Win a SMALL fortune with counting cards-the math of blackjack & Co.
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Curious about how it is possible to make money in a casino, for example, by counting cards in Blackjack? Then this new Mathologer video about the mathematics of casino games like roulette, blackjack, etc. is for you.
The video is based on talks by my friend and colleague Marty Ross who who knows a lot about beating the casinos at their own game. I do a bit of an interview with Marty at the end in this video but just in case you are interested in seeing him in some real Marty action, here is a link to a video of him giving a talk about sports gambling at the Melbourne Museum in 2012:
• The Joy of Sports gamb...
Also check out his bad mathematics blog
mathematicalcrap.com
and his writeup of the solution our free coupon puzzle in Math Horizons
www.qedcat.com/articles/coupon...
Anyway, thanks a lot to Marty for all his help with this video and to Danil (Dimitriev) for his continuing work on providing Russian subtitles for all Mathologer videos and Michael (Franklin) for his help with recording this video.
For those among you interested in more information about the mathematics of casino games here are some more references:
a) wizardofodds.com/
Great free site with reliable details on all forms of gambling, discussion of principles etc.
wizardofodds.com/games/blackj...
wizardofodds.com/gambling/bet...
b) Theory of gambling and statistical logic by Richard Epstein
books.google.com.au/books/abo...
c) Professional blackjack
All round best practical manual
www.bookdepository.com/Profes...
d) Beat the Dealer by Edward Thorp
The original book.
www.edwardothorp.com/books/bea...
d) The Theory of Blackjack by Peter Griffin
Does a lot of the theory underlying and evaluating blackjack systems, linear regression and so forth.
www.bookdepository.com/Theory...
e) Here’s a counting practice app:
itunes.apple.com/us/app/21-pr...
Enjoy!
P.S.: My t-shirt today features a famous mathematical limerick: Integral zee squared dzee//from 1 to the cube root of 3//times the cosine//of three pi over 9//equals log of the cube root of e.
![ไม่ต้องมีที่ที่ให้ฉันอยู่ แต่ขอแค่มีฉันอยู่ก็พอ (Spaceless) - getsunova [SHORT FILM]](http://i.ytimg.com/vi/MuT0d_cvJkc/mqdefault.jpg)
Back from an extended holiday. Still working on the ultimate Zeta function video, but to get things rolling again here is a video on the math of casino games. The video is based on talks by my friend and colleague Marty Ross who who knows a lot about beating the casinos at their own game. I do a bit of an interview with Marty at the end in this video but just in case you are interested in seeing him in some real Marty action check out the links in the description :)
Mathologer your shirt is so poetic :)
This is my favorite video of yours yet, keep it up!
ultimate zeta function video? man i love your videos you explain math better than many other youtubers
I am looking forward to the ultimate Zeta function video!
So, what's the price of the $10 coupon ?
How to leave a Casino with one million dollar:
Enter with two ;)
Or enter with a thousand, but be the house.
2 dollars /= 1 million
π : He meant enter with 2 [million].
Get it now?
owe one!
That's a 500 thousand to one profit ratio, that's pretty good.
If you lose $1, $2, $3, ..., then you gain $1/12.
Try it and let me know how you go with this gambling scheme :)
we all know and have no dubt that it is true only on infinte tries. btw isn't $1/12 your loss and not your win?
actshually, 1+2+4+... = -1 (assuming you're adding the power of 2)
1+2+3+4+... = -1/12 is the relation you're looking for i think.
both are infinite divergent positive sum, to what we assigned a negative value, so both work for the joke. i was just nitpicking the fact that he said 1+2+4+...= -1/12 which is not the usual value. He then even changed his comment
@Hstar5712 Yea, I noticed and fixed that.
There is one simple way to change any game with a negative expectation to a positive expectation. Just move to the other side of the table i.e. be the one who owns the casino. Unfortunately, I have not succeeded in putting this strategy into practice yet.
David Conrad buy shares in a casino company :)
Or just get a job.
Hi David, do you want me to coach you for free? I've been a successful counter for a few years now. Are you interested? I'll teach you everything you need to know to be successful to get results in the casino. I'm a mathematician myself.
That's not always true either. For instance, the casino has to pay their personnel a salary and keep the lights on and often provide free food. Casinos can lose money if the sucker money in doesn't meet the overhead. There are overhead costs to EVERYTHING. Take the stock market for instance. Maybe you'll do better to be long than be short, maybe you'll do better to be short, but either way, you have to pay the broker commission on the trades.
Someone makes a comment like this on virtually every video or article about advantage gambling. Even when, as in this case, it is clearly explained how to gain an edge as a player. You aren't clever or witty or anything, just unbelievably asinine, shallow and predictable, and lacking in imagination. There are lots of gamblers who have made money from casino gambling long-term, it isn't that uncommon. But doubtless you will continue making your fucking funny joke, and morons will continue to validate your misinformation.
The limerick on your shirt:
Integral z-squared dz
From zero to the cube root of 3
Times the cosine
Of three pi over nine
Is the log of the cube root of e
Nice , but its *from one to the cube root of 3 *
Also, casinos have “maximum bet limits,” on top of us not having “infinity money.”
And I like the phrase “infinity money,” and I’m going to start working it into my conversions.
Yes, everything is calculatable believe it or not...
just don't forget, as good as you may be with math, a real casino has the right to throw you out, and a virtual casino has the right to shut down and disappear with all your money
@TurboCMinusMinus I think he means if you loose a certain amount of money, the casino can choose to leave. Leaving u with no chance to win it back.
A virtual casino www.jackpotwheel.com kicked me out because I had a $40 coupon, I deposited $20 and tried to leave a few days later with $100 leaving a bankroll of $65 to keep playing later... They said I was a hazard to the casino and that they will refund the $20 in 21 days... LOL . I had to ask my bank to back charge the $20 (They took the $20 in a blink of an eye and refund it in 21 days ????).... This is why I just tested them... Bovada.lv is better they honor their losses... I will keep doing the same with all online casinos ($100-$150 from every online casino every few days is not bad. You get lucky usually the first few days (Until the casino robot learns your betting pattern, then it is time to go)... By the way, make sure you don't waste your time with www.jackpotwheel.com
WHY PEOPLE PLAY THESE GAMES???? The golden rule is always: "Casino wins, you shut up". It is not a fair game, it does not proobe you are brave or smart, and there is more fun ways to through to rubbish your (incredible amount of) money.
