It took seeing my comment a second time to realize it was mine. Holy crap, glad you were able to take the idea and make it work. Not too many people at my store were interested in it :p
It's brilliant and entirely unfathomable that reaching these legitimately astromonical numbers, was part of resolving *the first six triggers* of 8390 triggers, of just the first Precursor Golem. The numbers become nonsense so very quickly.
So, I did some maths, and we're nowhere near Graham's number, but we're still huge. Using Knuth's [up-arrow notation](en.wikipedia.org/wiki/Knuth's_up-arrow_notation), we end up with over 2^^^66 copies of each golem (which means about 2^^^66 golems overall). You start out with 6 (which is just under 2^^^2) doubling golems, and 64 Precursor golems. Casting Replication puts 64 Precursor triggers on the stack. Each Precursor trigger resolution puts a rite of Replication on the stack targetting each other golem. For each resolution of Replication targetting a golem, we create 5*2^D copies where D is the number of doubling golems. For now, we'll ignore the resolution of Replication against all but the doubling golems for reasons that may end up being obvious. The first time you resolve Replication targetting doubling golems, you get 5*2^6 = 320 new golems, for 326 doubling golems total The second time you resolve Replication targetting doubling golems, you get 326+5*2^326 > 6*10^98 (or 6E98) golems The third time you resolve Replication targetting doubling golems, you get 6E98+5*2^6E98 golems Working out the equations numerically is a little difficult, but we can make a lower estimate. We can dramatically underestimate it by saying that 6+5*2^6 is larger than 2^6, which is larger than 2^4 = 2^2^2 = 2^^3 At this point, it would be helpful to point out that 2^2^^i = 2^^(i+1) 1st Replication targetting doubling golems: over 2^6 > 2^^3 doubling golems 2nd Replication targetting doubling golems: over 2^2^^3 = 2^^4 doubling golems 3rd Replication targetting doubling golems: over 2^2^^4 = 2^^5 doubling golems Nth Replication targetting doubling golems: over 2^2^^(N+1) = 2^^(N+2) doubling golems The result of this is that each time you resolve N instances of Replication targetting doubling golems, you end up adding significantly more than 2^^(N+2) doubling golems. The first time you resolve Precursor, you get 6 Replication triggers targetting doubling golems. By the logic above (N=6), after resolving all the Replications from this step, the number of doubling golems is over 2^^(6+2) i.e 2^^8 The second time you resolve Precursor, you get 2^^8 Replication triggers on doubling golems, so the number of doubling golems after this step is over 2^^2^^8 The third time you resolve Precursor, you get 2^^2^^8 Replication triggers, so the number of doubling golems after this step is over 2^^2^^2^^8 At this point, it would be helpful to point out that 2^^2^^^i = 2^^^(i+1) Again underestimating, 2^^8 is over 2^^4 = 2^^2^^2 = 2^^^3 At this point, we have: 1st Precursor resolution: over 2^^8 > 2^^^3 doubling golems 2nd Precursor resolution: over 2^^2^^8 > 2^^^4 doubling golems 3rd Precursor resolution: over 2^^2^^2^^8 > 2^^^5 doubling golems Kth Precursor resolution: over 2^^^(K+2) doubling golems We have 64 Precursor triggers, so by the logic above (K = 64) we end up with 2^^^(64+2) = 2^^^66 doubling golems. At this scale, we can basically ignore the quantities of the other golems until now. If we look at the resolution of the Replications on the other golems Once again, for each resolution of Replication targetting a golem, we create 5*2^D copies where D is the number of doubling golems. 5*2^(2^^^66) is basically just a little larger than 2^^^66, so we can just count one resolution of Replication on the other golems and estimate 2^^^66 total golems. Each golem has 3 power, which means 3*2^^^66 total power, which is still about 2^^^66. Craterhoof Behemoth's ETB gives each creature +2^^^66/+2^^^66 and trample, so (2^^^66)^2 total power, but again that's basically the same as 2^^^66 power. Really the trample is the only significant effect of that. Even if you sac it to make token copies, the 2^^^66 duplicated ETBs would give each creature +(2^^^66)^2 power and toughness, which is (2^^^66)^2^2 total power, but that's still basically just 2^^^66.
There is a different way. Anikthea, Hand of Erebos can make token copies of your token doublers from the graveyard. You get one of them, and you only need to populate 4 times to get 10^620 tokens
starting with 6 (golem) doublers, even a non-kicked rite of replication is pretty much the same: first (2^6) : 64 new doublers second (2^(2^6 +6)) : ~1.18 e21 new doublers third (2^(2^(2^6 +6) + 2^6 + 6)): ~1 e(10^20) [a number with 10^20 zeroes in it] new doublers (If each atom had a universe inside it, and each atom in those universes had a universe inside it, you would need to do so more than 1 quintillion times to have as many total atoms as how many golems you get) Fun stuff!
This honestly makes me feel MORE significant because that number is meaningless. It has no physical relevance and can't even be comprehended by the humans who created it. It can't be communicated or written down or displayed or potentially even computed by the greatest supercomputer. It makes me feel amazing because it proves the imagination of humans transcends the physical and even transcends the limitations of our own fleshy brains. If life is the universe trying to make sense of itself this is us transcending that existence; living in a universe greater and more imaginative and more impressive and just larger than the one nature created.
When I used to do "infinite combos" in comprel I would choose Grahams number as my life total pretty often. I'd represent that with a capital G and then write down my life total as an equation e.g. G - 30. I'm not even sure how this interacts with the golems. From the wiki " Graham's number is an immense number that arose as an upper bound on the answer of a problem in the mathematical field of Ramsey theory. It is much larger than many other large numbers such as Skewes's number and Moser's number, both of which are in turn much larger than a googolplex. As with these, it is so large that the observable universe is far too small to contain an ordinary digital representation of Graham's number, assuming that each digit occupies one Planck volume, possibly the smallest measurable space. But even the number of digits in this digital representation of Graham's number would itself be a number so large that its digital representation cannot be represented in the observable universe. Nor even can the number of digits of that number-and so forth, for a number of times far exceeding the total number of Planck volumes in the observable universe. Thus Graham's number cannot be expressed even by physical universe-scale power towers...."
@@breadpower g(0) the first graham's number can be written down as 3↑↑↑↑3, but that is "just" a notation called "Knuth's Up-Arrow Notation", which is a shorthand denoting very large numbers. It's not the only such notation, and is not required to write down large numbers.
