now, this deck is honestly all about establishing a big ass board of monsters. It generally wants to play through disruption as opposed to playing more non-commital, and when going first, it often tries to either Iblee Lock the opponent or set up a bunch of roadblocks (like IP to go into cards on the opponent's turn like Apollousa or what have you, as well as in-engine disruption like Trouble Sunny). On top of this, your generic disruption is also a part of your engine in the form of the Runick package.
Yes! I am tracking the progress of your live twin runick deck i see you posting in the community notes. I am very invested to see how it evolves and how your making it. Your cooking up something great!
Perfect example for Upstart is in Kashtira. Upstart directly replaces limited NAMES and not handtrap or tech slots. Combo thin deck into Arise Heart, Upstart draw into disruption, trigger Arise attach off the banished Upstart.
I think this makes sense for general theory about ratios but sometimes drawing dupes isn't such a bad thing. I'd rather have 2 prank kids and play with a 4 card hand than have 0 and not be able to play. Sometimes cards are powerful enough that you want all 3 and you're going to draw 2 and that's ok - if I could play 8 copies of soul charge I'd throw all 8 in every deck I play for example because its so powerful that I'd rather have a dead second copy for a turn than not have it.
Yeah. I like these vids cuz having insight to the actual math is, well, insightful, and can play into how u deckbuild. But definitely as a viewer and player you gotta be able to discern the theoretical math from actual deckbuilding nuances.
For the 8 playset rule, it could have been articulated a bit better, but basically the more playsets you run, the higher chance your hand contains doubles. So its a 3% chance of drawing 2 red prank-kids but it could be like a 20% chance of drawing two of the same prank-kid (red, blue, green or brown) which is why your chance of essentially 4 card hands goes up
I'd love to see a video on 2 card combo decks! For example, a deck like virtual world have varying ratios across multiple deck profiles. Some play 3 of each name, some play 2 laolao/lili, some play 2 of the spells, etc. Maybe there is a list that runs the most optimal amount of engine and tech cards so that you see your 2 card combos most of the time as well as some amount of tech cards.
This is a good video to show to people begging for more Photon Galaxy starters when the Deck already has about 10-11. The Deck is consistent enough. 3 Galaxy Wizard 3 Galaxy Soldier 3 Galaxy Hundred 1 Foolish Burial 2 Photon Delta Wing The Deck hit that sweet spot long ago. Begging for more starters is going to give Photon Galaxy diminishing returns. At this point, what the Deck needs is a better grind game. Otherwise, what's that hyper consistent group of starters gonna do for the Deck?
While I mostly agree, I'd like to add that hyper consistency itself is not a bad thing - it only is if all the cards you add above like 12-15 cards are doing is add consistency to your one main strategy. However, there are a lot of engines you can add that can fulfill different roles in the deck. The one I'm currently playing around with the most is the Allure Queen engine, since it can be a starter for so many different strategies, but it can also act as a security engine (getting Herald of the Arc Light out within 3 summons) and it can also help break boards going second, since you can easily get a Light and Dark Chaos Angel out with it. If your deck is super linear with its starters then yeah, too much consistency is not a good idea. But those decks usually fold to like 1 hand trap, anyway, even if they can occasionally put out insane, literally unbreakable boards.
1) I know I'll be returning to this video regularly thank you 2) That megaman music gives me a pleasant feeling of nostalgia and anxiety from those tense levels XD
Your thoughts on the Duel Links format could be crucial. I find going to two is better for most cards, and I primarily run 30-card decks. The 8-card ED means that you will rarely have more than one of anything there too. There are a lot of 20-card builds that can do some work but end up being glass cannons.
another problem is the kind of starters. For example the deck with a lot of starters today: Snake-Eyes - We have the Normal summon Starters: Ash+Poplar. The problem in having a lot of "Normal summon starters" is obvious, you have 1 normal summon for the turn, if you got both you actually got 1. The deck where this was common, Spright. Any 2 lvl 2 is a combo. So if you go for a lot of monsters that on normal summon summon another one from the deck you are safe? no, since you can only make 1 normal summon. - Special summon Starters: Diabell, They don't cost turn resource to play. The major example is the banned "Mathmech Circular". In the later YCS RIO the "melodius" engine presented its power too - Starters that work as Extenders when hand trapped: Bonfire + Diabell. The "crème de la crème" of starters. This usually go along with the later group. You start with ash, get imperm... well, Bonfire and go on.
This birthday paradox thing in yugioh could be a magnum opus or college thesis. You should definitely try to get this published maybe on YGOMeta This is definitely why I don't like 3 Dark Magical Circle in Duel Links Dark Magician Decks. Players will have 3 DM, 3 apprentice illusion, 3 navigation 3 rod and 3 circle in 20 card lists, where the odds are that circle will likely only reveal a duplicate copy of cards that are already in your hand. 2 is plenty
You and Yishan are the only people I’ve seen go into the math of YGO. Thanks for posting, I actually started having more fun with math since I started playing
I would love to see the math on 60 card decks, I'm playing an HEAVY engine based deck that feels perfectly consistent, but I'd like to see how I could fine tune the exact ratios
I made a video with how to build a 60 card deck with math in it here: th-cam.com/video/80kBBIEdXV8/w-d-xo.html hopefully it answers all the ratio questions you have if it doesn't leave a comment or find me in discord and ill try to help more.
I've spent a good while now trying to math out Ritual Beasts after the new support. The deck has an incredible amount of 1-, 2- and 3-Card combos, access to Emergency Teleport which acts as starter, extender or interruption depending on the hand and has synergies with a lot of different engines, all while having enough space for nonengine as well. It's just a complicated mess of a spreadsheet and trying to figure out and test different ratios is a pain.
Awesome! So glad to know that you like listening to me rant about math and numbers! I always fear I would be putting people to sleep when i talk numbers so glad I can make it interesting! :D
Great video! However, I should probably add some things: 1) Some cards alter the statistics in this video. Chicken Game and Upstart Goblin, for example, would reduce the "real" number of cards in your deck and allow you to run 10-11 starters instead of the mentioned 12 depending on the number of these draw spells that you play. 2) You are absolutely correct about Swordsoul running 8 playsets being a bad thing, but only until you start taking Pot of Desires into consideration. XD
I loved your discussion on upstart and chicken. Those are meant to replace multiple copies of (HOPT) cards you can only play in your turn. I remember a custom format turnament of MBT where Pot of Greed was at 1 and some lists were not playing it, that was poor deck building to me.
Wow that is insane to me that people are choosing not to play PoG!? Even in the most consistant of decks you could still do your plays then do the draw at the end. So shocked. If this tournament was played on MD, Maybe they didn't have the UR dust to spend because thats the only way I can see them not playing PoG
@@JessePerezStrategyGaming th-cam.com/video/Z08fyvXpGUI/w-d-xo.htmlsi=KpuZPUJZJkiJzGW6 This was the format, oc played in a casual way. But this proves the preconseption you were adressing in your video: the avarage yugioh player doesn't understand what odds are
@@JessePerezStrategyGamingPoG is king, to the point of making it worth blowtorching your Deck to get to Pot of Greed for 2 of whatever was left, hence why Pot of Desires was so big, and if experience playing older formats, especially running Salamangreat around the time of TOSS Format, hyperconsistency was only ever used in Exodia Decks until Desires changed the math for a lot of people, and their gameplan became open at least 1 starter and 1 extender in every opening hand at all costs so they could drop a Desires without worrying about what they banished face-down or getting any of it back, because whatever they banished after their initial combo pulled 1 of everything they needed out of their Deck would be either a redundant starter (basically a Garnet), a redundant extender (basically a Garnet), or a non-engine card (no good to you in the Deck until you draw it), because drawing 2 off 1 card and getting the +1 was always worth it while using 1 to draw 1 was just asking to get Drolled, hence why the popular play in Salami was hyperconsistency + Desires, and everyone I saw running Swordsoul was also running Desires to pop off Chengying and get those precious draws for a +3-4 off one Spell after doing their initial combo to pull out 1 of everything they needed to not lose to Desires in order to play, and so it almost feels like now people are building hyperconsistent Decks while forgetting why they popped up in the first place, as almost nobody's running Desires anymore since it was eclipsed by Extravagance and then Prosperity.
Awesome! Glad it was helpful! Also there are so many new types of cards synchro, XYZ, Link etc, my advice which worked for my friends was just to focus on 1 of them and decks with that style and then when you feel comfortable with that mechanic you can learn another others. Trying to learn all at once was to hard for my friends so just focus on 1.
As someone who took a college stats class recently, yeah, all this sounds accurate. Cannot describe the number of people who get confused by the math behind probability when seen on paper vs practice.
What the fuck!? I started this video out of curiosity and I was like ahhh what kind of nonsense is this, but when you came down to cutting down handtraps with different handtraps I was like OMG!!! This is genius, like I finally understood what you mean and I was immediately able to spot the mistakes in my deck. Huge thank you!
Awesome! I am glad you liked the video! If you like the numbers - I have a bunch more math centered yugioh vids that you might like as well. In any event i really appreciate the comment and thanks for watching!
This is why recently i decided to play more than 40 cards in some cases. If all I have is engine, then sure I can have some tech cards, but if all I draw is engine and then my opponent does something crazy like use Maxx C or have board breakers, my one play was countered by the tech cards simply because I lost the coin flip and my opponent had just an ok board going 1st, but couldn't even play going 2nd because my single summon and magic card were both denied.
Man, I just found this video/your channel, and I never been good at figuring out how to make decks. i always go blank. And it might be easy for a lot of people, but not everyone is a mathematician, right? Not everyone is good at deck building... But you're a great teacher.