It is better to pay the university credit to some girl that trying to impress her spending money in a casino.
Yeah they do. Bastards. Card-counting literally isn't cheating.
And even though they have no right thy do have the ability to turn you into fertilizer or at the very least lump you up for your efforts.
Man, have I missed you. Happy for another lesson from you!
yea. He is good one
The zeroth theorem of gambling: "The house always wins"
Gambling is a tax for people who don't know math.
kurtu5 More of a tax on people who know too little math. People who know NO math have no reason to believe they can beat the casino. People who know too little math can really be fooled into believing in "systems" like Martingale.
@@TadRichard But I gamble for the rush. A rush I get by spending money, not to make money. Even if I win I always put it back, because it's about staying alive and the duration of being able to stay at the table, not about walking away with money. I guess this is something only high rollers understand, and it has nothing to do with logic but more with emotions and dopamine.
@@asanka4131 and that's how one goes broke and homeless. Just for the feeling of it. Be careful bro
I know more people that wins lottery than people crashed by a meteorite.
👌👌
Most casinos protect themselves against schemes like the Martingale by having minimum and maximum bets.
Thanks, Nillie. Yes, the maximum bet restriction protects the casino from vindictive billionaires, and the like. It doesn't change the fact that the Martingale has no effect on expectation.
That's probably true, but really unnecessary. The Martingale scheme never becomes positive with any number of bets available - the best case scenario for the gambler is that he has played "negative lottery" with potentially massive losses for very small gains and a negative net expectation.
I highly doubt that. The Martingale is a strategy that can not possibly bankrupt a casino due to negative win expectations and due to the gambler only winning a very small amount per successful gamble.
Minimum bets are probably to ensure the casino isn't wasting it's employee's time on customers that will hardly make them any money (as their income is proportional to the bet), whilst the maximum is most likely there to prevent having to pay out large sums of money to a billionaire that wants to make a huge gamble and gets lucky (though it may also help protect customers from themselves I guess).
Using martingale isn't needed in blackjack. It's about having enough bets to over come variance aka "bad luck" - It's like me saying you're going to win 52% of the time and lose 48%. You're still going to have a losing streak, but you will also have winning streaks. Overall you will tends towards the mean (you winning) due to the central limit theorem. If you want I can coach you for free in Blackjack, I have a private group I've just launched. Let me know if you're interested.
@@amritshinh6376 Wouldn't have to teach me. I win more than lose.
You have returned! Hooray!
Yes, busy 2nd semester here in Melbourne and some extended holidays have kept me away from any TH-cam action. Anyway, good to be back :)
Goal in blackjack is actually beating the dealer. Use basic strategy always! Card counting is recommended. Good video!
Wow! Thank you! Never knew that casino gambling has become a discipline in and of itself. The references are fascinating, too!
I love this video, I watched it more than 30 times already! ^ ^ very educational
@Walter Will Thank you for your concern. I also learn study and do my research from other resources before I take any further risks. ^ ^
Thanks for a great video. And thanks to Marty for being in the video too.
Long time no see! Thanks for the video.
Watch this one th-cam.com/video/zpzaUPGKusw/w-d-xo.html this is one of our team new project. What do you think about this one?
1:50 10-10/x approaches 10, so it should be slightly less than 10 (due to a combination of 1) casino games don't go to infinity and 2) the ratio of payout is usually slightly lower than 1/chance
Outstanding explaination! Thanks for positng it.
Thankyou for this, so well explained
I'm not much good at math and I have zero interest in gambling, but I watched the entire video! How fascinating!! (on another note, I met a girl once at a party who was a maths historian...I never even knew such an arcane field existed!
Arcane? Anyway I was also surprised there was such a thing. Most math majors take a course on the history of math. I always found it amazing how every culture indepenedtly discovered the same mathamatical principles. How it helped them understand the world and universe around them at nearly the same time.
For 2 yrs now I have applied these principles to option trading, along with the 'Kelly Formula", and "Gamblers Ruin Formula" using my trading platforms probability algorithm to provide the required inputs for those formulas - to adapt trading strategies to suit different market conditions. So far its worked very well, beyond my hopes and expectations.
How do you use both Kelly Formula and Gamblers Ruin Formula?
Fantastic video. Thanks for the links!
Mathologer, good to see you!
Good to be back :)
One of my friends used to be a professional gambler. He researched betting sites all over the world to find bets that had opposite values from two different sites and when he found those put half of his kitty on one and the half on the other. He made small income on this but after few years found out that certain sites started to refuse his bets. This complicated things so much that he stopped that and went to do something else.
sometimes they will refuse to pay you and there is little you can one the laws of where they are stationed and two its usually illegal in the US to gamble online.
brb gonna bet my life savings on red.
Throw it on some 00s go for broke.
why not bet on black... law of averages says black has a better chance of coming up next
@@arcanerecovery2567 Hi, first, for an unbiased wheel the probability if red is 18/37 and the probability of black is 18/37. Second, if a wheel had 60 out of 100 red then it is not an unbiased wheel, it has a slight bias to red.
@@victorcroasdale4992 That isn't something one can deduce from the last 100 spins. This is why i didn't understand why he said red (given that we don't have any info as for whether it's bias or not). I'd love to hear if there's something i missed...
Also, he forgot to mention that the main reason for the Martingale's failure is the upper bet limit. I guess that he's not much of a gambler (good for him). The video was great though.
@@matane.5427 If we were tossing a coin, getting 60 reds in the last 100 throws is about 0.14 times as likely as getting 50 out of the last 100 spins. In the case of a roulette wheel the presence of 0 which is neither red nor black would make 60 reds out of 100 spins even less likely. If 60 reds out of 100 spins occurred I would be willing to bet that the wheel is biased toward red, which means I would bet on the next spin being red. I would have a slightly better than 50% chance of winning.