So, I did some maths, and we're nowhere near graham's number, but we're still huge. Using Knuth's [up-arrow notation](en.wikipedia.org/wiki/Knuth's_up-arrow_notation), we end up with over 2^^^66 copies of each golem (which means about 2^^^66 golems overall, for about 2^^^66 total power). My working out is in its own top-level comment here: th-cam.com/video/zNQiS5bw5JE/w-d-xo.html&lc=Ugyz550pHZrzgugP4Qt4AaABAg
even if you cast rite of replication multiple times after casting it for the first time you'd be nowhere close to grahams number. You could cast rite of replication a trillion times and you wouldn't even end up anywhere near it, because the speed of growth is too limited in this combo. you probably wouldn't even get to G(1), let alone g(64) because each time you copy a doubler it you're just adding a 2 to the power tower equal to the amount of doublers you have, and you do that an amount of times equal to the amount o precursor golems you have since I'm pretty sure each of them would copy the rite of replication. so if we look at Knuth's Up-Arrow Notation, if you would depict the growth of the amount of golems with a function where x is the amound of times you cast rite, the function would only be in order of 4 up arrows. g(1) on the other hand has an amount of up arrows equal to 3⬆⬆⬆3 meaning it just absolutely dwarfs the amount you culd ever make with this combo, even if you cast rite 3⬆⬆⬆3 times, you still wouldn't come anywhere close to g(1), and grahams number is g(64).so if you infinite combo and set your life to grahams number and your opponent pulls off this combo you could confidently tell them that you would still survive, except if they cast a craterhoof because you die to commander damage.
You manage to pull this off, an opponent casts Doom Blade on any of your golems and copies the spell to destroy all of them. But you have an ace up your sleeve! In response you cast Blessed Defiance, a white instant for one white mana that literally nobody in the history of Magic has ever played that reads "Target creature you control gets +2/+0 and lifelink until EOT. When that creature dies this turn, create a 1/1 white Spirit creature token with flying." Now you get to make more spirits than you had golems and WolframAlpha servers explode :D
I used to have an adrix & nev mutate deck, where I'd mutate onto adrix & nev and the start casting copy spells targeting them. First you get 2 copies, then 8, then 128, then 2^139, which is a lot. Highlights were gaining 21 million life by making a lot of verdant sun's avatars, and making so many creatures the I had to use a big number calculator, which spat out a number that took 10 full seconds to scroll through on my phone. Doubling is fun
Getting into the largest named finite numbers is an insanely humbling experience. Try looking up Graham's Number sometime. And then realize that all of these numbers, no matter how mind-shatteringly large, are not only smaller than infinity, but actually INFINITELY smaller than the *smallest* infinite number. And infinite processes exist all around us at all times.
At 8 minutes into the video, the Right of Replication targeting a golem creates 8000 spells on the stack for each of the 64 smart golems in play, because each forking trigger resolves separately. Edit: yay, you got it!
@@PleasantKenobi Okay... follow me here. Information is entropy. Entropy is energy. Energy is mass. If you have enough information is a small enough space, it creates a gravitational effect that can actually bend spacetime and create a black hole. It is possible that if you were to actually fully comprehend how many golems were created here, it would collapse your mind into a black hole.
@@BrotherAlpha black holes are created from the gravity from giant stars, and energy is not mass as it goes faster than light and something with mass can't go ftl.
Vince, I think this is my all time favorite video of yours. As a Magic nerd, a math nerd, and a philosophy nerd, this just hits all of my buttons in a good way.
Decidedly not infinite, and yet simultaneously ends up making more tokens than pretty much any player presenting a true infinite loop will ever declare.
Cool combo you've got there. Thanks for the win, I cast Time Stop when all the creatures resolve and then cast Insurrection on my turn. Good game shake my hand.
I made an EDH kinda similar with a little different set-up. started with the typical doubling season + opalescence. Then I went with mirror gallery + kiki-jiki with a splinter twin on it (tap to copy kiki-jiki for each doubling season, each of which target to copy doubling season) and a freed from the real. On the turn I "go off" I cast Celestial Dawn and have serra's sanctum, which fuels my untaps of kiki-jiki by freed from the real. I then have Garruk's Packleader (which is a may so you don't deck yourself) to fuel Mind Over Matter, to untap my serra's sanctum, so it can produce mana equal to the number of doubling seasons I have each time I go through all the kiki-jiki copying for each mana I produce. Once I'm nearing the end of my drawn hand (and can't draw more), I cast Wort the raidmother, and use a copy spell on Wort (there probably better ways to do this next part, but this deck is pretty old, and this was the best option at the time), I use praetor's council and copy it for every wort, the raidmother I have to refill my hand from all the discarded cards. Between each resolution of Council, I do the entire set of loops, which as a reminder is: -discard a card to untap serra's sanctum, tap to add W for each enchantment I control (copies of doubling season included). -for each W I have, I can untap "Kiki-Jiki" with "Freed from the Real" (thank's to celestial dawn). -for each time I untap kiki-jiki, I can tap to create copies of kiki-jiki 2^x times where x is the number of doubling seasons. -for each kiki-jiki copy created, each one taps to copy doubling season (creates 2^x each time, x growing between each kiki-jiki activation). This deck intentionally cannot go infinite (assuming no outside interference)
What an absolute masterpiece of a video, the deck doesn't win with damage you win the by sheer amount of existential dread you cause the other players with your unfathomable mass of cookies.
Years ago, Brudiclad was the first commander I fell in love with. I thought it would be pretty cool to have 10 Sharding Sphinxes attack and make 100 thopters, then turn those thopters into more Sharding Sphinxes and attack with all 110 and kill everyone with 12100 thopters on the board. I never would have imagined this when I was driving to Target to buy the War of the Spark Planeswalker deck. Man I love this game
Once plotted out a similar thing with Rhys the Redeemed+Mondrak+Dollhouse of Horrors+Mirror Box The idea is that you reanimate Mondrak with Dollhouse, turning him into a construct with P/T equal to the number of constructs you control. Then you double once, for three. Then you double again, for 27. And then you double again, for a number with several billion zeroes. Presumably you could double again and again, for similarly abstractly large numbers of dolls, but by iteration three you're already doing enough damage that in the metacontext of the game(in which you are a planeswalker dueling another planeswalker) you're shattering open gateways to the blind eternities.
I am so hype for this video. My first "modern" deck had some splicers, this BEAUTIFUL Golem and Cackling Counterpart. Yes it was terrible, but I made lots of golems a few times, and it eventually evolved into a more "midrange flicker" Modern deck, and sparked my joy for modern :D Now, LETS GET STUPID!
Vince channeling his inner Rhystic Studies in this one. side note: I love weird and unique cards and Precursor Golem has been one of my favorite cards since SoM released. I've built multiple iterations of Riku decks that abuse it, though to a more practical extent than this. I was part of a commander group back in 2014-15 and we would do monthly deckbuilding challenges and the winner got a custom playmat with a card from their deck on it. I won the event with the first iteration of the riku deck and my playmat has a big-ol low-res Precursor Golem on it. Happy to see it get the attention it deserves.
@@louismaciver8262 Nah. Zada and Co require you to play other creatures to make use of them. Precursor is an army in a can that can grow exponentially and lead to some wild stacks.
At this point, even if I had an actual infinite amount of creatures I feel like there would be more golems because with an infinite combo you have to name the number of loops. I just couldn't name a number large enough.