Thats why alot of ur starters not only start but also continue your plays, think w sky strikers, ur starters r raye, roze, engage, hornet, linkage, and even the field spell however not only are they starters they also help you play your turns after
While watching this I was comparing the deck I use which is @Ignister. It has 11 one card starters. Of which 8 are Normal summons or ways to get to them or get an extender from the deck. 6 normal summons are one card starters. 2 are extenders that if they are in your hand at the same time are a full combo as well. 4 different Cyberse type monsters that can be used as Link material easily. 12 hand traps. I don’t own 20 of them. Two garnets that I don’t want to draw but are needed for the deck to function. One of them is a pseudo garnet as I can search it from the deck if I draw the other. I need both for it to work. My friend hate that deck because it is too strong for them. It seems like I was following the same logic as you. Except I opted for more stuff to counter my decks counters. Hand traps are good in all when you’re using them but when your deck crumbles from a single hand trap you need to have something in place to let you keep going. Which is why I run more extenders in my deck over hand traps as well as anti hand trap cards such as Prohibition, Called By, and Crossout. Is my deck meta? Most certainly not as I am one of a few players who pilots the deck. Especially after a major engine got hit badly. I used Mathmech Circular as an enabler for a very nasty 13 interruption combo. Five negates, multiple bounces, quick effect destruction, hand rip, and revival from the graveyard on command. If I had a copy of S:P Little Knight add another two interruptions. But sadly the deck did get hit badly. I have been tinkering with it for so long that my friends are tired of facing it. Now if I want to duel them I have to use a structure deck. Disappointing really. I would love to hear your thoughts on this type of deck. My side deck is in the same ratios as my non engine so I can swap them out for different matchups. I also run a few hand traps that hard counter my own deck in there as crossout targets. I also play other card games where you can run up to four copies of each card in the deck. In those games there is a resource system in place so the deck building philosophy of Yu-Gi-Oh cannot be applied. Still my decks show results despite some of my friends who play the game questioning my deck building choices. For example me running Prohibition they find weird. Called By cannot stop Nibiru or Imperm so I run it as a counter along side Crossout. Odds are I have a counter to what my opponent is playing in my deck and even if I don’t I can still put them into a very tough spot. My extra deck is built for a one turn blowout. Either ending the match instantly or putting my opponent in a bind. Before Circular was banned the deck could stop a Dark Ruler with ease. Man I want circular back at 1 at the very least.
Wow yes! It seems you were using the EXACT thing i was trying to point out! You also supported your ignister engine with the mathmech one as additional utillity, built your deck to current local counters and did everything great! Shame what happened to circular :( On the deckbuilding side you get an A+! Now for the playing part practicing using new combos and finding a good replacement is probably the hard part. I think it was Bruce lee that said I fear not the man that learned 10000 punches but the man that practices 1 punch 10000 times.
I'm really glad you came back to the normal summon topic and dwelled deeper into that. Your videos are always helping . At least those have helped me to break away from some 'rules' with actual statistical data and concepts when it comes to deckbuilding. Especially the playset one. I assume that one applies only to hopt cards right?
Yes! the playset rule ONLY applies to HOPT cards. So for example, feel free to play as many copies of imperm as you want as that will not count toward this rule.
Its crazy to find out that when i made decks i was indirectly always avoiding making my decks hyper consistent its like finding out something u do everyday has a word to sum up what u do and u never knew the word
i havent played for 20 years! got into MasterDuel and I liked the cyber dragon deck. I bought all the URs n looked at similar decks and I literally run like 2 engines. this video solves my issues! I got to Platinum like a cakewalk but then my deck was no longer viable lol
All of this math is hinged upon perfect rng/shuffling formula which just isn’t the case in tournaments, clashes with law of probabilities // 50/50 laws, is or it ain’t BRUH, just ain’t it.
Interesting point on the shuffling. Its true the math on this is in regard to TRUE randomness and perfect rng. Applies more to Master Duel then in person TCG but interesting to note and good observation.
This video is wonderful, criminally underrated. Both easy and informative. I now actually know why it's wrong to run 3 sinful spoils and 3 poplar. Thank you❤❤
I really love these videos, I think taking this kind of maths approach to deck building helps know you just got unlucky and the issues isn't that you just build your beck badly. One suggestion I would add is at the end of these types of video it would be nice to end on some kind of very clear, actionable application to everything you explained - somethings the application of this gets a little lost in the details. For example, a potential application of this video (if i am understanding the explanation correctly) would be to avoid playing a playsets of a card if its effect is once per turn, and you can change out 1 copy from the playset to other card that does a similar or the same thing. Playsets of cards should be saved for cards that a absolutely essential for the deck to function or have very high power level (I assume something like Maxx C would fall into this category). Or put simplify, if you never want to see 2 copies of the same card in your opening hand, to lower that chance from happening, only play 2. A practical example would be - x3 "Dark Ruler No More". I almost never want to see 2 copies of that in my opening hand, so instead, replace the 3rd copy with something like x1 "Ultimate Slayer" or x1 "Droplet". I think that what we are trying to say in this video - but let me know if I am wrong.
I like how you explain this. Im still tweakin my Voiceless deck. Cz i dont like my ratio rightnow depend on my local meta with so much deck variant. Playing diviner build is bad on my local. Some time i need tech card. But still didnt find the right one. Too much HT so bad. But less HT not good at all. I see your video about boardbreakers and i still think to put some on my deck.
Diviner is such a great card, it has so much utility! if it can send a fairy to the GY and not get negated it can get so much value! Not to mention the tribute effect or it can also be a tuner too!
I'm a huge Infernoid fan, and with the deck coming back, I'd love to see analysis of 60-card decks, ESPECIALLY those with archetypal bricks Similarly, discuss "when to go over 40" like we're seeing with Rescue-Ace profiles
Hey man. Just saw many of your videos to get a sense of the entry level math that takes part in deckbuilding. I know that these calculations are kind of simple and try to encompass a more general way of thinking, but I would love to see the more niche, and specific calculations of yugioh. I find that so interesting as well (ex. how to evaluate cards that are starters and also extenders, quantifying synergy between a card that works only with one card and where the combo is very linear vs a card that has multiple uses in the deck, etc.) I subbed because I think the math that you portray in your videos has been super useful to me, and I would love to see more of your content once you get to the really hard maths lol. Thank you! 🤟🏼
I am glad you love the math of the game as much as me :) Often times people think its very boring and just want to be shown what to do but I like the reasoning and math behind why that is the answer.
Prank Kids breaks this argument though, because the starters are also combo pieces. Maxing out on them doesn't necessarily hurt you outside of "starting" with Rocksies. 1 for 1 is not ONLY a start but also an extender. After any Prank Kids combo you thin the deck and are likely to draw non engine after from things like Pranks or Maxx C (master duel)
currently droll is played at >13% representation and assuming those that play droll run it at three copies that gives about a 4% chance that you will be drolled in a random game. That low amount is too low to be considered a threat at this point but that is good to keep in mind for future and past formats. In formats where droll raises from 4% to 15% or more (like some heavy search superheavy sam formats etc.) then you can consider watching out for droll. So for now I wouldn't worry about droll. Its like telling OCG or Master duel not to play Maxx C because of Floo its currently seen too little and counterable. Also, you don't have to do the draw 1 first. in fact its better thin the deck then do the draw at the end because your likely to run into more Tech/handtraps/traps yourself to futher boost your followup turns. Finally, if you did decide to use the draw first it still could be a better play to bait ash and have a total smaller decksize in cases where ash is used.
Now, I’d like you to show an example of a rogue deck with a massive engine like Hero. What are the ways to cut down on deck size and what are the optimal ratios for starters extenders hand traps or board breakers? How would you account for an extra deck monster as a starter, such as Destiny hero dangerous? Spells count as starters too such as fusion destiny and foolish burial.
You might enjoy the content in the free to access prob 140 course’s book from Berkeley. It’s in the drop down menu. It has great content on the birthday attack among other things and might give you inspiration for future videos.
In all the years I've played Yu-Gi-Oh, I've never really come across a video like this. It's kind of weird now that I think about. I have played MTG for longer, though. Which I have a deck building mindset from that. So, I would just build decks, play test, and make adjustments if needed. I guess I'm just somewhat acknowledging stuff I didn't know that I knew. Or rather, barely thought about, again from having the MTG background. All in all, just saying this video is neat.
I've been coming across this when making random yubel decks. The cards you'd normally run at three are dropped to two or a single copy in order to open up more fluent hands instead of bricking every time.
I’m playing 50 Branded. I believe I have no more than 4-5 Playsets (Albaz, Fusion, Albion, Aluber) I have a few down to 2 because I do not want to draw too many of them but I have a ton of 2 ofs like Allure, Fusion Deployment and I also run Pot of Desires. By the time I comb off turn one, I’m down to 20 cards or less after interruption.
i can see this applying to normal summons but if it can special itself from hand, it is immediately more valuable since your first starter is likely to get negated
If your first starter is negated and it is a HOPT then it doesn't matter if you can special summon another one of those copies because its a hard once per turn. If you mentioning "extenders" then your likely refering to decks that are 2 card combos who has math that is compeltely different from this video that i have in another video and you can find the 2 card "extender" math here. th-cam.com/video/dUB_C53DAt4/w-d-xo.html When including extenders or cards that have 2 card combos the math to get the 85% range or to play around handtrap range for a 2 card combo the math becomes you want to run 20-23 starters. Hope that helped and clarified some things.
Great vid, math looks good and the graphs are awesome. I do think the way you are phrasing your argument is a little awkward. The point of having super synergistic cards is so that one can have a "hyper" consistent engine using as few cards as possible. I think it's very intuitive to say that having massive amounts of consistency is not worth the loss of deck space, and by extension utility. The graphs present the optimal ratio for maximizing consistency while minimizing the number of cards used. Taking my intuition and then giving numbers that back it up and add specifics. Great vid, just earned a new subscriber.
Yes, I have to make sure I'm being more clear in my explanations I'll try to be a bit clearer lol. It's called teachers syndrome where I don't know where I am being confusing because it makes sense in my head so sometimes I'll glance over something that might need further insight. Great comment again & thanks for watching!
Reminds me of my syth lock deck. I added a cyber twin dragon otk engine Dragoon for burn Mirrorjade for board wipe. I got told to remove cyber dragon by a judgr laughing at me But dispite it not be 100% consistency However if i need it I can do more
Amazing vid. Couple minor mistakes imo but breaking down the ratios especially in graph for was super useful. Would love for 2 card combos and ratios on 50/60 card decks broken down too
never thought about the playset thing. but after your video I checked my two recent decklists. somehow I did this 8 playset rule withouth knowing about it.
I often forget to like videos I find entertaining or informative but man I had to make sure I couldn't leave this video before leaving a like. This video is very informative and i could tell you definitely did your research. Keep up the good work my man!
I would love to see how this math applies in branded, you have in a 40 build 3 of aluber, albaz, deployment, fusion, opening and sometimes nadir and SOMEHOW, i never saw a branded player brick in any way
Very underrated YGO channel. I believe you have to make videos with explaining the maths on actual decks. It will be mind blowing to find underrated decks! Keep it up Professor! Awesome work !