The Martingale depends on two things; 1) there is no wager limit (unlikely) and 2) the gambler has funds at least as great as the casino (only possible when trump has bankrupted the casino).
I finally understand roulette now. Thanks man.
nice explanation, thanks
"Beat the dealer" is a great book. But Black Jack is now 6 decks and the last 20% of the cards are not used. I have done some simulations which shows that the casino now wins (with a very little margin) if you use the system in the book.
Thanks. I didn't truelly understand what man on video mean.
But can somebody explain how it actually work? We don't really change probability of any card coming then use 6 decks (it is same time for all players shuffle in one deck, right?). And i don't see why 20% broke strategy.
Still works today. I'm a mathematician and have been counting for a number of years now. If you want I can coach you. If 20% is cut off you can still gain a positive expectation. Less cut off the better.
@@user-zr3vb1rx2q because each card now has an unequal chance of being drawn. You're right that adding more decks doesn't change the odds of drawing a specific card (it just goes from 1/52 to 6/312), but it does make it harder for the player to card count, as you have to keep track of 312 cards instead of 52. However, purposefully not using the bottom 20% of your 6-deck, introduces information that is utterly opaque to the player, as well as changing the odds of any given card in an unknown and unknowable way (for example all six of the king of clubs may be in that bottom 20% meaning it's draw odds are 0)
+Martin ... Pedersen Yes, Beat the Dealer was a very good and seminal book, it was the first to explore how math could be used to play blackjack and gain an advantage, but it was written back in the 1960s I think, or maybe even the late 1950s. Since then an entire cottage industry has been developed, a veritable science devoted entirely to the study of the mathematics of the game of Blackjack. Millions of dollars were spent on in-depth research done by mathematicians and computer scientists using sophisticated programs to analyze the game in exquisite detail.
The findings led to the creation of the so-called "basic strategy" for blackjack, as well as systems used to "count cards," keep track of the cards which have been played thus giving the player knowledge of those remaining, the relative composition of the "pack," and whether it is advantageous or not. It was found that high cards are good for the player and low cards less so, low cards tend to help the dealer who is compelled to make certain plays based on the house rules i.e. Dealer hits 16 and below and stands on all 17s and above. The player is of course free to make his own decisions and is not compelled to hit or stand, therefore he can stand on12 and win(something which the dealer cannot do) if the dealer busts. It is in this way that lower cards help the dealer, they help him/her make a hand when they are forced to hit. The player can elect to stand on 12 while the dealer is showing a 5 for instance. If the hole card is a 10 that means the dealer has 15 and he MUST hit according to the rules of the game. Again, low cards would help him/her make a hand, but high cards would make him bust thus losing the hand. This is why the Basic Strategy says for the player to stand on hard 12 vs. a dealer, 4, 5 , or 6, the odds of the dealer busting are pretty high, and they become even greater the more low cards are removed from the pack.
What card counting does is keep track of the relative amounts of high cards to low cards remaining to be played, it typically does this by assigning a number value to a card as it is played and thus COMES OUT of the pack. The pack refers to the cards which are and remain to be played, which is not always a deck, hence the designation.
I don't know why I'm writing all this, it's not actually for you but the person asking questions below you, I just thought I'd start my comment by responding to what you said about the book Beat the Dealer. Anyway, I should just say to anyone wanting to better understand card counting to go and watch a video on card counting, the systems developed are very different and more precise than the one presented in "Beat the Dealer," a strategy which even the author himself believed was cumbersome and not particularly practical for typical players, not to mention use in multiple deck games.
@@mydogskips2 I barely know about blackjack and cardcounting, but I thought that the hole point of counting cards is to know if you have more chances to get a blackjack, and when you do have more chances of getting it, you start betting more. And also it increases the chances of the croupier to have it, so safe betting is also a smart thing to do.
The basic strategy is the same if you are cardcounting or not.
I don't understand casinos.
I mean, card counting is basically just paying attention. Why is paying attention against the rules?
"Hey, customer! Looks like you've had a bit too much to think!"
Really though, they can just reshuffle after each hand to make this pointless.
@Viktor Blomstergren sorry but I don't understand that answer. How does making their games cater to people who pay attention and then making paying attention illegal increase their competitiveness?
@@Nerobyrne Valid points always attract shitty replies...
Counting isn't illegal, and businesses have the right to not serve anyone they want
The reason they don't shuffle after every hand is it would take too long. Time spent shuffling cards is time not spent making money, and the vast majority of people who play are not counting cards. (Also, even if you ARE trying to card count, it's hard to do with all the distractions in a casino, and doing it incorrectly is worse than not doing it at all.)
Card counting itself is not illegal and isn't breaking any rules of the game, but casinos are private property, and they have the right to ask anyone to leave for any reason. They will definitely exercise that right if they catch you card counting.
@@Nerobyrne It's not illegal. You can't be arrested for card counting. But as casino's are private establishments, they can ask you to leave for any reason they want. If you refuse, you could then obviously be arrested for trespassing.
As for why they do it, because they'll make more money taking from idiots. Allowing people that can game the odds in their favor to play loses them money. Your question is the only thing that doesn't make sense. Casinos exist to take your money, not give it away. Why WOULDN'T they make card counting against their rules. The other point is to just make card counting impossible. The issue is that reduces the odds for the player, which means they'll be less likely to throw their money into your pocket. The best way for them to make money is then obviously to attract as many idiots as possible and deal with the card counters as they come.
Great video! I really liked it. Was interesting to watch. Are you plnning to make more like this?
Thank you. I have heard of this, now I have some idea of what is involved. I cannot see myself putting down big bets, so maybe I won't be trying it out. Good to know.
I want to cancel the 3*pi/9 so hard, it’s not even funny.
If it makes you feel better, the angle is being expressed in terms of pi/9
Your T-shirt actually says 2/3 * 1/2 = 1/3 . Nice !
I JUST finished teaching my stats students this section in class. I wish i had seen this video before. I would have shown them this.
I was excited about the card counting right up to the end and you popped by bubble . Dammit.
