[TLD]

I just came upon the thread at the Prescription wherein the gentleman who goes by the moniker “heatohio” was claiming that he could consistently win at craps by structuring his bets a certain way. He didn’t deny the mathematical flaws in his approach, but insisted that mathematics is only relevant to theory, whereas he’s concerned with winning in the real world and he has the empirical evidence of his own experience to know that his system accomplishes just that.

You issued him a challenge in the thread, but he was uninterested since he spotted immediately that you were just some guy who likes to use big words to trick people into thinking you’re intelligent.

But I am curious about your challenge even if he isn’t. You said: “I'd propose a minimum amount of bets you'd need to make, based on some total maximum bankroll you could spend. I'd be betting you that your returns would be statistically no better than break even.”

But isn’t there an obvious problem here? Why wouldn’t he just do some Martingale type thing to make it almost certain he’d win? Betting strategies like that don’t change the long run negative EV, but surely they affect the likelihood of winning or losing a given session. Instead of having a slightly below 50-50 chance of winning, with the winning and losing sessions being about the same size on average, you can easily structure your bets to have a 70% or 90% or 95% or whatever chance of winning, just with the drawback that when you do have a losing session, it’ll be many times bigger on average than your winning sessions. But if you’re talking about an even money bet that he just has to do better than break even to win, it doesn’t seem like he’d have much trouble collecting.

I assume you would block a strategy like that in the way you specify the details of the “minimum amount of bets” and the “total maximum bankroll,” but how? Could those things be restricted so radically that no strategy would be more likely than not to do better than break even? And if so, wouldn’t that make just about any strategy people like him believe in unavailable for the challenge, and hence result in him crying foul at your arbitrary rules? (“I just said I can win betting my way. I never said I can win with all these silly restrictions on my bets that no casino in the world places on its customers,” etc.)

Or is there something else going on in how you worded the challenge that I’m just missing?

[BuddyBear]

I don't know anything about except that craps is not beatable......anyone who tells you it is beatable is lying or is the person running the craps table. It has a negative mathematical EV. There is no point in going near a craps table.

[tacomax]

Originally Posted by TLD

He didn’t deny the mathematical flaws in his approach, but insisted that mathematics is only relevant to theory, whereas he’s concerned with winning in the real world and he has the empirical evidence of his own experience to know that his system accomplishes just that.

Without even reading the thread, I know he's onto a loser. Unless he can gain some advantage due to something like weighted dice where he gains an advantage (and hence this wouldn't be a random game) then his "theory" is nothing. And if there is a mathematical flaw in his approach, there is a real world flaw in his approach.

Originally Posted by TLD

But isn’t there an obvious problem here? Why wouldn’t he just do some Martingale type thing to make it almost certain he’d win? Betting strategies like that don’t change the long run negative EV, but surely they affect the likelihood of winning or losing a given session.

There is no certainty that Martingale will make you a winner. This has been discussed time and time again here. Raiders thinks it's a 100% winning system in theory but that shows how much he knows. I'm sure that Ganch will provide you with the maths. Assuming he's not working out the finer points of the bet with the person in question, that is.

Originally Posted by TLD

Or is there something else going on in how you worded the challenge that I’m just missing?

Again, I've not seen the challenge. But I'm pretty damn sure that if Ganchrow worded a bet, it would be a sure fire winner.

[TLD]

Originally Posted by tacomax

There is no certainty that Martingale will make you a winner.

Absolutely true. And in the long run it's just as negative EV as any other way of structuring your bets.

But if the challenge is about whether one will do better than break even in one session, and it is at even money, you don't need certainty for it to be a good bet.

So i'm just trying to figure out the "trick." Does "your returns will be statistically no better than break even" mean something other than winning or losing the session? Is it intended to be something other than an even money bet?

If the challenge was "I can prove mathematically that your strategy has a long run negative EV," I know what side I'd want to be on. But this is different. This is "Let's meet at a craps table in Vegas, and I bet you'll break even or lose." Surely a Martingale approach can give you a better than 50% chance of winning a short run session like that.

[DrSlamm]

pretty sure you are misunderstanding the challenge.. its certainly not.. i bet you cant win 1 dollar at craps

[tacomax]

Originally Posted by TLD

Absolutely true. And in the long run it's just as negative EV as any other way of structuring your bets.

But if the challenge is about whether one will do better than break even in one session, and it is at even money, you don't need certainty for it to be a good bet.

It is all about the length of the session - that is the key variable. Here's a good thread about betting "systems".

http://wizardofodds.com/gambling/bettingsystems.html

The key bit of the text is this:

Originally Posted by wizardofodds.com

Usually the Martingale bettor would show a profit represented by the bell curve on the far right, peaking at $51; however, on the far left we see those times when he couldn't cover a bet and walked away with a substantial loss. That happened for 19.65% of the sessions. Many believers in the Martingale mistakenly believe that the many wins will more than cover the few loses.

If the maths isn't with you then over the long term, any craps system is a crap system.

Originally Posted by TLD

So i'm just trying to figure out the "trick." Does "your returns will be statistically no better than break even" mean something other than winning or losing the session? Is it intended to be something other than an even money bet?