The math may say play 2 predaplant Orphys Scorpio and 1 Darlingtonia Cobra with 3 lonefire blossom but I’ll open with the 1 cobra without fail every dang time
Hey, I love the idea of using the Birthday paradox to solve how many Playsets you want to run. Do you think you could go into more detail on how you calculated the 8 playsets or maybe a resource for how to calculate it When deck building? thanks!
I need a deck that is hyper consistent because I brick anything.. my favorite deck of all time is branded and I brick with that, I have blue eyes and floo… you can imagine the neighborhoods I have built with those two. I can shuffle every way possible but I always get a bad hand and my opponent gets a good hand…
While certainly a reasonable and interesting theory I cant help but feel theres a few *very* flawed assumptions. 1) The assumption that every starter is only a starter, and that a second one cant be used for anything else 2) The assumption that all cards are HOPT, and cannot be useful if a second is drawn 3) The assumption that all cards are equally powerful (yes Ash Blossom is HOPT, but replacing it with a more situational hand trap isnt necessarily worth it) 4) The most fatal assumption in my opinion, that drawing two starters is equally as bad as drawing none at all. Drawing a 0 card hand is infinitely worse than drawing a 4 card hand.
Great comment, I literally say exactly your points in other videos because I don't think i was clear in this one. I call it Noob Deck building protection. Cards like Diableellestar can turn your dupes and extra starterss into at the very least discard fodder. So if your over commiting to the amount of starters adding in cards like diabllestar, droplet, super poly or engines like horus that have discard outlets etc to make use of discards is great. I also mention the HOPT statement in alot of other vids its weird when TH-cam will reccommend these videos and they are sometimes the first in the series that are watched some stuff is missed in the series as a whole but i try not to repeat many things otherwise all my videos would be the same and like 2 hours each. Alot of concerns should be more addressed in other vids its weird that this one was recommended first as this one took off unexpectedly so does have alot of information missing or out of context. But yes all your points are valid and correct! I talk about them in different aspects of other videos! Thank you for commenting, watching and hope you check those other videos out!
Regarding Swordsoul: against which three-ofs would you actually advise? Triple Longyuan seems mandatory, either for an early Baronne (if she's legal) or to get draws with Qixing Longyuan. Going second, there are also other options such as Longyuan and Adhara to make Yazi which gets you to Tai A or Mo Ye. You'd also want to run at least two Ecclesiae (siding in a third one for going second) because while starting with her is weak to Ash, it's not _too_ bad (maybe Psy-Frame Gear Gamma is worth considering?) and she's also a free Tuner/non-Tuner if your opponent controls a monster. Mo Ye is the best Normal summon without any setup but there are many two card combos that let you start your plays without using your Normal summon immediately, in which case Tai A is just as good, if not better (Foolishly Burying a card may be better than drawing a random one). Emergence, too, is something you'd probably want to run at three because it's not just a starter but also a utility card, searching any Wyrm you want besides your starters (usually Protos). I suppose the Tenyi support spells should be at less than three, maybe two each (if you even run both). Adhara or Vishuda might be enough at two but Ashuna is certainly worth playing at three.
PointA: got confused about the 2nd point ~5:28 Pointb: you did not say that getting 2 normal summons in your starter hand is basically bricking 1 card (the 2nd normal summon) and that normal summons usually get negated/interrupted. However, a starter that is NOT a normal summon is excempt from this unless they are hopt. point c: you said this in the video, i just want to reiterate, this also applies to hopt cards. you can't play triple tactics talent twice in the same turn, so seeing 2 in ur hand is also bricking 1 card So if ur playing a playset of ur starter and talent, ur bricked hand could be: starter, starter, talent, talent, handtrap. Out of 5 cards u got 3 usable ones and of those 3 u got 1 starter. Normal summon> get ashed, u lose the turn and possibly the duel.
Ngl, deck building in YGO is way overwhelming for me due to how many cards there are with very niche and specific effects. Even in Master Duel I just kinda get lost and dunno where to start.
It's like making a bouquet of flowers. Start by focusing on one card/strategy you want then build supporting cards around that and then tech cards around those.
@@JessePerezStrategyGaming You say that like I've ever made a bouquet of flowers! And yeah I maybe know what vaguely interests me in terms of direction or archetype, but finding cards and whatnot that support them is like... Ah yes, finding a needle in a haystack, since there's thousands of cards with unique effects... Knowing where to begin searching for effects that compliment and help build a cohesive deck is the problem.
What annoys me most about master duel in regards to the playset paradox is that u have to play 3 playsets in every deck. You have to play 3 maxx c, 3 ash blossom and called by + cross out is a playset. I don’t care about the bug gameplay wise, just purely from a deck building perspective, it limits you so much. Ash isn’t even good against snakes, but u have to play it. It stops u from experimenting with tech cards or different hand traps, while giving less room for engine. For example in rescue ACE, the archetype requires so much room, u barely have room for non-engine and the non engine u have to play is maxx c and it’s counters.
I'm really enjoying these math videos. I've been interested in trying to learn the math behind deckbuilding and feel some of the advice has helped so far. Looking forward to more content, keep up the good work 👍
Looking at all these statistics and being mad that archetypes I like tend to struggle because they have little to no single card starters and have to fill out the deck with pieces of the puzzle so they can’t fit very many tech cards or hand traps. Atleast red dragon archfiends last update added crimson gaia and soul resonator, so gaia and and resonator call can both search soul who can search bone archfiend who can put crimson resonator in the graveyard making me go from 0 single card starters to 9 single card starters.
Hi, I discovered your channel yesterday and I find it very interesting ! I never thought about the probabilities behind deck building and relied on the belief to have a good list. Could you share the mathematical methods to obtain your stats/graphs? Because I think it could be interesting to teach to everyone the math behind their own decks! 🙏
hello! glad you find the channel helpful! The first thing is to use probability to determine your odds. Luckily science and math have advanced where there is calculators to do this for you if you don't know the math by hand. stattrek.com/online-calculator/hypergeometric This is a tool that you can use for basic probability calcs. Population size = deck size Number of successes in population = number of X Special cards your looking for Sample size = Hand Size Number of successes in sample = Number of X Special Cards you want in hand. That should be a good start! Let me know if that helps :)
Your videos are top tier content. Been working on a spreadsheet of my own since discovering your page. Figuring out statistic’s with my unchained deck has been particularly challenging lol. the plethora 2 card combos and 3 card combos (since 3 card combos are very common to open in unchained) between the unchained cards themselves and the dark contract has been a bit of a headache. lol.
One issue i have is that you don't specify if the 12 starter limit should apply only to 40 card decks or not, because if you play lets say a 60 card deck,that will grow the same limit of starters,or, if you play a hyper consistent 40 card deck,you can also add more hand traps,or board breakers or other such stuff instead of replacing cards,just to keep the constancy under the "hyper" But there ret,man,this video is numberphile level of quality ngl
Roulette has 1 to 36 odds. Which means you are guaranteed to draw a card you do not need compared to a visit to a casino where you are even more likely to lose at ( But at least the deck is shared in that instance) . Imagine playing a game from a low level deck the casino opponent never draws from for their own hand , you would know it is rigged if it was played that way.
A counter argument example would be superheavy samurais. the deck ran 12 starters in 40 in a handtrap format and bricked too much. running 15ish starters would have been much better. in around 25 games, you bricked around 4 games. You also definitely want enough extenders to push through.
Superheavy samurai while some cards are a 1 card combo - most others are 2 card combos (they have to equip or need another on board). In 2 card combos the optimal ratios are running 20-23 cards to facilitate that. I should have put that in this video but I fear it was getting to long as it is. I have the math for 2 card combos here: th-cam.com/video/dUB_C53DAt4/w-d-xo.html But yes your conclusion is correct. For something like super heavy I would even take it a step further and run 20-23 of them to facilitate their 2 card combo strategy instead of 15 and consider the 1 card combo/starters more of a luck. Thats what the math shows for them to have that 85% area and not be hyperconsistant. Also SH isn't limited to the 1 normal summon for the most part like the prank kids. Since they have sooo many extenders that can special themselves playing through the handtraps is very important and getting the extenders by playing the 2 card combo ratios 20-23 will allow to play through an extender. TLDR: You are correct a deck like superheavy should be playing more than the 12 starters and should be playing an upwards of 20-23 SH cards that can facilitate their plays.
One of these days, I was building a custom deck (with cards that would be flip monsters support), but the important thing is that my game plan didn't just depend on opening with 1 flip monster in my hand (1 flip monster could be a starter, but any other flip monster would become a combo extender), therefore, I decided to use a hypergeometric distribution calculator to evaluate the best combinations to have the greatest chances of getting 2-3 cards of a certain type in my hand and while experimenting with different combinations, I saw that a combination of 18 cards in a 42 card deck gives a very good chance of exactly having 2-3 cards (Incredibly, I already had this idea of not abusing 3-set cards, because in theory I could search any flip monster, so it would be better diversity for combo extension and in these 18 cards I don't use any 3-set cards, instead I use 6 2-set cards). Could you tell me if these numbers make any sense in practice?
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Thanks for the video! Could you explain the underlying math a little bit more?
I really don't understand why we assume exponential growth of the probability to see at least one dupe. Isn't it just the # of playsets times 3,64%?
For eight playsets in my 40 card deck, drawing a 5-card starting hand, I draw at least one dupe with a probability of 29,1% (I think). Where does the exponential growth come from, seeing that the cards/playsets are independent from each other.
The best way to visualize this without being confused by numbers is this. Imagine you have a 42 card deck and 14 playsets. We will take the draw of 5 one at a time instead of all at once.
To start you draw your first card you have out of 5. We will call it A. (A) draw has to doge itself on its second card.
Now we draw card 2 you have to dodge copy of A with 2/41 chance to draw a dupe.
Say you dodge and draw card B. Now on your 3rd draw A and B BOTH have to dodge thier respective dupes. Which means now 4/40 percent chance to draw a dupe on draw 3. (10%)
Your 3rd card you draw is C. Now your 4th card has you have dodge A,B & C and you have 6/39 chance to draw a dupe.
Now the forth card is D. That means your 5th card odds to draw are dupe is 8/38. Which that draw alone is 21%
When you take all of these factors together you have about a 33% chance of dupe. You can see how because their was a guaranteed chance of getting a playset card in your hand it now made things exponentially worse. If you drew a non playset card like a 1 of then that card "draw" is safe and won't effect. Therefore the more playsets the deadliest it is. Your 5 card hand will become 4 in about 1 in 3 games if you have 8 playsets I can show this math on discord but this one takes a long time so bring popcorn.