I've heard that this is a really good way to see the back room of a casino with some big dude named Giuseppe.
I used to work as a dealer at a casino. We had a customer that hunted "biased" roulette wheels. He claimed he found a few and one a lot of money by betting the sections the ball was most likely to land in due to the fact the wheel was biased.
As you said roulette wheels are mechanical, so I think it may be possible to find an unbalanced/biased wheel perhaps.
There was a family that did this until they got caught.They would save all the numbers that would come up and enter it into a computer.They made a documentary about them but the casino kicked them out for it.
Also there are dealers that have enough control with the ball to hit sections.
Oh its very possible to find biased wheels, but highly difficult and getting harder each year. Newer wheels are built with this in mind and have systems in place to alert casinos when the wheel is off even by a little bit. But its fascinating that you can still find biased wheels even today.
Joseph Jagger a distant ancestor of the Rolling Stone's lead was the 'Man who broke the bank in Monte Carlo' from the song in Lawrence of Arabia. He was a textile engineer from Bradford whose engineering knowledge allowed him to work the biased odds on certain roulette machines and make a fortune.
That shirt is the best representation of 1/3=1/3 I've seen in my entire life. The choice of z and a cosine certainly made me think it had something to do with delays and discrete filter design, but I should've known better 😂
I would love to see some analysis of this roulette wheel questions. The simple answer would be that probability of black coming up is still the same as red as it should be independent events. However we cannot dismiss the non zero probability that the wheel is biased, which indicated that probability of red is higher than probability of black (even if only by a very small amount). Thus red would be the better bet. What if we add the possibility of being allowed to not place a bet? Is the expectation of betting on red positive here? Maybe the a better question, what is the probability that betting on red has a positive expectation? Some statistical analysis would be required to answer that question.
I got hung up on this too. I'm completely new to this probability mathematics aspect of things, but let's just say, hypothetically speaking, you flip a coin 10 times. 6 times it comes up heads. Just because historically there's a 60% chance of heads coming up, that doesn't mean there's a greater chance of heads coming up on the next flip. each flip has its own 50/50 chance, right? I'm under the impression that each iteration is independent of past iterations and if you flip a coin enough times, it will eventually average out to 50/50 (assuming there's no weighted bias, or roulette bias in this case). Is there something that I'm missing?
@@danaguinaga183 4 months late, but your initial thoughts are correct in thinking that if each flip is independent of the previous flips, you would have a 50/50 chance of it being either heads or tails, but if you flipped a coin 1000 times and got 60% heads and 40% tails, you can reach a reasonable conclusion (without going into the math) that the coin is biased. Therefore you would bet on heads. Same idea with the wheel (with enough spins of the wheel going one way you can conclude with a certain probability that the wheel is biased).
Nice video! (Wopping actually). Could you make a video about poker?
That would be great indeed!
Oh Mathologer, how I have missed thee!
Great video. I love tracking dealers on roulette.. Some dealers have a signature which swings the odds into the players favour
Really ? Then you must be making a living playing roulette .
"I'm not going to tell you the answer, but you're WRONG." Thanks...
What’s wrong？
that's why I play poker, because it's against real people and the house makes its profit from the winner and not the loser
Phi6er true but aren't the odds better if you know what you're doing?
Being good at poker isn't about mathematical perfection; it's about the ability to deceive the other players. Along with some grounding in the odds, of course.
If you have those abilities, you *can* win at poker, even with the house 'skimming' its cut.
".. poker players grossly over estimate how much they can affect other players' actions."
Fact is, there are champions in the game, who can consistently beat the great majority of opponents. They are quite few in number, it's true. But one of their advantages is exactly the over-self-estimation tendency you point to, in a great number of their opponents.
I agree - poker is MUCH more luck than people think. But you can win. The best way is to find ONE guy at the table who plays horribly, and play against him much more. If it comes down to just you two in the pot, and you know what kinds of cards he plays and where he values those cards at, you can beat him most of the time. I took about 3 rebuys off a guy today in just under 20 minutes because I saw he was valueing a pair of aces as all in with his entire stack. So if I could beat that, I would either call his bets or bet him all in by the end.
Phi...
There is no such thing as a "perfect poker player"; otherwise he would win every time.
Brilliant vid, was always wondering how to count cards. Must show this to my maths students. Btw do you voice over for Klaus on American Dad? Uncanny resemblence.
I love you. Finally got that nerve racking question answered!! Than you so so much! Love your work, illustrations and audience considerations
The advice to bet on red is based on the idea that if the wheel is truly random, it would be extremely rare for red to come up that many times (it's a binomial distribution and I believe someone already calculated below that we should see 60 or more red in 100 spins only 1.4% of the time; I hope they remembered that the expected frequency of red on a fair wheel is 18/37, not 0.5). Therefore, the conditional probability of the wheel being biased for red is high, and you should bet on red.
In reality this is probably wrong, and to some degree based on a very subtle fallacy. Modern roulette wheels are precision manufactured and carefully maintained. The relevant conditional probability consideration is, if it's a well maintained roulette wheel in a modern casino, any seeming relevant deviation from random is short term variance, and the actual expectation of betting on red or black is about - 3%, as explained.
The subtle fallacy is treating the observation of 100 accidentally observed past spins as if they were a prospective study. If you want to know if the wheel is biased, formulate that hypothesis and observe the next thousand or so spins (or however many you need to get to your acceptable p value). Simply accidentally seeing red "come up too often" and concluding bias is not quite valid. There is no justification for not performing the simple prospective study to more rigorously rule out random variation. Given our knowledge that roulette wheels are carefully designed, though, it probably makes more sense just to admit that it was probably coincidence, rather than waste our time.
A far worse fallacy would be thinking that black is "due", the so called gambler's fallacy, which is actually an application of the law of large numbers, to excessively small numbers. However, although this would be logically worse, the expectation would still be -3%, just like thinking red is favored.
I thought the same. There was a guy who had people in casinos studying the roulette tables and after many spins he found bias in some tables more than others and made a lot of money. Sorry but I don't remember his name. And today they are very well maintained.