As a mathematician, this is perhaps the second coolest piece of math I've seen in MtG (behind the guys who made a Vintage legal Turing machine). I just want to point out that every time you try to describe how large the numbers are, your words are woefully inadequate. The first rite of replication puts into play 5 doublers, which because of all the doublers already on the battlefield means 320 doublers. At this stage, the very next doubling season will make the number of doublers larger than the number of atoms in the observable universe. It is only barely smaller than a googol in this context. The number of doublers have gone from 6 -> 326 -> Atoms in the known universe, with only 2 rites of replication. We have three more to go. "Make each atom in the universe its own copy of the universe and count the resulting number of atoms" isn't nearly going to cut it. "Make each atom a copy of the universe, and then repeat this recursively a number of times corresponding to the number of atoms in the universe, then count the number of resulting atoms" is about the correct ballpark. After the third rite of replication. And we still have two more rites of replication to go. I hope I have properly conveyed just how much you're thinking way too small with these numbers.
.... man i just realized that march of the machines shuts down a lot of fast mana in cedh and treasure tokens. It sounds goofy if you play casual, but in cedh thats like almost good enough to be considered a legitimate tax peice
@@PleasantKenobi imagine it, a world where your sitting there, thoracle combo in hand, and you just cant get to it because the jackass across the table played mom.
I've been quietly lurking this channel for years and this video is precisely why I love PK and his content. Also, why WotC should learn math is not just for blockers.
One, this is the first non-infinite combo I've ever seen that beats my personal record for tokens (though mine was also more tokens than atoms in the known universe). Second, yes, if each atom had its own universe, you'd still easily exceed the number of atoms in each of those universes. That statement was absolutely correct (by a lot). Thirdly, I was teaching my students about the number googol, and as I'm trying to get their heads around how big it is, and one students said, "Why do we even bother with numbers this big if there aren't even that many things?" My response, "Well...this one time I was playing Magic: The Gathering..."
TLDR; The board state after everything resolved can be described this way: D_64 doublers P_64 precursors G_64 +5x2^(D_64) 3/3 golems with: D_n=A_(sum[i=0;n-1;D_i]) with D_0=6 and A_n=fⁿ(6) and f(k)=5x2^k+k P_n=R(P_(n-1), D_n)+P_(n-1) with P_0=64 and R(T, N)=Tx5x2^N G_n=(P_n-P_(n-1))x2x2^(D_n)+R(G_(n-1), D_n)+G_n with G_0=8319 Warning! I wrote all this as I did the maths, so it might be hard to follow (I even made a mistake at one point that I caught after) ok! so, let's do the maths! first, let's remember what's on the board as the rite of replication is cast: 8390 golems separated as follow: 6 doublers 8320 basic golems 64 precursor so the stack is: The original rite targeting a random basic golem + 64 precursor triggers and it becomes: Original rite (OR)+63 precursor trigger (PT)+(8383+6) copy of rite -> OR+63PT+8383+5, we create 5x2^6 (320) doublers so we have 326 doublers OR+63PT+8383+4, we create 5x2^326 (683515851494691226366406945974256676672865447154128886383053314503110312249804976007347867819704320) doublers so we have 683515851494691226366406945974256676672865447154128886383053314503110312249804976007347867819704646 doublers OR+63PT+8383+3, we create 5x2^(5x2^326+326) doublers (this number has more digits than the number of atom in the observable universe, so we'll keep it as is), so we have 5x2^(5x2^326+326)+5x2^326+326 doublers OR+63PT+8383+2, we create 5x2^(5x2^(5x2^326+326)+5x2^326+326) doublers, that's becoming a bit unwieldy, so let's create a function to help us, f(n)=5x2^n+n is the amount of doublers we have after a rite resolve if we had n doublers before. so 326=f(6), 6835...04646=f(326)=f(f(6))=f²(6), we currently have f⁴(6) doublers, we'll call fⁿ(6) A_n so we have A_4 doublers after 4 rites resolved we can directly skip after the rites targeting doublers resolved: OR+63PT+8383, we have A_6 doublers and A_6>10^10^10^10^10^98 so we now create 8383x5x2^(A_6) golems OR+63PT, we just finished resolving ONE TRIGGER! so, how many copy of rite does the next trigger create ? we have A_6 doublers and 8383x5x2^(A_6)+8383 golems (other than the one we targeted with OR) so... OR+62PT+(8383x(5x2^(A_6)+1)) rites targeting golems+A_6 trigger targeting doublers we can easily reduce the stack to: OR+62PT+(8383x(5x2^(A_6)+1)) rites targeting golems and we have A_(A_6+6) doublers. I just realised that because i'm keeping the calculations fully written It's going to be a bit hard to not mess up the amount of token created, so let's create a new function: R(T, N)=Tx5x2^(N) being the number of tokens we create after T copies of rites targeting (non-doubler token) resolve while we have N doublers on the board. so the stack can be describe this way: OR+62PT+ (R(8383, A_6)+8383) rites targeting golems. OH!!! F***!!!!!!!! I just realised i didn't take into account the tokens created by precursor golems as we create copy of them... SO! let's solve this issue... we had 64 precursors, each were targeted with a rite after the A_6 doublers were created. so we created R(64, A_6) precursor golems each creating 2x2^(A_6) golems so the board is: A_(A_6+6) doublers R(64, A_6)+64 precursor golems R(64, A_6)x2x2^(A_6)+ R(8319, A_6)+8320 basic golems (one of them is targeted by the OR so it doesn't get copied) and the stack should look like: OR+62PT+(R(64,A_6)+64) Rites on Precursor+(R(64, A_6)x2x2^(A^6)+R(8319, A_6)+8319) Rites on basic golems. -> we won't be able to just continue by hand like that, so let's continue to abstract those numbers: we'll index our numbers by the number of Precursor Golem triggers that have fully resolved (they resolved and the copy they created resolved) so D_n is the number of doublers after n Precursor triggers fully resolved. we know that D_0=6, D_1=A_6, and D_2=A_(A_6+6). I'm conjecturing that D_n=A_(D_(n-1)+D_(n-2)) P_n is the number of Precursor at the n-th step, so P_0=64, P_1=R(64, A_6)+64=R(P_0, D_1)+P_0. I'm conjecturing that P_n=R(P_(n-1), D_n)+P_(n-1) G_n is the number of *other* golems at the n-th step (we won't count the one being targeted by OR). we currently know that G_0=8319, G_1=R(64, A_6)x2x2^(A_6)+R(8319, A_6)+8319=(P_1-P_0)x2x2^(D_1)+R(G_0, D_1)+G_0. This one, i'm a bit less certain but let's conjecture that G_n=(P_n-P_(n-1))x2x2^(D_n)+R(G_(n-1), D_n)+G_(n-1). Now, let's check if these conjectures make sense: D_n: we know that to get from D_n to D_(n+1), we have to resolve all the triggers targeting a doubler, and the number of trigger targeting a doubler is exactly the number of doubler on the board, so D_(n+1) is D_n triggers after D_n, so if D_n is A_xxx, D_(n+1) is A_(xxx+D_n) so: with the conjecture, we get A_(D_(n-1)+D_(n-2)+D_n)=D_(n+1) there's no simplification so the conjecture was wrong, but we can see that the real answer is D_n=A_(sum[i=0; n-1; D_i]). now let's check P_n: P_n to P_(n+1), is fairly straight forward as the copies aren't influencing each other, so the number of new precursor is just the amount created by all the rites targeting each precursor already there, so we create R(P_n, D_(n+1)) precursor (D_(n+1) because we resolve the rites targeting the doublers first), and so the amount of precursors at the end is just R(P_n, D_(n+1))+P_n. the conjecture is confirmed. now for the hard part; G_n: G_n has 2 things (other than doublers) influencing it directly: the rites copying them and the precursors creating them. So the number created by the precursors is clearly (the number of precursors created at this step)x2x2^(number of doublers) which is just (number of precursors there-number of precursors already there the step before)x2x2^(D_n) so (P_n-P_(n-1))x2x2^(D_n). so the first part of the conjecture seems correct. now for the second part, it's like for the precursors so we get R(G_(n-1), D_n)+G_(n-1) and by summing the two parts we get the formula previously conjectured. so we can now describe how the board looks like at the end of all those triggers: D_64 doublers P_64 precursors G_64 basic golem tokens AND the original rites can now resolve!!! so we add 5x2^(D_64) basic golems to the board. I won't try to find an explicit formula for those numbers because arithmetic and recursive functions aren't my forte.