@@JessePerezStrategyGaming Ahh, now I see where the misunderstanding comes from. With exponential growth, you are referring to the number of cards drawn from deck.
The number of playsets in the deck itself does not contribute to exponential growth in the probability of duplicates on a starting hand of 5. In fact, the probability per playset decreases slightly due to the cases where you draw two duplicate pairs.
So, let's take the example of 40 main deck and 5 hand cards:
The probability of having at least one duplicate in hand depending on the number of playsets is:
1 - 3,6%
2 - 7,2%
3 - 10,8%
4 - 14,3%
5 - 17,7%
6 - 21,2%
7 - 24,5%
8 - 27,8%
9 - 31,1%
With 8 playsets in my 40-card deck, I therefore draw a dead card in over a quarter of all games, provided I always go first.
If I go second, i.e. draw 6 cards, the probabilities look much worse due to the exponential growth depending on the cards drawn that you mentioned:
1 - 5,4%
2 - 10,6%
3 - 15,7%
4 - 20,6%
5 - 25,5%
6 - 30,2%
7 - 34,7%
8 - 39,1%
9 - 43,4%
If I draw 6 cards from my 40-card deck, that contains 8 playsets, I will have a dead card in my hand 40% of the time!
To summarize, the probability of having duplicates in the starting hand increases exponentially with the number of cards drawn and (almost) linearly with the number of playsets in the deck. The number of playsets in the deck raises the exponential curve to a higher trajectory, so to speak.
@@JessePerezStrategyGaming you are correct about this math. But there's no exponential growth here. Each playset that you add has roughly the same chance of getting you a dupe that the previous one. So there's no reason why you should stop at X playsets or whatever. The cost on them is linear so if you think the 9th is bad, the 1st one is also bad
@@lautaromonsalvo8808 there is exponential growth. I made a video specifically going into great detail on it you can find here. th-cam.com/video/_Ia9pq9F4b0/w-d-xo.html
@@JessePerezStrategyGaming The probability of having at least one duplicate in hand depending on the number of playsets is:
1 - 3,6%
2 - 7,2%
3 - 10,8%
4 - 14,3%
5 - 17,7%
6 - 21,2%
7 - 24,5%
8 - 27,8%
9 - 31,1%
Can you see how each playset that you add, increases the chance to dupe by almost the same amount? There's no exponential growth there. Playset 9 is as bad as playset 1, they both increase duping by 3.6%. Any rule where you have to play less than X playsets is nonsense because playsets don't get marginally worse as you add more.
The math might say one thing, but when I go into twelve straight games without drawing a starter, I start becoming suspicious of causality itself.
BEST COMENT OF THE WEEK I SAW
As a wise walking monitor that plays card games said once, "no amount of strategy and deck building can defeat bad RNG".
try running cup of ace... I've started tallying my successes and fails becuase I'm so convinced the universe is against me!
Have you tried different shuffling methods? Like not only riffle shuffling. This used to happen to me and by just shuffling differently it just stopped happening
@@joseprojo975 I often do stack shuffle and then a combination of riffle and overhand. It ain't my shuffling, pretty sure.
Jokes on you, my all garnet deck has 100% lose rate
:D :D
@@JessePerezStrategyGaming my deck may be a brick, but I can still try to beat my opponent's head with it
I need to see this mirror match.
Brings “Ah man, I drew brick” to a completely different level
Ive been looking for someone to make comprehensive deck building videos for years. Finally! I love how you break things down in an analytical sense also.
I am so glad you enjoy the videos! I love doing these mathematical breakdowns i have so much fun with them. Glad there are others to that enjoy numbers like i do. Thank you for watching!
-Ash and wanted have NOT been hit in the tcg
-Veiler and imperm are not once per turn, so they are still good to draw multiple of
-oversimplifying too much because you are not taking the gameplay of the deck into account. snake eye doesnt care about drawing multiple starters because they often need to discard a card. also drawing wanted/diabelle/bonfire on top of one card combo is how you play through handtraps. they are both starters or extenders and necessary during this handtrap heavy format
-prank kids needs kids in the deck to summon them. if you dont have 2 of a type in the deck you cant xyz summon that level (ie if you draw 1 of them and only play 2). also they are good to draw in multiples because you can fuse with the ones in your hand and save bodies on the board. not every deck is based on one card combos. labrynth is another good example. good deck building involves understanding how that specific strategy functions and optimizing that, rather than focusing on a specific magic number of starter/nonengine cards
-if you run 12 starters, and play 7 rounds of swiss, about 3 games you will draw no starter. probably not going to top doing that. better to see 2 starters some games than have too many games where you cant play, at least in a tournament
all that being said this is a good overview of how ratios will affect your starting hand, and the diminishing returns, especially for those new to deck building; you explained it well. i do agree people focus a bit too much on consistency (like always running 40) and less so on other things, such as how well you can play around hand traps/breakers, what nonengine people are playing at the moment, knowing the weaknesses of other decks in the format and how to counter them etc. these things are more instrumental to the success of top players than consistency alone
This!
But this is not getting any love by Jesse.
I believe this is a valid point.
Sorry for late reply wanted to make sure I address everything as this was a great comment!
Sorry ash is limited in MD and OCG & wanted is limited in MD. It is very hard to remember the exact forbidden limited lists for every card in every format. This point was really just a point of interest and not really a major point i just spontaneously said that because it was on my mind at the time. Apologies for the error nonetheless.
I thought I mentioned that the playset rule only applies for cards that are HOPT effects. If i missed that then apologies also. Which is why i didn't have imperm in the original playsets. I do talk about imperm specifically how that is good and doesn't follow the birthday paradox but that was in another video and not this one so i might have gotten that confused but yes non HOPT wont be counted to the playset rule/birthday paradox.
I could have went further in depth on prank kids but i didn't want to confuse the audience with what pk did and just was using it for a general example. The math does change if you go in depth with prank kids as they can even preform certain 2/3 card combos, the discard with fansies or the banish and draw 1 with rockies or the +1 with plan at the end of the turn benefit thinning strategies. But so many people would be confused and i made an artistic choice to deliberately leave that out as prank kids was not the point of the video. Ultimately, It seems like it came at the cost of confusing the more well known players and skilled players especially those who are skilled at using prank kids in favor of helping those less versed in prank kids.
However, Not drawing a starter though in your round of swiss example doesn't automatically equal a loss. If you have 0 starter that means your 5 card hand is all tech/handtraps which is likely enough to force a simplified gamestate and get you another turn at which point you have a big chance of gettiing your starter topdeck or side engine rolling (adventure/kastira as used in example)
All in all great points and I agree. Well written comment and well said! Thank you for watching I appreciate comments like these the most.
just responded to it i gave it some love :)
@@JessePerezStrategyGaming hey thanks for the thoughtful reply! no need to apologize, it definitely is hard to keep track of the banlists between 3 different formats. also w the imperm thing i see it as less of a correction and more just pointing it out so people in the comments are aware if they didnt see the other video; so no need to apologize there either:) glad to hear this didnt come off as a dig or anything, just wanted to point these things out as i think they’re important details. I take your point that you were just trying to show a clear example of not playing too many normal summons as starters basically. branded comes to mind as a good example of this, some players only play 2 aluber for this reason. perhaps it would help in the videos to have a clarifying statement like “there may be other reasons you choose to play more starters in a deck, like if the cards have other uses, but this is an example of a starting point when deck building to not have too much engine”. or something like that if that makes sense. would help to clarify the snake eyes bit too. glad to see thoughtful discussion from you in the comments as always Jesse. Love the energy and keep up the good work :)
I would like to add to this that some cards are just better to draw than others in many situations and so are way better to draw 2 of than others that are different but are way less impactful.
Swordsoul is a 2-card combo deck, it needs to see a normal summon and a wyrm or swoso card. Traptrix is another deck that breaks the 8 playset rule because by design it can't combo with 1 card.
Yes! swordsoul is a 2 card combo! It has diffrent math you can find here th-cam.com/video/dUB_C53DAt4/w-d-xo.html
generally, for 2 card combos, you want to play 20-23 cards to be in that 85% range. Hopefully this helps
This is EXTREMELY well articulated not even for just yugioh but the break down of statistics was pleasing to listen too. I hope to see more video on your channel
I am glad you like these kind of videos! Great to find a fellow statistics enjoyer!
Very enjoyable
For the Snake-eyes cards I'm not sure this is the best exemple
Diabellstar is both a starter and an extender (so is bonfire) and this would actually change the math because it's great to see 1 Diabel, 1 wanted or 1 bonfire on top of your first starter (the card has multiple uses)
The Prankids exemple is perfect though
That's what I thought as well
The prank kids example is also not good. Rocksies can banish card from hand, so 2 starters in hand is no problem.
@@rhyned Not to mention, if you use Pandemonium you're locked into Prank Kids names, which means you can't always reliably go into those strong game-ending link monsters (Borrelsword, Accesscode, etc.) Often Prank Kids will run over 2 turns, and therefore needs more than of each name (Unless you're running Plan to recycle, since you can't always rely on getting to your one copy of Pranks)
Besides, all of the Prank Kids can summon from deck OR hand, so yeah- you'd rather have a hand trap in hand, but they're not bricks in hand...
There's a reason why literally every single Prank Kids top ran 3 of all of the names besides MAYBE Rocksies. The math may be there, but math isn't always the answer. Sometimes logic is.
The Prankids example is technically bad, too, because the deck Fusion summons, so it has use for more bodies in the hand, but the way it was described here focusing on the ratio of Normal summons, it works.
@@jonathonyeary509during adventurer format some pk lists ran 2 of each name and 2 place, including elijah green's ycs winning list
Although those versions of the deck had 4k damage from the adventurer engine + 2.5k from dpe so pushing for game wasn't an issue, nor was playing a longer game with less pk cards since dpe thrives in simplified gamestates
Basically the ratios depend on the format and build of the deck
One of my first decks I built for competitive was a hyper consistent Live Twins. I at first was frustrated with how all my opponents seemed to draw their nonengine against me while I kept flooding with normal summons and extenders until I realized I that i was causing myself this problem.
i too made that mistake with MANY of my decks for the longest time. it wasn't until way later i realized there is so much more a deck should do then try to turbo out 1 thing as close to 100% as possible.
what a mood this is with live twins, it's so tempting to run the 6 twins, 3 sunny's snitch, and 3 password, but that's just way too much to be optimal
@@Wyrmimy spright twin i play 3 sunny snitch and 6 twins in MD and it looks normal to me
I like this math! Keep it up!