But the question asked what should we put our money on, and using the information available would suggest that we are at worst getting standard odds backing red, with some possibility of it being an unfair table. The question compels us to make the bet, and maximise our potential return. Arguing that you would be better off not gambling is moot.
It's nice to see that there are a few intelligent people in here that are not sheep and are able to think for themselves instead of going along with the general consensus.
There was actually a group (in Las Vegae) years back that studied roulette tables and realized that they were not random. Based on speed and where the ball was released, they could predict-with some variance-where the ball would land. They made some big money before caught. They used some devices to help with calcs which is a no-no. en.wikipedia.org/wiki/Eudaemons
The wheel is not biased. It was tested at the factory and the frequencies of every played are analyzed to reveal exactly such a problem. That is, the probability of the wheel being biased is always far less than the possibility of 60 natural reds out of 100. The chance that the wheel *became* biased, in the 100 spins you played, given the age of the table and apx. 1000 spins a day, is super small.
"When not dropping rocks, Galileo also dabbled in these ideas..." Hilarious!
A huge change is blackjack 3 to 2 vs the 6 to 5 on a blackjack and multi decks. It used to shore up losses. I also saw a gambling tip on craps where you just continually bat in this pattern and you don't make a lot of money but you can slowly win money over time. I live in Las Vegas I don't really gamble a lot but I have seen some of the stuff.
I can bet you the gambling tip doesn't work. In fact, I'll bet that there is a 100% chance that you will eventually run out of money, even with the betting pattern.
You must love the shirt!
The best option is to sell it to another punter for real money, preferably over $5. The best gambling odds are achieved by not gambling at all.
David Knight or playing poker
to stupid for a Name interestingly a short google search suggests the house Edge is around 5% so no, blackjack is the slowest way to lose your cash. Of course this assumes the player’s skill doesn’t appreciably affect the odds so a good player may argue differently perhaps.
David Knight it’s worth close to $10. If you bet it on red, say then you stand to walk away with $10 x 18/37 of the time. $4.86 on average.
But you bet it on a single number, then you stand to walk away with a useful $350 x 1/37 of the time. $9.46 on average.
Sean Kelleher, the proper response is to just say "Okay, I'll buy it from you for $5", and then make $4.46 yourself.
The best way to gambling is go against noob and when other experienced player join the table just walk away with your win, don't give a shit about your ego, respect or anything money is money.
As easy as I said it as hard as implement it, your "feeling" often beat your "logic"
I can't help but feel like casinos shouldn't even host blackjack games.
So you're telling me that I can bet as much or as little as I want, based on the information you've given me through playing the game UNLESS I use that information to give myself an advantage?
Card counting is fair play. If casinos don't like it, then they should just accept the fact that black jack is a game that favors the player, rather than the dealer, and not host it.
Hi Dan. Many would agree with you. The casinos, and plenty of government regulators try to paint card counters as cheats. That is ridiculous, of course.
And apparently also people who can do math.
They're screwing them by not allowing them to play.
the thing is, gambling in a casino is a privilege, not a right. Sure, morally and legally, there is nothing wrong with using your memory and mathematical skills to give yourself an advantage. However, a casino is also a business and like any other business, they are interested in making money. So, if you cost them too much money ba playing too well, they will simply decide that they don't want to offer you their services any longer.
Well, it's a charmingly American approach that businesses can do what they damn well please.
If you have an idea on how to organise casinos in a way that they have to let everyone play, without sucking the fun out for everyone else by adding a million rules, speak up.
10:36 You can also get the 4/5 by comparing the 4/9 chance of doubling with the 1/9 chance of bankrupting, since the chance of getting even doesn’t affect you.
Back in the early early days of Amazon (when they only sold books) I looked for this book on there so that I could learn how this works. The library didn't have it either. Now I could probably torrent it. :-P Thanks for the simple explanation. I don't plan to use this for gambling but my curiosity is sated. Maybe I'll write a JavaScript tutorial in how to do this.
I'd love to have an exam on probability so I could write in a proof: IF E
Coupon allow you to gamble with 2 possible endings; 10$ or 0$. So depending on the odds, lets say roulette, its little above %50 for 0$ and little below %50 for 10$....
So its worth little under 5$...If you are gambler....If not then its 0.
You are quick (and right) :)
If you're playing a fair game then the expected value is 0, additional bets will not make you any more money.
Thanks! Wondering the 2. question's answer, why red?
Is it because
1-The table is fair (1/37 18/37 18/37) > It doesnt matter Red or Black
2-The table have flaw so red come up more frequently, so its wise to choose Red
So considering both, choosing red is more logical?
Yeah, I think that might be the point he's going for. The two options you outlined could be broadly described as "frequentist" and "Bayesian". Which approach you find more plausible will shape your answer to the question.
Ahmet's calculation is a bit off. If the game is 50/50 to win or lose and the winnings are equal to your bet on a win then if you bet $10 you end the game with $20, not $10. So if you place your $10 coupon on a single 50/50 bet then your expected total money in your pocket after the bet is 0.5 * $20 + 0.5 * $0 = $10. Thus if the game is slightly less than 50/50 probability to win the coupon is similarly worth slightly less than $10. In actual roulette, as mentioned in the video, you lose about $0.03 per $1.00 bet so betting $10 total leaves you with an average of $9.97 afterward, meaning a $10 coupon to bet on roulette is worth $9.97 on average in real money after you use the coupon.
So the coupon isn't worth a little less than $5, it's instead worth a little less than $10.
The corollary of the second theorem is that as the safest way to win when E>0 is with many small bets, then from the other players perspective the greatest danger is with many small bets.
So if you are playing for the win, rather than the fun of the game, the best strategy is to blow all your riskable funds in one bet that potentially delivers the amount you are aiming for.
Example:
You have $10 but the bus fare home is $20 and there is no option to ride part way for the $10 you have.
You are willing to risk going broke in return for the chance of a ride home.
On a roulette wheel your best strategy is to put it all on a single bet that would double your money (black, red, odd, even, high, low are all equally good).