4:48 this took me a second to understand so for those like me here’s how I understand it: y = number of tokens made x = number of “doubling” cards Whenever tokens are created, create y * (2^x) tokens instead. (Side note, I know I don’t need to put 2^x in brackets I just did it for clarity’s sake)
This massively underrepresents just how crazy the number is. I would venture to say it is larger than the number of even possible, hypothetically imaginable (fininte) universes. I wonder how big it is relative to Graham's number.
Strange but I was recently contemplating a similar thing when i cast a croaking counterpart on a precursor golem with a vesuvan duplimancy in play, and then flashback it!
I did the same thing with Anikthea. It’s a little slow, but it’s so silly that I feel like I’ve won as long as I assemble the pieces. Pro tip: watch out for Insurrection-that does give them haste.
I think this combo probably makes more golems than most infinite combos, because technically with an infinite combo you have to pick a number and nobody would pick one this big
My Solarion calculator deck walked so that this deck could run! 2005 deck tech- I would make a Solarion double its P/T until it was in scientific notation, then atta ch an armadillo cloak. Deck wasn't resilient, but it was fun.
And this is where your opponent targets precursor with swords to plowshares. Sure you gain an enormous amount of life but it puts a stop to this shenanigans.
This is a deck where, for the sake of your own workflow, you show up with a set of tables with precalculated results for every series of actions you can take with every possible combination of cards that gets beyond easy enough to work with. And a method of attempting to have a reasonable way to have usable counters. And then you get told to play something else because either your deck is too intimidating or nobody else wants to bother with the hassle/time involved.
This takes "not infinite, but really big" to a whole new level
You swing, then the opponent hits you with that settle the wreckage and you feel your soul leave your body
At least you can take out all of your basics out of your deck
What about echoing truth
all these tokens are summoning sick, so your opponent can just board wipe!
That’s RAMP
BABYYYYY
@@tonyleier not with craterhoof
“And that’s how I created Mirrodin.” Karn, probably
"I cast Craterhoof. It's power and toughness approach infinity."
Technically every craterhoof behemoth's power and toughness approaches Infinity.
In response : my calculator explodes
In response I fog?
@@RainbowblitzFTWin response, stomp you?
To be fair, this is just what ceaterhoof usually feels like
It took seeing my comment a second time to realize it was mine. Holy crap, glad you were able to take the idea and make it work. Not too many people at my store were interested in it :p
Pat yourself on the back for sending Kenobi deeper into madness than WotC has ever managed.
Glad you brought it up! This was super cool!
The man, the myth, the legend
great comment made!
The “well, math IS for blockers” at the end kinda hits different.
Well, I don't think most blockers are gonna have to do much math at all after this one.
This has a real Rhystic Studies vibe to it. Great video
Glad you like it!
Good guy Pleasant "Vince" Kenobi solves world hunger, is quoted as saying "Let them eat gingerbread"
So, now we know why The Big Bang happend.
Someone in previous universe executed this combo IRL...
Our reality is just the shahrazad sub-game of magic, utterly pointless and only ends ups losing someone half their health.
It's brilliant and entirely unfathomable that reaching these legitimately astromonical numbers, was part of resolving *the first six triggers* of 8390 triggers, of just the first Precursor Golem. The numbers become nonsense so very quickly.
So, I did some maths, and we're nowhere near Graham's number, but we're still huge.
Using Knuth's [up-arrow notation](en.wikipedia.org/wiki/Knuth's_up-arrow_notation), we end up with over 2^^^66 copies of each golem (which means about 2^^^66 golems overall).
You start out with 6 (which is just under 2^^^2) doubling golems, and 64 Precursor golems.
Casting Replication puts 64 Precursor triggers on the stack.
Each Precursor trigger resolution puts a rite of Replication on the stack targetting each other golem.
For each resolution of Replication targetting a golem, we create 5*2^D copies where D is the number of doubling golems.
For now, we'll ignore the resolution of Replication against all but the doubling golems for reasons that may end up being obvious.
The first time you resolve Replication targetting doubling golems, you get 5*2^6 = 320 new golems, for 326 doubling golems total
The second time you resolve Replication targetting doubling golems, you get 326+5*2^326 > 6*10^98 (or 6E98) golems
The third time you resolve Replication targetting doubling golems, you get 6E98+5*2^6E98 golems
Working out the equations numerically is a little difficult, but we can make a lower estimate.
We can dramatically underestimate it by saying that 6+5*2^6 is larger than 2^6, which is larger than 2^4 = 2^2^2 = 2^^3
At this point, it would be helpful to point out that 2^2^^i = 2^^(i+1)
1st Replication targetting doubling golems: over 2^6 > 2^^3 doubling golems
2nd Replication targetting doubling golems: over 2^2^^3 = 2^^4 doubling golems
3rd Replication targetting doubling golems: over 2^2^^4 = 2^^5 doubling golems
Nth Replication targetting doubling golems: over 2^2^^(N+1) = 2^^(N+2) doubling golems
The result of this is that each time you resolve N instances of Replication targetting doubling golems, you end up adding significantly more than 2^^(N+2) doubling golems.