@Wyrmi I didn't even stop there. I ran 2 of each costume Twin and a Home along on top of 3 Parallel Exceed. Half the deck was Starters or extenders.
cards that are not once per turn are a great way to bypass the 8 playset rule.
Also I wouldn't rune any less than 3 ash blossoms in snake eyes as it fufills the very valuable anti maxx "c" roll that I wouldn't run any less than the allowed 6 of, with maxx "c" being basically an auto win against you if you don't draw a counter. This can also make drawing 2 ash less painful because you ash their maxx "c" and then you ash them on their turn (or vise versa if you are going second).
yes! i forgot to mention cards like imperm etc that are not HOPT do not count towards the 8 playset rule. TY!
Running only 12 Starters means you brick 15% of the time which is acceptable casually, but if youre playing competitive then you need your Deck to do its thing more than just 85% of the time. Diminishing returns is real but I don't think it applies
You should play prospy which can be either a starter, extender or non engine
you run engines and other stuff, better than have a higher chance of being ashed and loose 2 to 3 cards in hand because you are hyper consistent
@@kenshi1985br Unless all your starters are normal summons, then that won't happen. Like if you're playing Invoked then you don't play too many normal summons. However there are plenty of starters that are spells and special summons. Also, even in a deck like Prank Kids, imagine not opening a single Prank Kid 1/4 games, because you're afraid of a hypothetical hand trap. That's not good deck building theory. If youre afraid of hand traps then max out on starters, extenders, and cards like crossout/talents to keep playing. Don't just cut your starters
Yeah it's not diminshing returns because while the percentage gain decreases as you get closer to 100%, the value of each percent also increases. 95% consistency (brick 1 in 20 games) is literally twice as consistent as 90% (brick 1 in 10 games) consistency.
The increase in consistency is actually linear with the number of starters.
I don't deny there are a lot of players that just simply add everything related 3x or simply max copy everything without any thought like just putting a pile of related cards together when comes to deck building, which usually means bad, and you did have a point on the part on the concept of "better choice". However , the main thing about this ain't as simple as "you got starter you are good", it is about "do you really need those in 3 copies?" or may be even "how many copies of this card do I need?", "will this amount of copies synergies each other or just brick me when all drawn to the hand?".
99% hyper consistency is not necessary means bad, it really depends on will it brick, or just can have other uses when multiple of it drawn to hand. Take snake eye as an example. You got diabellstar, blue snake eye, bonfire into the hand, it is still not a bad hand as you can just thrown a card for diabellstar, summon blue snake eye search for kurikara, bonfire into red or may be other useful things, in the mean time you can even force trade your opponent hand trap if you got so many starters. Snake eye got like so many "starters" , but it is never brick due to how flexible it is to the point your opponent has to force their hand trap into your cards so that you can never get that much of value before it start snowballing.
The case become slightly different when comes to prankids. Prankids themselves are bound to consume big slots as it don't actually works by themselves if just play to field without legal targets in the deck, which means you pull 1 prankids to the hand, 1 less you can recruit from the deck because of how prankids works. You got 3 prankids in the hand, which can also be bad if you summon 1 and leave the other 2 doing nothing. However , I want to mention if you have a prankids fusion or equivalent in the hand , multiple prankids become somewhat acceptable instead of a bad brick as you save a normal summon while you got 2 or may be 3 pankids to the field which can leads to big board if play properly. Things can even get complicated if you run rank 3 or/ with adventurer engine as well. you can link 2 into burning abyss dark fairy for a set of adventurer while allowing prankids, to build a bunch, transition into apollousa, and may be with a thunder dragon fusion into boss prankids follow up by a thunder dragon colossus, depending on build and situation, which may leads to more complicated when considerating the copies of the same card in the deck as well.
Also , I will want to mention with this amount of generic searcher nowadays, there is more to consider when comes to card drawing. Chicken Game and Upstart is good by paper because it can means a -6 to your deck size, but that is assuming you are able to play it on your turn. If you go second, those cards literally doing nothing on your opponent turn and just stuck there. If your deck aren't blind second oriented, those are actually pretty bad if you go second and want to interrupt your opponent turn 1, especially you pull a hand trap that is good for opponent first turn instead of other things on your going second game. If i play a deck that is running heavy hand traps that is good to disrupt opponent turn 1, I will not want to use this in the place of hand traps that allow me to disrupt opponent play on opponent turn 1. Furthermore, there are spells, it also means that the card that synergy will be different as well. It is more synergy to decks like sky striker, spellbooks or decks running reasoning/monster gate that needs to stack spells on the graveyard which in current card pool they are either underwhelming power or just don't see much synergy with majority of decks as majority of decks are more monster oriented rather than spells. Also, 6 slots of the deck space can be a lot, might be better to include another engine depending on deck type and build as well.
Hence, if you want a good consistency, frequent testing on pulling the first 5 cards and see will it brick becomes important when comes to deck building (thank god master duel implement this feature). You can hardly build a decent deck without some sort of testing and filter out those bricks as sometimes things are not that obvious and interrupts from your opponent can make things even complicated when comes to consistency.
You are absolutely correct, there are certain 3 card combos in PK like have 2 kids and a fusion that work for hyperconsistancy.
The math for 2 and 3 card combos are different.
For 2 card combos you want to run between 20-23 starter/combo cards to get that 85% range. You CAN build your Prank kid deck to facilitate this style of play and this can work as well if you want. For simplicity sake i didn't want to confuse the audience that were not familiar with prank kids and go into the fusions - can banish 1 with rockies to go +1 the discard with fansies etc. So I deliberately left this out as an artistic choice so i wouldn't confuse but you are absolutely right and if this video was an hour I would certaintly touched on your points.
Funny enough I did not do did math for 3 card combos yet as it seems like you would need to run so many cards for it to reliably work that I treat it as a bonus and wasn't worth my time to do the math but I might do it in the future if I get more requests for it.
I also completely agree with your take on upstart & chicken game. My goal was to say that chicken game should not be taking the place of a handtrap and i hope that point got across.
Thank you for this detailed comment, well put and well written. Thank you for watching!
I understand the point about 3x everything bad, but at the same time I want to add that just starting out learning a deck, it's great to see how things interact. Part of my process in learning a new deck is to start by playtesting three of each and scale back as I figure it out. As I start to see I don't want certain cards in hand as often I scale them back: I can search this card reliably, so I only need one or two; et cetera.
It simultaneously builds knowledge of the deck and gives insight into numbers of copies.
@@Damini368 People tend to do this for different reasons. There are also player who just bad in deck building claiming the deck suck just because they add every card together like grouping a pile of cards but claim it suck when they brick very hard. Also the same type of player telling others "don't build deck yourself, just copy one and you good".
Anything that draws 1 to replace itself went from awesome Exodia fuel to just bad the day Droll & Lock Bird was released, that's why all these old Exodia FTK enablers are being released off the banlist.
@@autobotstarscream765 exodia been always a meme deck even with igknight FTK build. Lately OCG just got new support for it, but still a question will it be close enough for a competitive deck.
I think that some rules dont Apply to card without once per turn and non normal summon reliant cards.
Yes! Cards like imperm that are not HOPT should not count to the 8 playset rule! I forgot to make that clarification you are absolutely correct!
what a coincidence, I've been binging Phoenix Wright Trials & Tribulations and here you are using the OST & making your case for NOT being hyper consistent with so many multiple copies.... I love it!!!
Also took this principle with Heroes & my going second build.... you're phenomenal man
I Love the Phoenix Wright series :) such great memories. I would play it together with my friends huddled around my DS in a car. LOL. Glad you caught that OST.
@@JessePerezStrategyGaming A true man of culture LOL much respect to you man
"You need about 20 handtraps in modern Yu-Gi-Oh."
This game is hopeless.
something i remember hearing from johnny li in a true draco sky striker deck profile on cimo's channel was something along the lines of "too many starters and your deck will be consistent but weak, too many extenders and your deck will be powerful but bricky"
One of my biggest challenges as a deck builder is often trying to figure out how much engine I need in my deck, mainly because it often depends on what you're piloting.
Most decks want to have plenty of space for non-engine, and the type of non-engine depends on the deck. For example, i've been messing with Shining Sarc lately, and this deck cares a lot about including handtraps and quick-play spells for non-engine since it synergizes with Future Silence. But if you're playing either a mishmash of archetypes or just a ramp or combo deck in general (insert obligatory jab at Branded players), the engine to non-engine ratio isnt always very clear because in some instances, you're basically falling back on either extenders or a secondary engine as opposed to non-engine pieces.
I think an excellent example of this is Live Twin Runick Spright. While its not seeing a lot of meta play right now, this deck is honestly all about establishing a big ass board of monsters. It generally wants to play through disruption as opposed to playing more non-commital, and when going first, it often tries to either Iblee Lock the opponent or set up a bunch of roadblocks (like IP to go into cards on the opponent's turn like Apollousa or what have you, as well as in-engine disruption like Trouble Sunny). On top of this, your generic disruption is also a part of your engine in the form of the Runick package.
Yes! I am tracking the progress of your live twin runick deck i see you posting in the community notes. I am very invested to see how it evolves and how your making it. Your cooking up something great!
Perfect example for Upstart is in Kashtira. Upstart directly replaces limited NAMES and not handtrap or tech slots. Combo thin deck into Arise Heart, Upstart draw into disruption, trigger Arise attach off the banished Upstart.
I think this makes sense for general theory about ratios but sometimes drawing dupes isn't such a bad thing. I'd rather have 2 prank kids and play with a 4 card hand than have 0 and not be able to play. Sometimes cards are powerful enough that you want all 3 and you're going to draw 2 and that's ok - if I could play 8 copies of soul charge I'd throw all 8 in every deck I play for example because its so powerful that I'd rather have a dead second copy for a turn than not have it.
Yeah. I like these vids cuz having insight to the actual math is, well, insightful, and can play into how u deckbuild. But definitely as a viewer and player you gotta be able to discern the theoretical math from actual deckbuilding nuances.
For the 8 playset rule, it could have been articulated a bit better, but basically the more playsets you run, the higher chance your hand contains doubles. So its a 3% chance of drawing 2 red prank-kids but it could be like a 20% chance of drawing two of the same prank-kid (red, blue, green or brown) which is why your chance of essentially 4 card hands goes up
Other than that, super interesting and cool video!