This is also an example of when it is sane to gamble even though the monetary E
I recently got to thinking about this whole thing about making money via Blackjack after winnign about $100 while not even knowing how to play (the dealer and friends helped me decide the best moves to make). I've since then researched it heavily in the past few days, and my conclusion is that the game is a waste of time, as are most other casino gambles. Better to get a real hustle going where nobody's going to have a problem with you making money, in my opinion. Still, I enjoyed this video. Thanks!
Minor quibble: at 42 s, you says the wheel "is numbered from 0 to 37". You meant 0 to 36. There are 37 total slots..
Nice catch
Richard Otter i just came to the coments to see if someone has pointed this or not
Dont most casinos have a 0 spot AND and 00 spot on the wheel? so, 38 slots?
+Scorch428 Yes, I believe so, in America. But I think in Europe many roulette wheels do only have a single 0. I'm not sure about Asia.
And the house advantage for a wheel with both 0 and 00 is actually 2/38, there are 38 spaces, 18 black, 18 red, and two green, 0 and 00. So if you bet black or red you have a 18/38 chance to win and a 20/38 chance to lose. Therefore your chance of winning is 18/38 - 20/28 which is -2/38, or -5.26%.
@@mydogskips2
Uhm, that terminology ain't right, because the chance of winning isn't less than nothing. You'd mean the expected earnings, I gather.
How to get thrown out of a casino 101.
The ultimate house edge for casinos has nothing to do with math, it’s psychology. All games have a negative EV with some expected positive fluctuations. When a gambler is ahead but $300, he ‘feels’ great and is willing to risk more and increase his bets because...”it’s the houses money”. That accelerates his looses and guarantees his ruin.
Thought experiment: if you had a contractual agreement with a casino they would accept your bets for a 24 hour period, no limits. And if you had free use of $10 million dollars. You have zero risk: at the end of the day if you lose the whole 10 mil, no problem, no payback. But you get to keep any profit above 10 mil.
Perfect setup right? Gambling with someone else’s money lol.
You then could enter into a low risk martingale game with an initial bet of $1,000. If you lose, the progression is 2k, 4K, 8k etc and you’d have to experience a lot of losses in a row before you lost the whole 10m.
So you can reasonably expect to play for a little while and bank $1k profit per hand/spin. Now, for most of us 1k is real, nice money. We’d be happy to walk out of any casino with 10k profit.
You know mathematically that you cannot play forever - at some point there will be 50 losses in a row and the 10m will be long gone. But that probably (haha) won’t happen with the first game you play that day. So it’s safe to play martingale for a little while under these condition (huge bankroll and house agreed rules to not cut you off).
So you are playing and banking $1k profit every 45 seconds or so. In the wink of an eye you have $10k profit, then $35k. You KNOW that it won’t continue forever. You KNOW that you should stop and go home a winner, 35k is serious money - that’s a new truck or a year of college for one of the kids. But it was only a few easy minutes and winning like this is FUN!
When to stop?
Most people push it too far. Most people won’t look down at their chip stack and say ‘damn, that’s $34,690’ and stop right there. They’ll say:
“Cool, I’ll quit a $35k”
“If I make it to $50k I’ll cash out”
“Damn, a win like that will generate a W2G and I need to pay taxes, so that’s really only 22k, I’ll play it up to 75k and pocket 50k after taxes”
“That only took 20 minutes, so in an hour I should be well over $100k”
And THAT is the house edge: That voice in your head is what guarantees a win for the casinos.
Exactly!
About the "unfairness" of not "allowing" card counting: With every game of luck, the casino offers a bet. They bet against the player, and usually win in the long run. If they realize, that against a specific player their odds are worse than usual, they will stop offering bets to him.
The player sure has every right to watch the game to improve their odds, but the casino never abandoned their right to do the same. No one is obligated to offer or accept a bet, when the odds are against him. Not the player, but also not the casino.
What do you guys think about poker? At a table where players play each other, the house makes a profit by taking a cut from each pot, but the odds of winning itself is not stacked in favour of the house (unlike every other casino game). This means if you are more talented than the other players, you can actually expect to come out ahead.
@Fester Blats
No, that's a bad example.
;-)
Possible but watch out for signalling, teams, etc. Think Caesar's scene in Rounders.
Good players always make you thing you are "more talented" than them.
nice video! one thing you, Mathologer, could have mentioned though is, that in the same way betting small is favourable if you have a positive expected value, betting big is favourable when betting with negative a ev. So if you want to win 200$ on roulette, bet it all in one go, and dont try splitting the bets.
Hi Juk3, that's a good point. It's just the same doubling proof in the video, but seen from the point of view from the person with the worse odds.
I've always wanted to see a couple pro card counters check out the blackjack section of the Dead or Alive Extreme games and see how well betting schemes can work against that.
I think that the value of the coupon must be $10 times the odds of you winning. If the probability of winning is always less than 0.5 then the maximum value of the coupon is $5 or less
About blackjack, I remember playing a modified version of it with a handyman in my primary school. These were the mods:
1) An ace equals 11
2) Jack equals 2, queen equals 3 and king equals 4
3) You can win by having 2 aces
4) There were no "starting cards", just after each turn we decided if we want to stop or take another card
5) Normally starting player was the one, who lost previous game
?????
Cool video. What about that yellow card slipped into the deck after shuffling that buries a slice of the deck?
TY again.
..
I agree with puzzle answer-- you should bet red. The 60% history indicates a possible bias (wheel imperfection) favoring red. If there is no real bias, your bet is no worse than any other bet. But if there is a bias favoring red, that improves the odds of a bet on red over any other bet. However, not betting at all and walking away is the best strategy.
Ya biased roulette wheel? Sure!
What does Dh stand for on the black jack chart?
Double your wager if allowed to by casino rules. Otherwise, hit. 'Ds' means double or stand. 'Rh' means surrender (return half your wager) otherwise hit.
@@InvaderMixo In BJ, My opinion is, if the house is offering anything? Decline.
Such as equal money when holding a bj, taking insurance on a bj, vs.an A.
surrender when the dealer has an A up.
Is the house going to offer anything that is to my advantage?...