The first time you resolve Precursor, you get 6 Replication triggers targetting doubling golems. By the logic above (N=6), after resolving all the Replications from this step, the number of doubling golems is over 2^^(6+2) i.e 2^^8
The second time you resolve Precursor, you get 2^^8 Replication triggers on doubling golems, so the number of doubling golems after this step is over 2^^2^^8
The third time you resolve Precursor, you get 2^^2^^8 Replication triggers, so the number of doubling golems after this step is over 2^^2^^2^^8
At this point, it would be helpful to point out that 2^^2^^^i = 2^^^(i+1)
Again underestimating, 2^^8 is over 2^^4 = 2^^2^^2 = 2^^^3
At this point, we have:
1st Precursor resolution: over 2^^8 > 2^^^3 doubling golems
2nd Precursor resolution: over 2^^2^^8 > 2^^^4 doubling golems
3rd Precursor resolution: over 2^^2^^2^^8 > 2^^^5 doubling golems
Kth Precursor resolution: over 2^^^(K+2) doubling golems
We have 64 Precursor triggers, so by the logic above (K = 64) we end up with 2^^^(64+2) = 2^^^66 doubling golems.
At this scale, we can basically ignore the quantities of the other golems until now.
If we look at the resolution of the Replications on the other golems
Once again, for each resolution of Replication targetting a golem, we create 5*2^D copies where D is the number of doubling golems.
5*2^(2^^^66) is basically just a little larger than 2^^^66, so we can just count one resolution of Replication on the other golems and estimate 2^^^66 total golems.
Each golem has 3 power, which means 3*2^^^66 total power, which is still about 2^^^66.
Craterhoof Behemoth's ETB gives each creature +2^^^66/+2^^^66 and trample, so (2^^^66)^2 total power, but again that's basically the same as 2^^^66 power.
Really the trample is the only significant effect of that.
Even if you sac it to make token copies, the 2^^^66 duplicated ETBs would give each creature +(2^^^66)^2 power and toughness, which is (2^^^66)^2^2 total power, but that's still basically just 2^^^66.
I don't care what anyone says, this will forever be an iconic piece of content. Not even 5 stars - googol/10
So many Golems, and your opponent just needs that Rakdos charm to calm it all down :P
This is one of the most fun magic videos I've seen in awhile. Cheers man.
Amazing. My supreme verdict has never been such good value
I now have an uncontrollable urge to build and play this deck...
Right??? The problem is getting all 7 (4+ mana) pieces on board without someone killing you. But I want to try.
It isn't. With an altar, each golem produces two mana.
There is a different way. Anikthea, Hand of Erebos can make token copies of your token doublers from the graveyard. You get one of them, and you only need to populate 4 times to get 10^620 tokens
I do a similar thing with Ink-Treader Nephilim, cloning the whole board over and over again, it's fun as hell
starting with 6 (golem) doublers, even a non-kicked rite of replication is pretty much the same:
first (2^6) : 64 new doublers
second (2^(2^6 +6)) : ~1.18 e21 new doublers
third (2^(2^(2^6 +6) + 2^6 + 6)): ~1 e(10^20) [a number with 10^20 zeroes in it] new doublers (If each atom had a universe inside it, and each atom in those universes had a universe inside it, you would need to do so more than 1 quintillion times to have as many total atoms as how many golems you get)
Fun stuff!
someone send this to the guy on numberphile who likes talking about absurdly large numbers, stat
This honestly makes me feel MORE significant because that number is meaningless. It has no physical relevance and can't even be comprehended by the humans who created it. It can't be communicated or written down or displayed or potentially even computed by the greatest supercomputer. It makes me feel amazing because it proves the imagination of humans transcends the physical and even transcends the limitations of our own fleshy brains. If life is the universe trying to make sense of itself this is us transcending that existence; living in a universe greater and more imaginative and more impressive and just larger than the one nature created.
“You must construct additional golems!”
When I used to do "infinite combos" in comprel I would choose Grahams number as my life total pretty often. I'd represent that with a capital G and then write down my life total as an equation e.g. G - 30. I'm not even sure how this interacts with the golems.
From the wiki " Graham's number is an immense number that arose as an upper bound on the answer of a problem in the mathematical field of Ramsey theory. It is much larger than many other large numbers such as Skewes's number and Moser's number, both of which are in turn much larger than a googolplex. As with these, it is so large that the observable universe is far too small to contain an ordinary digital representation of Graham's number, assuming that each digit occupies one Planck volume, possibly the smallest measurable space. But even the number of digits in this digital representation of Graham's number would itself be a number so large that its digital representation cannot be represented in the observable universe. Nor even can the number of digits of that number-and so forth, for a number of times far exceeding the total number of Planck volumes in the observable universe. Thus Graham's number cannot be expressed even by physical universe-scale power towers...."
is graham's number the one thats like 3⬆️⬆️⬆️3
@@breadpower g(0) the first graham's number can be written down as 3↑↑↑↑3, but that is "just" a notation called "Knuth's Up-Arrow Notation", which is a shorthand denoting very large numbers. It's not the only such notation, and is not required to write down large numbers.
Funnily enough, when Jimmy Wong first said "Math is for blockers", it was to Graham Stark.
Coincidence ? I think not.
So, I did some maths, and we're nowhere near graham's number, but we're still huge.
Using Knuth's [up-arrow notation](en.wikipedia.org/wiki/Knuth's_up-arrow_notation), we end up with over 2^^^66 copies of each golem (which means about 2^^^66 golems overall, for about 2^^^66 total power).
My working out is in its own top-level comment here: th-cam.com/video/zNQiS5bw5JE/w-d-xo.html&lc=Ugyz550pHZrzgugP4Qt4AaABAg
even if you cast rite of replication multiple times after casting it for the first time you'd be nowhere close to grahams number. You could cast rite of replication a trillion times and you wouldn't even end up anywhere near it, because the speed of growth is too limited in this combo. you probably wouldn't even get to G(1), let alone g(64) because each time you copy a doubler it you're just adding a 2 to the power tower equal to the amount of doublers you have, and you do that an amount of times equal to the amount o precursor golems you have since I'm pretty sure each of them would copy the rite of replication. so if we look at Knuth's Up-Arrow Notation, if you would depict the growth of the amount of golems with a function where x is the amound of times you cast rite, the function would only be in order of 4 up arrows. g(1) on the other hand has an amount of up arrows equal to 3⬆⬆⬆3 meaning it just absolutely dwarfs the amount you culd ever make with this combo, even if you cast rite 3⬆⬆⬆3 times, you still wouldn't come anywhere close to g(1), and grahams number is g(64).so if you infinite combo and set your life to grahams number and your opponent pulls off this combo you could confidently tell them that you would still survive, except if they cast a craterhoof because you die to commander damage.
i know i sound sarcastic but i really think this is a masterpiece of a video thanks for all that helped making it
You manage to pull this off, an opponent casts Doom Blade on any of your golems and copies the spell to destroy all of them. But you have an ace up your sleeve! In response you cast Blessed Defiance, a white instant for one white mana that literally nobody in the history of Magic has ever played that reads "Target creature you control gets +2/+0 and lifelink until EOT. When that creature dies this turn, create a 1/1 white Spirit creature token with flying." Now you get to make more spirits than you had golems and WolframAlpha servers explode :D
Spooky 👻
I used to have an adrix & nev mutate deck, where I'd mutate onto adrix & nev and the start casting copy spells targeting them. First you get 2 copies, then 8, then 128, then 2^139, which is a lot.