I'd love to see a video on 2 card combo decks! For example, a deck like virtual world have varying ratios across multiple deck profiles. Some play 3 of each name, some play 2 laolao/lili, some play 2 of the spells, etc. Maybe there is a list that runs the most optimal amount of engine and tech cards so that you see your 2 card combos most of the time as well as some amount of tech cards.
I have a video that you can look at with 2 card calculations here:
th-cam.com/video/dUB_C53DAt4/w-d-xo.html
Thank you for watching!
@@JessePerezStrategyGaming Awesome, thanks!
This is a good video to show to people begging for more Photon Galaxy starters when the Deck already has about 10-11. The Deck is consistent enough.
3 Galaxy Wizard
3 Galaxy Soldier
3 Galaxy Hundred
1 Foolish Burial
2 Photon Delta Wing
The Deck hit that sweet spot long ago. Begging for more starters is going to give Photon Galaxy diminishing returns. At this point, what the Deck needs is a better grind game. Otherwise, what's that hyper consistent group of starters gonna do for the Deck?
While I mostly agree, I'd like to add that hyper consistency itself is not a bad thing - it only is if all the cards you add above like 12-15 cards are doing is add consistency to your one main strategy. However, there are a lot of engines you can add that can fulfill different roles in the deck. The one I'm currently playing around with the most is the Allure Queen engine, since it can be a starter for so many different strategies, but it can also act as a security engine (getting Herald of the Arc Light out within 3 summons) and it can also help break boards going second, since you can easily get a Light and Dark Chaos Angel out with it. If your deck is super linear with its starters then yeah, too much consistency is not a good idea. But those decks usually fold to like 1 hand trap, anyway, even if they can occasionally put out insane, literally unbreakable boards.
I'd like it if you added a summary at the end of the video. Thanks for making these.
1) I know I'll be returning to this video regularly thank you
2) That megaman music gives me a pleasant feeling of nostalgia and anxiety from those tense levels XD
Your thoughts on the Duel Links format could be crucial. I find going to two is better for most cards, and I primarily run 30-card decks. The 8-card ED means that you will rarely have more than one of anything there too. There are a lot of 20-card builds that can do some work but end up being glass cannons.
another problem is the kind of starters.
For example the deck with a lot of starters today: Snake-Eyes
- We have the Normal summon Starters: Ash+Poplar. The problem in having a lot of "Normal summon starters" is obvious, you have 1 normal summon for the turn, if you got both you actually got 1.
The deck where this was common, Spright. Any 2 lvl 2 is a combo. So if you go for a lot of monsters that on normal summon summon another one from the deck you are safe? no, since you can only make 1 normal summon.
- Special summon Starters: Diabell, They don't cost turn resource to play. The major example is the banned "Mathmech Circular". In the later YCS RIO the "melodius" engine presented its power too
- Starters that work as Extenders when hand trapped: Bonfire + Diabell. The "crème de la crème" of starters. This usually go along with the later group. You start with ash, get imperm... well, Bonfire and go on.
This birthday paradox thing in yugioh could be a magnum opus or college thesis. You should definitely try to get this published maybe on YGOMeta
This is definitely why I don't like 3 Dark Magical Circle in Duel Links Dark Magician Decks. Players will have 3 DM, 3 apprentice illusion, 3 navigation 3 rod and 3 circle in 20 card lists, where the odds are that circle will likely only reveal a duplicate copy of cards that are already in your hand.
2 is plenty
You and Yishan are the only people I’ve seen go into the math of YGO. Thanks for posting, I actually started having more fun with math since I started playing
I would love to see the math on 60 card decks, I'm playing an HEAVY engine based deck that feels perfectly consistent, but I'd like to see how I could fine tune the exact ratios
I made a video with how to build a 60 card deck with math in it here: th-cam.com/video/80kBBIEdXV8/w-d-xo.html
hopefully it answers all the ratio questions you have if it doesn't leave a comment or find me in discord and ill try to help more.
Reeeeeally appreciating the AA music helping me concentrate and understand everything that's being said ^^
I've spent a good while now trying to math out Ritual Beasts after the new support. The deck has an incredible amount of 1-, 2- and 3-Card combos, access to Emergency Teleport which acts as starter, extender or interruption depending on the hand and has synergies with a lot of different engines, all while having enough space for nonengine as well. It's just a complicated mess of a spreadsheet and trying to figure out and test different ratios is a pain.
I don't even play Yu Gi Oh anymore. I just wanna hear this guy talk about it.
Awesome! So glad to know that you like listening to me rant about math and numbers! I always fear I would be putting people to sleep when i talk numbers so glad I can make it interesting! :D
Great video! However, I should probably add some things:
1) Some cards alter the statistics in this video. Chicken Game and Upstart Goblin, for example, would reduce the "real" number of cards in your deck and allow you to run 10-11 starters instead of the mentioned 12 depending on the number of these draw spells that you play.
2) You are absolutely correct about Swordsoul running 8 playsets being a bad thing, but only until you start taking Pot of Desires into consideration. XD
I loved your discussion on upstart and chicken. Those are meant to replace multiple copies of (HOPT) cards you can only play in your turn. I remember a custom format turnament of MBT where Pot of Greed was at 1 and some lists were not playing it, that was poor deck building to me.
Wow that is insane to me that people are choosing not to play PoG!? Even in the most consistant of decks you could still do your plays then do the draw at the end. So shocked. If this tournament was played on MD, Maybe they didn't have the UR dust to spend because thats the only way I can see them not playing PoG
@@JessePerezStrategyGaming th-cam.com/video/Z08fyvXpGUI/w-d-xo.htmlsi=KpuZPUJZJkiJzGW6 This was the format, oc played in a casual way. But this proves the preconseption you were adressing in your video: the avarage yugioh player doesn't understand what odds are
@@JessePerezStrategyGamingPoG is king, to the point of making it worth blowtorching your Deck to get to Pot of Greed for 2 of whatever was left, hence why Pot of Desires was so big, and if experience playing older formats, especially running Salamangreat around the time of TOSS Format, hyperconsistency was only ever used in Exodia Decks until Desires changed the math for a lot of people, and their gameplan became open at least 1 starter and 1 extender in every opening hand at all costs so they could drop a Desires without worrying about what they banished face-down or getting any of it back, because whatever they banished after their initial combo pulled 1 of everything they needed out of their Deck would be either a redundant starter (basically a Garnet), a redundant extender (basically a Garnet), or a non-engine card (no good to you in the Deck until you draw it), because drawing 2 off 1 card and getting the +1 was always worth it while using 1 to draw 1 was just asking to get Drolled, hence why the popular play in Salami was hyperconsistency + Desires, and everyone I saw running Swordsoul was also running Desires to pop off Chengying and get those precious draws for a +3-4 off one Spell after doing their initial combo to pull out 1 of everything they needed to not lose to Desires in order to play, and so it almost feels like now people are building hyperconsistent Decks while forgetting why they popped up in the first place, as almost nobody's running Desires anymore since it was eclipsed by Extravagance and then Prosperity.
I really appreciate this. I just got into Yugioh for the first time in 20 years and this has been super helpful
Awesome! Glad it was helpful! Also there are so many new types of cards synchro, XYZ, Link etc, my advice which worked for my friends was just to focus on 1 of them and decks with that style and then when you feel comfortable with that mechanic you can learn another others. Trying to learn all at once was to hard for my friends so just focus on 1.
As someone who took a college stats class recently, yeah, all this sounds accurate. Cannot describe the number of people who get confused by the math behind probability when seen on paper vs practice.
7:23 isnt that example equal still 12 normal summons though? bc is not like that field cant get you an extender right? or am i missing something?
What the fuck!? I started this video out of curiosity and I was like ahhh what kind of nonsense is this, but when you came down to cutting down handtraps with different handtraps I was like OMG!!! This is genius, like I finally understood what you mean and I was immediately able to spot the mistakes in my deck. Huge thank you!
Awesome! I am glad you liked the video! If you like the numbers - I have a bunch more math centered yugioh vids that you might like as well. In any event i really appreciate the comment and thanks for watching!
14:17 i can legally publicly shame you for this singular typo.
(Great video lol)😊
lmaooo. :D
This is why recently i decided to play more than 40 cards in some cases. If all I have is engine, then sure I can have some tech cards, but if all I draw is engine and then my opponent does something crazy like use Maxx C or have board breakers, my one play was countered by the tech cards simply because I lost the coin flip and my opponent had just an ok board going 1st, but couldn't even play going 2nd because my single summon and magic card were both denied.
Helping the yugioh community one equation at a time❤
Man, I just found this video/your channel, and I never been good at figuring out how to make decks. i always go blank. And it might be easy for a lot of people, but not everyone is a mathematician, right? Not everyone is good at deck building... But you're a great teacher.
Thank you! Comments like these really make my day!
Thats why alot of ur starters not only start but also continue your plays, think w sky strikers, ur starters r raye, roze, engage, hornet, linkage, and even the field spell however not only are they starters they also help you play your turns after
While watching this I was comparing the deck I use which is @Ignister. It has 11 one card starters. Of which 8 are Normal summons or ways to get to them or get an extender from the deck.
6 normal summons are one card starters. 2 are extenders that if they are in your hand at the same time are a full combo as well. 4 different Cyberse type monsters that can be used as Link material easily. 12 hand traps. I don’t own 20 of them. Two garnets that I don’t want to draw but are needed for the deck to function. One of them is a pseudo garnet as I can search it from the deck if I draw the other. I need both for it to work. My friend hate that deck because it is too strong for them. It seems like I was following the same logic as you. Except I opted for more stuff to counter my decks counters. Hand traps are good in all when you’re using them but when your deck crumbles from a single hand trap you need to have something in place to let you keep going. Which is why I run more extenders in my deck over hand traps as well as anti hand trap cards such as Prohibition, Called By, and Crossout. Is my deck meta? Most certainly not as I am one of a few players who pilots the deck. Especially after a major engine got hit badly. I used Mathmech Circular as an enabler for a very nasty 13 interruption combo. Five negates, multiple bounces, quick effect destruction, hand rip, and revival from the graveyard on command. If I had a copy of S:P Little Knight add another two interruptions. But sadly the deck did get hit badly. I have been tinkering with it for so long that my friends are tired of facing it. Now if I want to duel them I have to use a structure deck. Disappointing really.
