Win a SMALL fortune with counting cards-the math of blackjack & Co. 

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 ?

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.

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.

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.

Nice , but its *from one to the cube root of 3 *

@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.

Yes, everything is calculatable believe it or not...

They will usually gladly increase the maximums upon request.

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.

yea. He is good one

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.

@@АлёшаИнкогнитов 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.

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.

👌👌

How do you use both Kelly Formula and Gamblers Ruin Formula?

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.

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.

@Walter Will Thank you for your concern. I also learn study and do my research from other resources before I take any further risks. ^ ^

Watch this one ru-vid.com/video/%D0%B2%D0%B8%D0%B4%D0%B5%D0%BE-zpzaUPGKusw.html this is one of our team new project. What do you think about this one?

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).

@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.

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).

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.

That would be great indeed!

Yes, busy 2nd semester here in Melbourne and some extended holidays have kept me away from any RU-vid action. Anyway, good to be back :)

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.

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"

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.

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.

Good to be back :)

If it makes you feel better, the angle is being expressed in terms of pi/9

Really ? Then you must be making a living playing roulette .

?????

@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.

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.

Ya biased roulette wheel? Sure!

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.

What’s wrong？

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.

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.

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.

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.

it's a maths and statistics video not a blackjack video

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.

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

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 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.

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.

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

With 60 red out of 100 spins, your p-value is only .027.

the probability is already small enough to lead you to favor red over black. i wouldn't bet my HOUSE on the hyopthesis that the roulette is biased (2.7% out of all 100-long series of FAIR roullete rounds would end up giving that result naturally and without any bias) - but it's still a pretty good chance that something isn't balanced. The same way, if you see 2 or 3 unrelated people running away from a building, you would do well to get the hell away from it too - because it is much more likely that SOMETHING bad is going on there (fire, terrorist, etc.) than the coincidence that all of them happen to be in a hurry to go somewhere at the same time, and happened to be in the same building shortly before... You don't need to see hundreds of people running from it in different directions before you conclude that it's reasonable to assume that something's wrong.

Just to clarify, I have won enough gambling from 24-30 to never work again :) but I am basically banned from every casino now, or a solid for safety

You are absolutely right and I actually talk about this at the end of the video. Also there are links to some very good books in the description :)

Hi Sma Das, Marty here. You sound as if you are more experienced than me. (Despite what Burkard said, I'm merely a keen amateur.) I agree with all you say.

Sma Das ..... I hear all casinos would make you leave the table if they catch you card counting but then it brings up the question of ... Why is it wrong to use your memory and maths/probability to win a game given that you are doing it in your head ? Can't you fight casinos then since they are asking people not to use their brain ?

John Smith Casinos don't want to lose money, they generally don't ask you directly but use Financial Risk Managers to manage this I would recommend the movie 21 to see a visual representation of the casinos Just note there are multiple really incorrect variables introduced and take them with a grain of salt

People do, all the time. It's called "Arbitrage".

This guy is right.

Gregg... And that's all you can say?

No.

At least on the roulette question. If, without investigation, you infer that the wheel is "rigged" it will be a great fallacy for you to bet on red because even though previous percentages have made it 60%, the probability for each individual spin never changed. You still have a little less than 50% chance. If the wheel is "rigged" , it would either a) be grooming you to bet red and lose, or b) paying out at a pre determined ratio like an electronic roulette wheel. If it were a mechanical error, I doubt we could conceivably take advantage from it very long before the casino corrects it, they are on top of that stuff so to speak. But to deduce that a wheel is hot for red is gambler logic and probably why they make millions on intelligent (and not so intelligent) people each year.

Depends on the method of experimentation for the roulette. If it's the first 100 spins you witness, the odds that this happen by pure luck is only 1%, there is 99% of the chances that the roulette is biased into red. I estimate that you'd have a expected win of 1.5% if you play on that table. If you sit in front of the table all day, counting the spins.. and once during the day it reach 60 red in 100 spin.. then it's just a methodology error.