Highlights were gaining 21 million life by making a lot of verdant sun's avatars, and making so many creatures the I had to use a big number calculator, which spat out a number that took 10 full seconds to scroll through on my phone.
Doubling is fun
Getting into the largest named finite numbers is an insanely humbling experience. Try looking up Graham's Number sometime. And then realize that all of these numbers, no matter how mind-shatteringly large, are not only smaller than infinity, but actually INFINITELY smaller than the *smallest* infinite number. And infinite processes exist all around us at all times.
At 8 minutes into the video, the Right of Replication targeting a golem creates 8000 spells on the stack for each of the 64 smart golems in play, because each forking trigger resolves separately.
Edit: yay, you got it!
Very cool, isn't it?
@@PleasantKenobi
Okay... follow me here. Information is entropy. Entropy is energy. Energy is mass. If you have enough information is a small enough space, it creates a gravitational effect that can actually bend spacetime and create a black hole. It is possible that if you were to actually fully comprehend how many golems were created here, it would collapse your mind into a black hole.
@@BrotherAlpha iam14andthisisdeep
No no its more, the second will also target the new copies... (and the third and the fourth etc)
@@BrotherAlpha black holes are created from the gravity from giant stars, and energy is not mass as it goes faster than light and something with mass can't go ftl.
Vince, I think this is my all time favorite video of yours. As a Magic nerd, a math nerd, and a philosophy nerd, this just hits all of my buttons in a good way.
The most impressive thing about this combo is that the number of golems is decidedly NOT infinite.
That's what I love about it so much. It's so much more interesting than "I tap this permanently a load of times."
Decidedly not infinite, and yet simultaneously ends up making more tokens than pretty much any player presenting a true infinite loop will ever declare.
Yeah, go figure the number of triggers each sequential spell sees as it resolves. Damn, it goes wild, even with just five entering the stack.
Me walking to the commander table with a deck and calculator in hand
Friends: Why do you need a calculator?
Me: Oh... You'll see.
One of the best MTG videos I've watched in quite a while. Bravo, love this stuff
Wow, thanks!
[[heavy breathing in smothering tithe+thousand year storm+ wheel]]
Thanks!
I'm so happy, as a math person, that you did this. I never got to do this at a table because I don't have friends
This reminds me of the most damage possible on turn 1 deck. The damage is so high, they use Graham's Numbers to represent the damage.
After running the numbers, I think it’s safe to say- I cast fog
Cool combo you've got there. Thanks for the win, I cast Time Stop when all the creatures resolve and then cast Insurrection on my turn. Good game shake my hand.
Nah, they just cast act of treason instead. Don't need to break the bank.
However Kenobi does have a sac outlet
Your tapped out.
And the universe just collapsed.
I made an EDH kinda similar with a little different set-up. started with the typical doubling season + opalescence. Then I went with mirror gallery + kiki-jiki with a splinter twin on it (tap to copy kiki-jiki for each doubling season, each of which target to copy doubling season) and a freed from the real. On the turn I "go off" I cast Celestial Dawn and have serra's sanctum, which fuels my untaps of kiki-jiki by freed from the real. I then have Garruk's Packleader (which is a may so you don't deck yourself) to fuel Mind Over Matter, to untap my serra's sanctum, so it can produce mana equal to the number of doubling seasons I have each time I go through all the kiki-jiki copying for each mana I produce. Once I'm nearing the end of my drawn hand (and can't draw more), I cast Wort the raidmother, and use a copy spell on Wort (there probably better ways to do this next part, but this deck is pretty old, and this was the best option at the time), I use praetor's council and copy it for every wort, the raidmother I have to refill my hand from all the discarded cards.
Between each resolution of Council, I do the entire set of loops, which as a reminder is:
-discard a card to untap serra's sanctum, tap to add W for each enchantment I control (copies of doubling season included).
-for each W I have, I can untap "Kiki-Jiki" with "Freed from the Real" (thank's to celestial dawn).
-for each time I untap kiki-jiki, I can tap to create copies of kiki-jiki 2^x times where x is the number of doubling seasons.
-for each kiki-jiki copy created, each one taps to copy doubling season (creates 2^x each time, x growing between each kiki-jiki activation).
This deck intentionally cannot go infinite (assuming no outside interference)
I’ve been wanting to do a similar thing with Anikthea. Turning your doublers into enchantment zombies, then populating them somehow
I've built it and it works amazingly. Best populate cards I've found are Song of the Worldsoul, Nesting Dovehawk and Sundering Growth, among others
I truly love this video, thanks for making it Kenobi.
I always thought and still believe that rakdos charm is the better tool for every situation 😂
Love this non-infinite golem nonsense
This is one of the best videos that you have made. I love everything about it so so much. Thank you for making it.
What an absolute masterpiece of a video, the deck doesn't win with damage you win the by sheer amount of existential dread you cause the other players with your unfathomable mass of cookies.
This is the best video you ever made. Congrat’s mate. I will share it with all my magic friends :) keep it up PK!
Wow, thanks!
I have been wanting to make a silly Precursor Golem deck for a while now. I'd love to see the full decklist!
Years ago, Brudiclad was the first commander I fell in love with. I thought it would be pretty cool to have 10 Sharding Sphinxes attack and make 100 thopters, then turn those thopters into more Sharding Sphinxes and attack with all 110 and kill everyone with 12100 thopters on the board. I never would have imagined this when I was driving to Target to buy the War of the Spark Planeswalker deck. Man I love this game
I revisit this video every now and again and it never disappoints
These are the sort of things that bring me joy, making things that aren’t supposed to happen happen. Nice one Vince, thank you.
Once plotted out a similar thing with Rhys the Redeemed+Mondrak+Dollhouse of Horrors+Mirror Box
The idea is that you reanimate Mondrak with Dollhouse, turning him into a construct with P/T equal to the number of constructs you control. Then you double once, for three. Then you double again, for 27. And then you double again, for a number with several billion zeroes. Presumably you could double again and again, for similarly abstractly large numbers of dolls, but by iteration three you're already doing enough damage that in the metacontext of the game(in which you are a planeswalker dueling another planeswalker) you're shattering open gateways to the blind eternities.
I love how big this number is without being infinite
3:29 wasn't expecting PleasantKenobi to get double caked up on a random Thursday.
man your videos are so fun no matter what weird stuff u doing
I am so hype for this video. My first "modern" deck had some splicers, this BEAUTIFUL Golem and Cackling Counterpart.
Yes it was terrible, but I made lots of golems a few times, and it eventually evolved into a more "midrange flicker" Modern deck, and sparked my joy for modern :D
Now, LETS GET STUPID!
Vince channeling his inner Rhystic Studies in this one.
side note: I love weird and unique cards and Precursor Golem has been one of my favorite cards since SoM released. I've built multiple iterations of Riku decks that abuse it, though to a more practical extent than this. I was part of a commander group back in 2014-15 and we would do monthly deckbuilding challenges and the winner got a custom playmat with a card from their deck on it. I won the event with the first iteration of the riku deck and my playmat has a big-ol low-res Precursor Golem on it. Happy to see it get the attention it deserves.