I would love to hear your thoughts on this type of deck.
My side deck is in the same ratios as my non engine so I can swap them out for different matchups. I also run a few hand traps that hard counter my own deck in there as crossout targets. I also play other card games where you can run up to four copies of each card in the deck. In those games there is a resource system in place so the deck building philosophy of Yu-Gi-Oh cannot be applied. Still my decks show results despite some of my friends who play the game questioning my deck building choices. For example me running Prohibition they find weird. Called By cannot stop Nibiru or Imperm so I run it as a counter along side Crossout. Odds are I have a counter to what my opponent is playing in my deck and even if I don’t I can still put them into a very tough spot. My extra deck is built for a one turn blowout. Either ending the match instantly or putting my opponent in a bind. Before Circular was banned the deck could stop a Dark Ruler with ease. Man I want circular back at 1 at the very least.
Wow yes! It seems you were using the EXACT thing i was trying to point out! You also supported your ignister engine with the mathmech one as additional utillity, built your deck to current local counters and did everything great! Shame what happened to circular :(
On the deckbuilding side you get an A+!
Now for the playing part practicing using new combos and finding a good replacement is probably the hard part. I think it was Bruce lee that said I fear not the man that learned 10000 punches but the man that practices 1 punch 10000 times.
I'm really glad you came back to the normal summon topic and dwelled deeper into that. Your videos are always helping . At least those have helped me to break away from some 'rules' with actual statistical data and concepts when it comes to deckbuilding. Especially the playset one. I assume that one applies only to hopt cards right?
Yes! the playset rule ONLY applies to HOPT cards. So for example, feel free to play as many copies of imperm as you want as that will not count toward this rule.
Its crazy to find out that when i made decks i was indirectly always avoiding making my decks hyper consistent its like finding out something u do everyday has a word to sum up what u do and u never knew the word
i havent played for 20 years! got into MasterDuel and I liked the cyber dragon deck. I bought all the URs n looked at similar decks and I literally run like 2 engines. this video solves my issues! I got to Platinum like a cakewalk but then my deck was no longer viable lol
more useful content then 99% of all other yugituber channels ngl. Learned more from this than anyone else in years on Yugioh. Subbed!
All of this math is hinged upon perfect rng/shuffling formula which just isn’t the case in tournaments, clashes with law of probabilities // 50/50 laws, is or it ain’t BRUH, just ain’t it.
Interesting point on the shuffling. Its true the math on this is in regard to TRUE randomness and perfect rng. Applies more to Master Duel then in person TCG but interesting to note and good observation.
best yugioh science channel
Thanks! glad you enjoy the videos! :D
This video is wonderful, criminally underrated. Both easy and informative. I now actually know why it's wrong to run 3 sinful spoils and 3 poplar.
Thank you❤❤
I'd love to see more videos about 2 card combos and 60 card decks!
You just made it make sense to me more than any other source I’ve looked at. Thank you sir. You just earned yourself a subscriber
I really love these videos, I think taking this kind of maths approach to deck building helps know you just got unlucky and the issues isn't that you just build your beck badly. One suggestion I would add is at the end of these types of video it would be nice to end on some kind of very clear, actionable application to everything you explained - somethings the application of this gets a little lost in the details.
For example, a potential application of this video (if i am understanding the explanation correctly) would be to avoid playing a playsets of a card if its effect is once per turn, and you can change out 1 copy from the playset to other card that does a similar or the same thing. Playsets of cards should be saved for cards that a absolutely essential for the deck to function or have very high power level (I assume something like Maxx C would fall into this category). Or put simplify, if you never want to see 2 copies of the same card in your opening hand, to lower that chance from happening, only play 2.
A practical example would be - x3 "Dark Ruler No More".
I almost never want to see 2 copies of that in my opening hand, so instead, replace the 3rd copy with something like x1 "Ultimate Slayer" or x1 "Droplet".
I think that what we are trying to say in this video - but let me know if I am wrong.
I like how you explain this.
Im still tweakin my Voiceless deck. Cz i dont like my ratio rightnow depend on my local meta with so much deck variant. Playing diviner build is bad on my local.
Some time i need tech card. But still didnt find the right one. Too much HT so bad. But less HT not good at all.
I see your video about boardbreakers and i still think to put some on my deck.
Diviner is such a great card, it has so much utility! if it can send a fairy to the GY and not get negated it can get so much value!
Not to mention the tribute effect or it can also be a tuner too!
I'm a huge Infernoid fan, and with the deck coming back, I'd love to see analysis of 60-card decks, ESPECIALLY those with archetypal bricks
Similarly, discuss "when to go over 40" like we're seeing with Rescue-Ace profiles
Hey man. Just saw many of your videos to get a sense of the entry level math that takes part in deckbuilding. I know that these calculations are kind of simple and try to encompass a more general way of thinking, but I would love to see the more niche, and specific calculations of yugioh. I find that so interesting as well (ex. how to evaluate cards that are starters and also extenders, quantifying synergy between a card that works only with one card and where the combo is very linear vs a card that has multiple uses in the deck, etc.) I subbed because I think the math that you portray in your videos has been super useful to me, and I would love to see more of your content once you get to the really hard maths lol. Thank you! 🤟🏼
I am glad you love the math of the game as much as me :) Often times people think its very boring and just want to be shown what to do but I like the reasoning and math behind why that is the answer.
Thanks a lot. I'm gonna watch all your content now. I'd love to see you build decks as well while explaining what you do.
Prank Kids breaks this argument though, because the starters are also combo pieces.
Maxing out on them doesn't necessarily hurt you outside of "starting" with Rocksies. 1 for 1 is not ONLY a start but also an extender.
After any Prank Kids combo you thin the deck and are likely to draw non engine after from things like Pranks or Maxx C (master duel)
The only thing chicken game and Upstart bait out is Droll, which messes up everything else you want to do as well
currently droll is played at >13% representation and assuming those that play droll run it at three copies that gives about a 4% chance that you will be drolled in a random game. That low amount is too low to be considered a threat at this point but that is good to keep in mind for future and past formats.
In formats where droll raises from 4% to 15% or more (like some heavy search superheavy sam formats etc.) then you can consider watching out for droll.
So for now I wouldn't worry about droll. Its like telling OCG or Master duel not to play Maxx C because of Floo its currently seen too little and counterable.
Also, you don't have to do the draw 1 first. in fact its better thin the deck then do the draw at the end because your likely to run into more Tech/handtraps/traps yourself to futher boost your followup turns.
Finally, if you did decide to use the draw first it still could be a better play to bait ash and have a total smaller decksize in cases where ash is used.
Now, I’d like you to show an example of a rogue deck with a massive engine like Hero.
What are the ways to cut down on deck size and what are the optimal ratios for starters extenders hand traps or board breakers?
How would you account for an extra deck monster as a starter, such as Destiny hero dangerous?
Spells count as starters too such as fusion destiny and foolish burial.
Glad to see somebody talking about the math behind the game, especially concepts like the birthday paradox. You studying data science by chance?
I used to tutor Honors stats in college for my undergrad. Bell curves, standard deviation all that stuff i found so interesting!
You might enjoy the content in the free to access prob 140 course’s book from Berkeley. It’s in the drop down menu. It has great content on the birthday attack among other things and might give you inspiration for future videos.
Keep on making these videos, I never improved so much at deck building thanks to you
these comments like these mean the most! thank you! that made my day. I am glad these vids are so helpful to you!
In all the years I've played Yu-Gi-Oh, I've never really come across a video like this. It's kind of weird now that I think about. I have played MTG for longer, though. Which I have a deck building mindset from that. So, I would just build decks, play test, and make adjustments if needed. I guess I'm just somewhat acknowledging stuff I didn't know that I knew. Or rather, barely thought about, again from having the MTG background. All in all, just saying this video is neat.
I've been coming across this when making random yubel decks. The cards you'd normally run at three are dropped to two or a single copy in order to open up more fluent hands instead of bricking every time.
I’m playing 50 Branded. I believe I have no more than 4-5 Playsets (Albaz, Fusion, Albion, Aluber) I have a few down to 2 because I do not want to draw too many of them but I have a ton of 2 ofs like Allure, Fusion Deployment and I also run Pot of Desires. By the time I comb off turn one, I’m down to 20 cards or less after interruption.
i can see this applying to normal summons but if it can special itself from hand, it is immediately more valuable since your first starter is likely to get negated
If your first starter is negated and it is a HOPT then it doesn't matter if you can special summon another one of those copies because its a hard once per turn.
If you mentioning "extenders" then your likely refering to decks that are 2 card combos who has math that is compeltely different from this video that i have in another video and you can find the 2 card "extender" math here. th-cam.com/video/dUB_C53DAt4/w-d-xo.html
When including extenders or cards that have 2 card combos the math to get the 85% range or to play around handtrap range for a 2 card combo the math becomes you want to run 20-23 starters. Hope that helped and clarified some things.
@@JessePerezStrategyGaming i meant if you had a second card that also functions as a starter for your deck, sorry for the late reply
Great vid, math looks good and the graphs are awesome.
I do think the way you are phrasing your argument is a little awkward. The point of having super synergistic cards is so that one can have a "hyper" consistent engine using as few cards as possible. I think it's very intuitive to say that having massive amounts of consistency is not worth the loss of deck space, and by extension utility.
The graphs present the optimal ratio for maximizing consistency while minimizing the number of cards used. Taking my intuition and then giving numbers that back it up and add specifics.
Great vid, just earned a new subscriber.
Thank you! You also make an excellent point about the phrasing of hyper consistantcy.
Yes, I have to make sure I'm being more clear in my explanations I'll try to be a bit clearer lol. It's called teachers syndrome where I don't know where I am being confusing because it makes sense in my head so sometimes I'll glance over something that might need further insight. Great comment again & thanks for watching!
Reminds me of my syth lock deck.
I added a cyber twin dragon otk engine
Dragoon for burn
Mirrorjade for board wipe.
I got told to remove cyber dragon by a judgr laughing at me
But dispite it not be 100% consistency
However if i need it
I can do more
Amazing vid. Couple minor mistakes imo but breaking down the ratios especially in graph for was super useful.
Would love for 2 card combos and ratios on 50/60 card decks broken down too
never thought about the playset thing. but after your video I checked my two recent decklists. somehow I did this 8 playset rule withouth knowing about it.
I often forget to like videos I find entertaining or informative but man I had to make sure I couldn't leave this video before leaving a like. This video is very informative and i could tell you definitely did your research. Keep up the good work my man!