@@gmoops8986 Basic strategy is verified mathematically to have the best expected value. If you're counting, there are certain indexes where taking equal money and taking insurance has the highest expected value.
Hey mathologer, please tell me that integral mentioned on your shirt. I tried that on Mathematica but the result was something else....Pls explain me that how LHS is equal to 1/3?
You probably typed in something wrong: Integrate[z^2, {z, 1, 3^(1/3)}] Cos[3 Pi/9] gives 1/3 :)
∫ z²dz = ⅓z³ + C; and cos(⅓π) = ½
So you have ⅓(3-1)·½ = ⅔·½ = ⅓
The ten dollar coupon is worth what you can exchange it for. For example, if your odds of winning $10 with the coupon on red are even, then you will win, on average, $5 for each coupon you "use." If you were given 100 such coupons, and used them betting on red, on half the bets you would get nothing, and on the other half you would get $10 x 50 = $500. If 100 coupons can be "exchanged" for $500, then the coupons are worth $5 each.
Most casinos in the US have two zeroes on the roulette wheel (0 and double 0), thereby doubling the house odds. So, roulette is generally less favorable than blackjack (if the house odds are truly 5%).
In Europe they only have 1 zero, but the rule is that when you play on red or black and green comes up you get to keep half your bet, so the odds are actually around -1.5%
In Some casino’s they even let you keep the full bet if you are playing the lowest denomination in chips, because they can’t halve it.
@@Keneo1 This is called the partage rule, but it only happens when you place an even-money outside bet (red & black, or odd & even, or high & low), so the house edge is still 2.7% in most cases.
@@Keneo1 So if the casinos can't split lowest denomination and if that grants an edge for the players, then abuse the heck out of that.
@@legendgames128 well the odds become 50/50, so no edge, and it only works with 1 chip of the lowest denomination so it doesn’t really scale
I abused it by buying the welcome packet that gives you a few drinks and appetizers and the amount in chips you pay for the welcome packet. But these are special chips you can never cash out, you have to loose them at the casino but if you win you get normal chips back, so I played the 50/50 ods until all the special chips were converted into normal ones and enjoyed the free alcoholic cocktails !
@@Keneo1 Ah, so the casino knew what they were doing... sort of.
I'll never HAVE TO WORK AGAIN. I'll run to the bank, get a loan, and head to the casino!
I had a blackjack game on an old telephone (pre-android). I learned the basic rules of blackjack and played by a simple strategy of standing after my hand got past a certain value - basically the dealer rules AFAICT. I would actually consistently do pretty well following this strategy. I wonder how this works out in real life?
I don't think that the telephone game had any more of those advanced blackjack moves.
Wait since red has come up more than the expected probability, then that shows the roulette wheel has some kind of wear/imperfection on it to more often come up red? Is that why you should bet red in this case?
there is a problem, blackjack is played with 6 decks, cut at a casual point so that the cut part remains out of the game. therefore you will play with a random number of cards where it is also possible that all the aces remain out of the game and you will find yourself, for example, without the possibility of blackjack.
even in some casinos the shuffle is continuous every hand played so therefore it is not possible to count in any way, no way.
I know this is old but you're wrong. The avg value of the cards using a balanced count will weight zero. So ~50% of the time a count -1 or lower will be in the pen and the other 50% of the time itll be +1 or greater. In the short term the variance will be irratic but given enough time this will balance itself out. Yes deeper deals are better but long term a counter is betting based on propability, not what's garunteed to be dealt.
I wrote a long thing on what I consider tolerable and not in regards to pen but decided against, just a bit too public.
Edit: i'll add that csms and 6:5 are only low limit tables for the most part. Go look at a green chip table or the high limit room. Most green chip are shoe games and high limit rooms are always shoe.
I've tried Martingale betting in simulations and it's worked everytime. In actual practice, casinos have systems in place. (a) you need to stick to your system at all cost (b) casinos have table limits; lower and upper. A $5 minimum table has an upper limit of $299. If you consider your worst case scenario; $5 lost, $10 lost, $20 lost; $40 lost; $80 lost; $160 lost; you now can't do a $320 bet and you just lost $335 dollars.
Don't forget table max - the casino can put a cap on the number of time you can double. If you ever revist this (or maybe I've missed it), it would be good to hear about betting strategies that account for risk of ruin and how to rationally decide whether to keep playing with your current winning given you can only maximally bet some set amount. Do these strategies relate to investing in the stock market in any way?
Betting amounts to avoid risk of ruin was discussed. Recall the part of the video where betting size was mentioned: the 4/9, 4/9 and, 1/9 was analyzed. To reduce your risk of ruin, never bet more than 0.05% of your bankroll. Keep in mind that the smaller your maximum bet, the smaller your per hourly amount you will earn. The counter point is that the larger your maximum bet, the more you can earn.
The first assumption to make is that we are dealing with a risk neutral individual. So we are referring to the value of the coupon to a risk neutral person (i.e. a rational person who is neither risk averse nor risk seeking). Following this assumption, we can equate the value of the coupon to the expected value of profit from using the coupon.
Therefore value of the coupon = (value of winnings*probability of winning + value of losing*probability of losing).
If we are playing roulette, the value of winnings is $10, the value of losing is $0, the probability of winning is 18/37 or 48.65% and the probability of losing is 19/37 or 51.35%. Therefore the coupon is worth $10*0.4865 + $0*0.5135 = $4.87.
Although each individual game will have an outcome that's either $0 or $10, $4.87 represents the average winnings from playing a $10 coupon over many, many times. This will always be the case that as the number of games played increases, the average winnings per game approaches the $4.87 number. The assumption of risk neutrality is important because the risk neutral person is indifferent to the risk inherent in one individual game, and will value the coupon based on its average expected value.
The risk adverse person will put more weight on the fact that in an individual game the outcome is less certain than the outcome of the average of many games and will therefore value the coupon lower to compensate for that greater uncertainty. The risk seeking person is willing to pay more than the average winnings for the possibility of getting the $10 outcome and will therefore value the coupon higher because he/she demands less compensation for taking the risk.