No love for ink-treader nephilim, mirrorwing dragon, or zada?
@@louismaciver8262 Nah. Zada and Co require you to play other creatures to make use of them. Precursor is an army in a can that can grow exponentially and lead to some wild stacks.
"How much damage?"
"Enough to make you all lose every game of Magic you're ever going to play."
At this point, even if I had an actual infinite amount of creatures I feel like there would be more golems because with an infinite combo you have to name the number of loops. I just couldn't name a number large enough.
This is the funniest video you've made so far and the funniest video I've seen lately. Thank you, Mr Pleasant.
Glad you enjoyed it, and thanks for the kind comment.
I run the golem in my feather deck along with clones and it's already insanity there. This is just next level.
As a mathematician, this is perhaps the second coolest piece of math I've seen in MtG (behind the guys who made a Vintage legal Turing machine). I just want to point out that every time you try to describe how large the numbers are, your words are woefully inadequate. The first rite of replication puts into play 5 doublers, which because of all the doublers already on the battlefield means 320 doublers. At this stage, the very next doubling season will make the number of doublers larger than the number of atoms in the observable universe. It is only barely smaller than a googol in this context.
The number of doublers have gone from 6 -> 326 -> Atoms in the known universe, with only 2 rites of replication. We have three more to go. "Make each atom in the universe its own copy of the universe and count the resulting number of atoms" isn't nearly going to cut it. "Make each atom a copy of the universe, and then repeat this recursively a number of times corresponding to the number of atoms in the universe, then count the number of resulting atoms" is about the correct ballpark. After the third rite of replication. And we still have two more rites of replication to go.
I hope I have properly conveyed just how much you're thinking way too small with these numbers.
Man I have to get my opponents to check my math when I've only got like 50 tokens entering at a time, I couldn't fathom this
.... man i just realized that march of the machines shuts down a lot of fast mana in cedh and treasure tokens. It sounds goofy if you play casual, but in cedh thats like almost good enough to be considered a legitimate tax peice
Yeah, I agree.
@@PleasantKenobi imagine it, a world where your sitting there, thoracle combo in hand, and you just cant get to it because the jackass across the table played mom.
Ngl, kinda expected you to end the video with "we can make all these golems... And the next player will cast a board wipe and it won't matter" 😂😂
They can't resolve a boardwipe if modo broke.
I've been quietly lurking this channel for years and this video is precisely why I love PK and his content. Also, why WotC should learn math is not just for blockers.
Holy shit - when that second rite was about to resolve, it finally hit me
Totally loved the madness of this! Awesome PK 😊
the fact that you could put all the doublers on the battle field and break it even more
I had literally built a 7 mana Atraxa Golem deck before Wilds of Eldraine came out. And now this exists. Amazing 😂
3 48 the piece mentioned is phyrexian altar not arena ofc
This made me happy and terrified at the same time, thanks for blowing our mind kinobi
One, this is the first non-infinite combo I've ever seen that beats my personal record for tokens (though mine was also more tokens than atoms in the known universe).
Second, yes, if each atom had its own universe, you'd still easily exceed the number of atoms in each of those universes. That statement was absolutely correct (by a lot).
Thirdly, I was teaching my students about the number googol, and as I'm trying to get their heads around how big it is, and one students said, "Why do we even bother with numbers this big if there aren't even that many things?" My response, "Well...this one time I was playing Magic: The Gathering..."
Thank you for giving me a purpose and reason to build another EDH deck for the first time in years!
TLDR;
The board state after everything resolved can be described this way:
D_64 doublers
P_64 precursors
G_64 +5x2^(D_64) 3/3 golems
with:
D_n=A_(sum[i=0;n-1;D_i])
with D_0=6
and A_n=fⁿ(6) and f(k)=5x2^k+k
P_n=R(P_(n-1), D_n)+P_(n-1)
with P_0=64
and R(T, N)=Tx5x2^N
G_n=(P_n-P_(n-1))x2x2^(D_n)+R(G_(n-1), D_n)+G_n
with G_0=8319
Warning! I wrote all this as I did the maths, so it might be hard to follow (I even made a mistake at one point that I caught after)
ok! so, let's do the maths!
first, let's remember what's on the board as the rite of replication is cast:
8390 golems separated as follow:
6 doublers
8320 basic golems
64 precursor
so the stack is:
The original rite targeting a random basic golem + 64 precursor triggers
and it becomes:
Original rite (OR)+63 precursor trigger (PT)+(8383+6) copy of rite
->
OR+63PT+8383+5, we create 5x2^6 (320) doublers so we have 326 doublers
OR+63PT+8383+4, we create 5x2^326 (683515851494691226366406945974256676672865447154128886383053314503110312249804976007347867819704320) doublers so we have 683515851494691226366406945974256676672865447154128886383053314503110312249804976007347867819704646 doublers
OR+63PT+8383+3, we create 5x2^(5x2^326+326) doublers (this number has more digits than the number of atom in the observable universe, so we'll keep it as is), so we have 5x2^(5x2^326+326)+5x2^326+326 doublers
OR+63PT+8383+2, we create 5x2^(5x2^(5x2^326+326)+5x2^326+326) doublers, that's becoming a bit unwieldy, so let's create a function to help us, f(n)=5x2^n+n is the amount of doublers we have after a rite resolve if we had n doublers before. so 326=f(6), 6835...04646=f(326)=f(f(6))=f²(6), we currently have f⁴(6) doublers, we'll call fⁿ(6) A_n so we have A_4 doublers after 4 rites resolved
we can directly skip after the rites targeting doublers resolved:
OR+63PT+8383, we have A_6 doublers and A_6>10^10^10^10^10^98
so we now create 8383x5x2^(A_6) golems
OR+63PT, we just finished resolving ONE TRIGGER!
so, how many copy of rite does the next trigger create ?
we have A_6 doublers and 8383x5x2^(A_6)+8383 golems (other than the one we targeted with OR)
so...
OR+62PT+(8383x(5x2^(A_6)+1)) rites targeting golems+A_6 trigger targeting doublers
we can easily reduce the stack to:
OR+62PT+(8383x(5x2^(A_6)+1)) rites targeting golems
and we have A_(A_6+6) doublers.
I just realised that because i'm keeping the calculations fully written It's going to be a bit hard to not mess up the amount of token created, so let's create a new function: R(T, N)=Tx5x2^(N) being the number of tokens we create after T copies of rites targeting (non-doubler token) resolve while we have N doublers on the board.
so the stack can be describe this way:
OR+62PT+ (R(8383, A_6)+8383) rites targeting golems.
OH!!! F***!!!!!!!! I just realised i didn't take into account the tokens created by precursor golems as we create copy of them...