I would love to see how this math applies in branded, you have in a 40 build 3 of aluber, albaz, deployment, fusion, opening and sometimes nadir and SOMEHOW, i never saw a branded player brick in any way
Ok this was better than i expected. Subscribed
awesome! I am glad you liked the content! Thanks for watching :D
Duel links actually has rules for how many limited/semi limited you can have in one deck as well.
Very underrated YGO channel. I believe you have to make videos with explaining the maths on actual decks. It will be mind blowing to find underrated decks!
Keep it up Professor!
Awesome work !
The Ace Attorney song during the graph really sold it to me
what was your metric for judging the range of probabilities to highlight in green for the starter ratio graph?
Is that an ace attorney soundtrack?? Love it
Yes! good ear! I love that game :)
The math may say play 2 predaplant Orphys Scorpio and 1 Darlingtonia Cobra with 3 lonefire blossom but I’ll open with the 1 cobra without fail every dang time
Hey, I love the idea of using the Birthday paradox to solve how many Playsets you want to run.
Do you think you could go into more detail on how you calculated the 8 playsets or maybe a resource for how to calculate it When deck building? thanks!
I need a deck that is hyper consistent because I brick anything.. my favorite deck of all time is branded and I brick with that, I have blue eyes and floo… you can imagine the neighborhoods I have built with those two. I can shuffle every way possible but I always get a bad hand and my opponent gets a good hand…
It sounds like Tenpai is your ideal Deck. Goes second, runs minimal 1-card starters, 20+ hand traps, and still has room for board breakers and tech. 🐉
While certainly a reasonable and interesting theory I cant help but feel theres a few *very* flawed assumptions. 1) The assumption that every starter is only a starter, and that a second one cant be used for anything else 2) The assumption that all cards are HOPT, and cannot be useful if a second is drawn 3) The assumption that all cards are equally powerful (yes Ash Blossom is HOPT, but replacing it with a more situational hand trap isnt necessarily worth it) 4) The most fatal assumption in my opinion, that drawing two starters is equally as bad as drawing none at all. Drawing a 0 card hand is infinitely worse than drawing a 4 card hand.
Great comment, I literally say exactly your points in other videos because I don't think i was clear in this one. I call it Noob Deck building protection. Cards like Diableellestar can turn your dupes and extra starterss into at the very least discard fodder. So if your over commiting to the amount of starters adding in cards like diabllestar, droplet, super poly or engines like horus that have discard outlets etc to make use of discards is great.
I also mention the HOPT statement in alot of other vids its weird when TH-cam will reccommend these videos and they are sometimes the first in the series that are watched some stuff is missed in the series as a whole but i try not to repeat many things otherwise all my videos would be the same and like 2 hours each.
Alot of concerns should be more addressed in other vids its weird that this one was recommended first as this one took off unexpectedly so does have alot of information missing or out of context.
But yes all your points are valid and correct! I talk about them in different aspects of other videos!
Thank you for commenting, watching and hope you check those other videos out!
@@JessePerezStrategyGaming Understandable, the algorithm works in strange and bad ways
Regarding Swordsoul: against which three-ofs would you actually advise?
Triple Longyuan seems mandatory, either for an early Baronne (if she's legal) or to get draws with Qixing Longyuan.
Going second, there are also other options such as Longyuan and Adhara to make Yazi which gets you to Tai A or Mo Ye.
You'd also want to run at least two Ecclesiae (siding in a third one for going second) because while starting with her is weak to Ash, it's not _too_ bad (maybe Psy-Frame Gear Gamma is worth considering?) and she's also a free Tuner/non-Tuner if your opponent controls a monster.
Mo Ye is the best Normal summon without any setup but there are many two card combos that let you start your plays without using your Normal summon immediately, in which case Tai A is just as good, if not better (Foolishly Burying a card may be better than drawing a random one).
Emergence, too, is something you'd probably want to run at three because it's not just a starter but also a utility card, searching any Wyrm you want besides your starters (usually Protos).
I suppose the Tenyi support spells should be at less than three, maybe two each (if you even run both).
Adhara or Vishuda might be enough at two but Ashuna is certainly worth playing at three.
PointA: got confused about the 2nd point ~5:28
Pointb: you did not say that getting 2 normal summons in your starter hand is basically bricking 1 card (the 2nd normal summon) and that normal summons usually get negated/interrupted. However, a starter that is NOT a normal summon is excempt from this unless they are hopt.
point c: you said this in the video, i just want to reiterate, this also applies to hopt cards. you can't play triple tactics talent twice in the same turn, so seeing 2 in ur hand is also bricking 1 card
So if ur playing a playset of ur starter and talent, ur bricked hand could be: starter, starter, talent, talent, handtrap. Out of 5 cards u got 3 usable ones and of those 3 u got 1 starter. Normal summon> get ashed, u lose the turn and possibly the duel.
Ngl, deck building in YGO is way overwhelming for me due to how many cards there are with very niche and specific effects. Even in Master Duel I just kinda get lost and dunno where to start.
It's like making a bouquet of flowers. Start by focusing on one card/strategy you want then build supporting cards around that and then tech cards around those.
@@JessePerezStrategyGaming You say that like I've ever made a bouquet of flowers! And yeah I maybe know what vaguely interests me in terms of direction or archetype, but finding cards and whatnot that support them is like... Ah yes, finding a needle in a haystack, since there's thousands of cards with unique effects... Knowing where to begin searching for effects that compliment and help build a cohesive deck is the problem.
What annoys me most about master duel in regards to the playset paradox is that u have to play 3 playsets in every deck. You have to play 3 maxx c, 3 ash blossom and called by + cross out is a playset. I don’t care about the bug gameplay wise, just purely from a deck building perspective, it limits you so much. Ash isn’t even good against snakes, but u have to play it. It stops u from experimenting with tech cards or different hand traps, while giving less room for engine. For example in rescue ACE, the archetype requires so much room, u barely have room for non-engine and the non engine u have to play is maxx c and it’s counters.
I'm really enjoying these math videos. I've been interested in trying to learn the math behind deckbuilding and feel some of the advice has helped so far. Looking forward to more content, keep up the good work 👍
Looking at all these statistics and being mad that archetypes I like tend to struggle because they have little to no single card starters and have to fill out the deck with pieces of the puzzle so they can’t fit very many tech cards or hand traps. Atleast red dragon archfiends last update added crimson gaia and soul resonator, so gaia and and resonator call can both search soul who can search bone archfiend who can put crimson resonator in the graveyard making me go from 0 single card starters to 9 single card starters.
Hi, I discovered your channel yesterday and I find it very interesting ! I never thought about the probabilities behind deck building and relied on the belief to have a good list.
Could you share the mathematical methods to obtain your stats/graphs? Because I think it could be interesting to teach to everyone the math behind their own decks! 🙏
hello! glad you find the channel helpful!
The first thing is to use probability to determine your odds. Luckily science and math have advanced where there is calculators to do this for you if you don't know the math by hand.
stattrek.com/online-calculator/hypergeometric
This is a tool that you can use for basic probability calcs.
Population size = deck size
Number of successes in population = number of X Special cards your looking for
Sample size = Hand Size
Number of successes in sample = Number of X Special Cards you want in hand.
That should be a good start! Let me know if that helps :)
You are a genius! Now I can laugh at my foes from the rooftops of my masters ranking.
Your videos are top tier content.
Been working on a spreadsheet of my own since discovering your page. Figuring out statistic’s with my unchained deck has been particularly challenging lol.
the plethora 2 card combos and 3 card combos (since 3 card combos are very common to open in unchained) between the unchained cards themselves and the dark contract has been a bit of a headache. lol.
One issue i have is that you don't specify if the 12 starter limit should apply only to 40 card decks or not, because if you play lets say a 60 card deck,that will grow the same limit of starters,or, if you play a hyper consistent 40 card deck,you can also add more hand traps,or board breakers or other such stuff instead of replacing cards,just to keep the constancy under the "hyper"
But there ret,man,this video is numberphile level of quality ngl
I don't even play Yugioh, but you've opened my eyes
Roulette has 1 to 36 odds.
Which means you are guaranteed to draw a card you do not need compared to a visit to a casino where you are even more likely to lose at ( But at least the deck is shared in that instance) .
Imagine playing a game from a low level deck the casino opponent never draws from for their own hand , you would know it is rigged if it was played that way.
A counter argument example would be superheavy samurais. the deck ran 12 starters in 40 in a handtrap format and bricked too much. running 15ish starters would have been much better. in around 25 games, you bricked around 4 games. You also definitely want enough extenders to push through.
Superheavy samurai while some cards are a 1 card combo - most others are 2 card combos (they have to equip or need another on board). In 2 card combos the optimal ratios are running 20-23 cards to facilitate that.
I should have put that in this video but I fear it was getting to long as it is. I have the math for 2 card combos here:
th-cam.com/video/dUB_C53DAt4/w-d-xo.html
But yes your conclusion is correct. For something like super heavy I would even take it a step further and run 20-23 of them to facilitate their 2 card combo strategy instead of 15 and consider the 1 card combo/starters more of a luck. Thats what the math shows for them to have that 85% area and not be hyperconsistant.
Also SH isn't limited to the 1 normal summon for the most part like the prank kids. Since they have sooo many extenders that can special themselves playing through the handtraps is very important and getting the extenders by playing the 2 card combo ratios 20-23 will allow to play through an extender.
TLDR: You are correct a deck like superheavy should be playing more than the 12 starters and should be playing an upwards of 20-23 SH cards that can facilitate their plays.
15 sounds like the ideal number in 40-card, it's been working great for Tenpai.
Basically, consistency and reliability vs diversity and power
One of these days, I was building a custom deck (with cards that would be flip monsters support), but the important thing is that my game plan didn't just depend on opening with 1 flip monster in my hand (1 flip monster could be a starter, but any other flip monster would become a combo extender), therefore, I decided to use a hypergeometric distribution calculator to evaluate the best combinations to have the greatest chances of getting 2-3 cards of a certain type in my hand and while experimenting with different combinations, I saw that a combination of 18 cards in a 42 card deck gives a very good chance of exactly having 2-3 cards (Incredibly, I already had this idea of not abusing 3-set cards, because in theory I could search any flip monster, so it would be better diversity for combo extension and in these 18 cards I don't use any 3-set cards, instead I use 6 2-set cards). Could you tell me if these numbers make any sense in practice?