20:55 mustache on card counter
When you said out of the last 100 spins black came up 60 times, I would say it doesn't matter, since the odds of getting black or red is still a little less than 50/50.
If the wheel is assumed to be fair, then it doesn't matter which colour you chose. However, if it is assumed not to be fair (which can happen in mechanical devices), then red is the best choice.
Duh
Great video - as always :)
for the coupon its 10 * (amount you gain on a bet 1 dollar beat) for the roulte table its 18/37 or 0.486486486 so around $4.86 is the amount but if you can find better bets its worth more.
why not apply this to the futures trading market.
People do, all the time. It's called "Arbitrage".
the first thing i did in this video was pause and solve the integral
That's the right spirit :)
i just couldn't help myself xD
i just wonder what the redundancies are supposed to mean. after all, why have cos(3pi/9) when it's trivially cos(pi/3), and such. was it supposed to have very many 3s in it? if so, why not have 3^2 instead of 9?
It's a math limerick. Quoting Mathologer in other comment: "Integral zee squared dzee//from 1 to the cube root of 3//times the cosine//of three pi over 9//equals log of the cube root of e."
Ryan Roberson And it is trivial because cos(pi/3) = 1/2 and ln(cuberoot(e)) = 1/3
idk about you, but he got the floki giggle thing going on perfectly
Is that Brady who says "cool" in the end?
I work in a casino and I can tell you this nobody knows when to to quit win or lose nobody knows when to quit.
Yup; the time to quit is before you start.
John...
You're talking rubbish; they always quit when they have no money left...
It's such a depressing job I've seen enough of it too... When you first meet them they play 10 or 20, have one more drink and they leave... And then one night theyre like just 10 more just 10 more and next thing you know they're thousands down and the reasonable happy guy you used to know is gone.
I once asked a roulette dealer if he ever saw anyone win consistently. Much to my amazement, he said "yes all the time".....but then went on to say that they give it all back. How true! Also, I remember talking to a guy who had lost his large house courtesy of a roulette addiction. He said casinos would go broke if players left when 50% up.
Doesn't look like it from your videos
I think you've validated an argument I made to a friend the other day!
Lets say all that matters to you is doubling your money in the next few hours. You've got 100 dollars and you need to spend 200 on a train ticket. Maybe you need a ticket out of town before the bomb that no one knows about goes off. So having half the money needed for a ticket is no better to you than having no money at all.
Then if you are playing roulette you are better off doing 1 single bet on red/black! Not lots of little bets because the expected value is negative unlike in the scenario described with the flow chart where lots of little bets forced the outcome more towards the expected outcome.
Thats right. I came to the same conclusion. But here is what happens. Customers of casinos believe that if they bet only one time and lose they wont be entertained. So they split their bets at more and that leads them to reduce their win percentage.
What about green double 00 on roulette table?
Finally i found a channel were studiying math make sense, imagine that i filed math exams like n times , well i study on part time, buts still to fail math n time is really bad luck , but i still trying to pass the exam ;)
I was in college when the film _21_ came out. One of my roommates had some trouble separating fantasy from reality, and he became obsessed with card counting after watching the movie.
He told everyone, several times a day, that we should go to Vegas and make a bunch of money counting cards. He was convinced that we could recreate the fortunes of the characters in the movie, because as the movie kept saying, it's just basic math, and we were a bunch of engineering students who were all quite good at math.
I tried to show him the actual math. Several times in fact. But he was just too enamored with the idea of going to Vegas a poor college kid and coming back a millionaire.
The MIT Team that the movie is based on, did exist and were quite good. I butted heads with them a few times. The one thing the movie didn't harp on was, the bankroll they were using. These "kids" had an investment stake of $89,000 at the beginning.
What the films and books dont seem to convey is that it is a slow grind and you will have very up days and very minus days. Thus you need a large bankroll. It is a game for people with a lot of time on their hands, and a big bankroll
But you will absolutely make money on it if you are allowed to play. If you are the person who goes to table max every time you get appropriate + count, you will be out of there in an hour. You may perhaps stay under the radar by being quite conservative with your increased bets, but eventually they will bar you. I have been barred in as quick as 6 hours, and at one casino i lasted 3 years, having gone there over 300 times. There are websites where they put you picture and name, and all casinos can access that info
All in all, it better be a hobby, because there are easier ways to make money
Be skeptical about books like "Bringing Down the House" , And "Busting Vegas" . They didnt bring down any house, nor bust vegas. Fact is, the whole counting flap has made the casino business money. These books are largely fiction, labeled as nonfiction. The hero in Busting Vegas has even stated that the book is "80% fiction"
Bro it literally is simple maths. Al the complicated math like figuring out your bet spread can be done with computer software.
All you need to be able to do Is elementary school math (+/-1 and basic division)
The hardest part is finding the discipline and dedication to practice enough. They estimate an average guy can learn it in 400hours.,, when I heard that , I went and looked at my play time on cod and realised I was wasting my life,,, it took me 200hours, if you were studying engineering I would suggest you guys could have learnt it in similar time.
At the right game you can come to an expected value of $1000 an hour.
Also I’ve met CCs with way below average IQ, it’s a myth you need to be a scholar or super smart to learn it. It’s just repetition practice that’s required.
@@archimedesmaid3602 exactly the condition that casinos have. With a slight edge of less then 1 percent they make hundreds of millions. Cause they are open 24/7 and make tens of thousands of bets per hour.
I agree its better as a side hobby. Just like anyone who gambles better be doing it as entertainments. In both cases there are better alternatives. Heck with those skills be a dealer and get great tips.
The Blackjack portion of the Blackjack video begins at 12:50.
it's a maths and statistics video not a blackjack video
Hey! Your T-shirt expression is equal to exact 1/3 where ln(e^1/3)=1/3 and int[3^1/3,1](z^2)dz *cos(3Pi/9)=1/3
What if you track each value of each card, and the exact number of cards dealt? I understand that the method would be much more difficult than the one shown, but would it give you a much better outcome?
It would give you a better outcome but when you crank the numbers you find that the difference is not worth the effort :)
Awesome! By the way, it's been 2 years, and I still haven't received my $10. :P