SO! let's solve this issue...
we had 64 precursors, each were targeted with a rite after the A_6 doublers were created.
so we created R(64, A_6) precursor golems each creating 2x2^(A_6) golems
so the board is:
A_(A_6+6) doublers
R(64, A_6)+64 precursor golems
R(64, A_6)x2x2^(A_6)+ R(8319, A_6)+8320 basic golems (one of them is targeted by the OR so it doesn't get copied)
and the stack should look like:
OR+62PT+(R(64,A_6)+64) Rites on Precursor+(R(64, A_6)x2x2^(A^6)+R(8319, A_6)+8319) Rites on basic golems.
->
we won't be able to just continue by hand like that, so let's continue to abstract those numbers:
we'll index our numbers by the number of Precursor Golem triggers that have fully resolved (they resolved and the copy they created resolved)
so D_n is the number of doublers after n Precursor triggers fully resolved. we know that D_0=6, D_1=A_6, and D_2=A_(A_6+6). I'm conjecturing that D_n=A_(D_(n-1)+D_(n-2))
P_n is the number of Precursor at the n-th step, so P_0=64, P_1=R(64, A_6)+64=R(P_0, D_1)+P_0. I'm conjecturing that P_n=R(P_(n-1), D_n)+P_(n-1)
G_n is the number of *other* golems at the n-th step (we won't count the one being targeted by OR). we currently know that G_0=8319, G_1=R(64, A_6)x2x2^(A_6)+R(8319, A_6)+8319=(P_1-P_0)x2x2^(D_1)+R(G_0, D_1)+G_0. This one, i'm a bit less certain but let's conjecture that G_n=(P_n-P_(n-1))x2x2^(D_n)+R(G_(n-1), D_n)+G_(n-1).
Now, let's check if these conjectures make sense:
D_n: we know that to get from D_n to D_(n+1), we have to resolve all the triggers targeting a doubler, and the number of trigger targeting a doubler is exactly the number of doubler on the board, so D_(n+1) is D_n triggers after D_n, so if D_n is A_xxx, D_(n+1) is A_(xxx+D_n) so: with the conjecture, we get A_(D_(n-1)+D_(n-2)+D_n)=D_(n+1) there's no simplification so the conjecture was wrong, but we can see that the real answer is D_n=A_(sum[i=0; n-1; D_i]).
now let's check P_n: P_n to P_(n+1), is fairly straight forward as the copies aren't influencing each other, so the number of new precursor is just the amount created by all the rites targeting each precursor already there, so we create R(P_n, D_(n+1)) precursor (D_(n+1) because we resolve the rites targeting the doublers first), and so the amount of precursors at the end is just R(P_n, D_(n+1))+P_n. the conjecture is confirmed.
now for the hard part; G_n:
G_n has 2 things (other than doublers) influencing it directly: the rites copying them and the precursors creating them. So the number created by the precursors is clearly (the number of precursors created at this step)x2x2^(number of doublers) which is just (number of precursors there-number of precursors already there the step before)x2x2^(D_n) so (P_n-P_(n-1))x2x2^(D_n). so the first part of the conjecture seems correct. now for the second part, it's like for the precursors so we get R(G_(n-1), D_n)+G_(n-1) and by summing the two parts we get the formula previously conjectured.
so we can now describe how the board looks like at the end of all those triggers:
D_64 doublers
P_64 precursors
G_64 basic golem tokens
AND the original rites can now resolve!!!
so we add 5x2^(D_64) basic golems to the board.
I won't try to find an explicit formula for those numbers because arithmetic and recursive functions aren't my forte.
4:48 this took me a second to understand so for those like me here’s how I understand it:
y = number of tokens made
x = number of “doubling” cards
Whenever tokens are created, create y * (2^x) tokens instead.
(Side note, I know I don’t need to put 2^x in brackets I just did it for clarity’s sake)
is there a decklist available for this, this sounds like a lot of fun to bring to a commander night
I woke up and couldn't get back to sleep immediately. I started to doomscroll and saw this video, and now I'm not sure I will ever sleep again.
This massively underrepresents just how crazy the number is. I would venture to say it is larger than the number of even possible, hypothetically imaginable (fininte) universes.
I wonder how big it is relative to Graham's number.
Suddenly, Rakdos Charm with a steel chair!
Its hard to tap mana when you are being sucked into a singularity.
Welcome to the joys of exponential functions, Vince! The bigger that the exponent gets, the more absurd the actual number is!
This just makes me happy (:
You make it fun to be a nerd ( well its always fun but you spread the Word )
Absolutely beautiful video
I saw Rite of Replication coming, but not the philosophical side.
imagine saying to the pod "i know you have cyc rift, but lemme cook" and you whip out 683 Trivigintillion tokens
You could use mystic reflection on the golem etb pointing to doubling seasons to do even more tokens
Woah, yeah. And each Gingerbread Precursor resolves separately, so if you time it right you don't even need rite of replication
Strange but I was recently contemplating a similar thing when i cast a croaking counterpart on a precursor golem with a vesuvan duplimancy in play, and then flashback it!
"A Bernard's Worth" is now an official number level for me. Up with a Marioplex, a Minecraftplex, and a "Holy f*ck ton"
“Concordant Crossroads? No? K, untap Wrath of God?” 😂 love the video
Altar of the Brood. ☺️
I play Precursor Replication in my Mind's Desire Talrand deck...cast the entire library over and over...It feels good.
I did the same thing with Anikthea. It’s a little slow, but it’s so silly that I feel like I’ve won as long as I assemble the pieces.
Pro tip: watch out for Insurrection-that does give them haste.
Even in this exercise in futility, we still found Solitude, Fury, Grief, Subtlety, and the other one
Finish resolving golems. Pass turn. Opponent casts Reins of Power
Run, run, beyond a numerically comprehensible, practically infinite span. You can’t catch me, I’m the gingerbread man.
I think this combo probably makes more golems than most infinite combos, because technically with an infinite combo you have to pick a number and nobody would pick one this big
My Solarion calculator deck walked so that this deck could run!
2005 deck tech- I would make a Solarion double its P/T until it was in scientific notation, then atta ch an armadillo cloak.
Deck wasn't resilient, but it was fun.
And this is where your opponent targets precursor with swords to plowshares. Sure you gain an enormous amount of life but it puts a stop to this shenanigans.
I dont think "enormous" begins to cover it.
I'm imagining the Teysa player with a Blood Artist in play and a Wrath of God in hand.
"Rakdos Charm."
"Oh you motherF" *Universe explode-implode-explodes*
Is there a deck list for this wonderful overbred creation?
When the computer server you're playing on decides to scoop, you KNOW it's broke.
At that point youd be getting into a number of golem tokens territory. Which is nuts
This is a deck where, for the sake of your own workflow, you show up with a set of tables with precalculated results for every series of actions you can take with every possible combination of cards that gets beyond easy enough to work with. And a method of attempting to have a reasonable way to have usable counters. And then you get told to play something else because either your deck is too intimidating or nobody else wants to bother with the hassle/time involved.