If the challenge was "I can prove mathematically that your strategy has a long run negative EV," I know what side I'd want to be on. But this is different. This is "Let's meet at a craps table in Vegas, and I bet you'll break even or lose." Surely a Martingale approach can give you a better than 50% chance of winning a short run session like that.

Playing Martingale, your winning sessions will be generally bigger that a flat bettor. But your few losing sessions will more than make up for that and give you a negative player edge equal to the house edge.

[tacomax]

Originally Posted by DrSlamm

pretty sure you are misunderstanding the challenge.. its certainly not..

I probably am misunderstanding the challenge - I've not seen it. What is it?

[sportsfan]

Originally Posted by BuddyBear

I don't know anything about except that craps is not beatable......anyone who tells you it is beatable is lying or is the person running the craps table. It has a negative mathematical EV. There is no point in going near a craps table.

I disagree here, if you take full odds on the passline you can cut the house edge down to less than a half of a percent. Add a good controlled dice-setter and some patience and you can make money.

[TLD]

Originally Posted by tacomax

Many believers in the Martingale mistakenly believe that the many wins will more than cover the few loses.

I certainly don't.

Originally Posted by tacomax

It is all about the length of the session - that is the key variable.

I'm guessing this is indeed what Ganchrow intends to manipulate to make himself the favorite in this bet, but I'm curious just how long it would have to be to get the likelihood of winning down to 50% or less. In the example you cite from the Wizard of Odds article, 80.35% of the sessions were winners, so clearly it would have to be a lot longer than the length of their sessions (or the range of allowable minimum to maximum bets would have to be significantly more restrictive, or both).

And really, when you think about it in context, that likelihood would have to be far, far below 50% for Ganchrow to like his challenge. 50% or below is enough for him to have a positive EV bet, but we're talking about a situation where he's basically said he'll acknowledge that this guy is capable of supernaturally violating the laws of mathematics if he wins. I don't think he's going to set it up in such a way that there is any realistic chance of his having to make that admission. So he must have something in mind where the true likelihood of the guy doing better than break even will approach zero.

And that--I would think--would require so long a run or such severe restrictions that the fellow could wriggle out of it as being too implausibly artificial a set of conditions compared to how he plays craps in real life.

Originally Posted by tacomax

Playing Martingale, your winning sessions will be generally bigger that a flat bettor.

I assume you meant to say something like "more frequent" rather than "bigger," but if so then you too should be puzzled by Ganchrow's confidence that the guy will break even or worse for the challenge session.

Originally Posted by tacomax

I probably am misunderstanding the challenge - I've not seen it. What is it?

I quoted it in the opening post:

“I'd propose a minimum amount of bets you'd need to make, based on some total maximum bankroll you could spend. I'd be betting you that your returns would be statistically no better than break even.”

[pags11]

being that I live near a lot of casinos, I think the thing that entices people to play crap is the excitement and team mentality of trying to beat the book...seems like the craps tables are busiest on Friday and Saturday nights (like most table games I guesss), but there's always yelling and crap coming from over there...

[raiders72002]

The only way to beat craps is through dice control and there are a couple of people that claim to be able to do it.

I don't know if they can or they can't but there are some with craps tables in their house that try to perfect it.

There was a friend of Fezzik's that claimed to be able to control the dice. Fezzik took him up on a $5k challenge and the guy beat Fezzik.

The bet really doesn't mean much since the house hold on craps is so low that one two hour session doesn't mean much.

What they do is throw the dice very hard against the back wall in such a way that they can make one of the die hit on high numbers or the low numbers depending upon the outcome that they want.

[Ganchrow]

Originally Posted by TLD

But I am curious about your challenge even if he isn’t. You said: “I'd propose a minimum amount of bets you'd need to make, based on some total maximum bankroll you could spend. I'd be betting you that your returns would be statistically no better than break even.”

But isn’t there an obvious problem here? Why wouldn’t he just do some Martingale type thing to make it almost certain he’d win?

Certainly Martingale would be a good choice if his were to strictly come out ahead using an arbitrarily large bankroll over a sufficiently small betting requirement (I talked about most recently in my last post on the Martingale.)

Originally Posted by TLD

Betting strategies like that don’t change the long run negative EV, but surely they affect the likelihood of winning or losing a given session. Instead of having a slightly below 50-50 chance of winning, with the winning and losing sessions being about the same size on average, you can easily structure your bets to have a 70% or 90% or 95% or whatever chance of winning, just with the drawback that when you do have a losing session, it’ll be many times bigger on average than your winning sessions. But if you’re talking about an even money bet that he just has to do better than break even to win, it doesn’t seem like he’d have much trouble collecting.

You're definitely asking a very interesting question (although probably not so interesting to those who missed the original thread -- not that I'd recommend anyone head to the RX, but hey you know where to look). I really do wish I had come across your question earlier in the "night" before I had gotten hung up on some new project.

Anyway, I'll give you the very quick answer that probably won't be all that satisfying, but it was certainly what I had in mind in anticipation of what I assumed the slim possibility that Mr Ohio (wasn't he on some VH1 reality show, btw?) would have accepted.

So here's what I said, "I'd be betting you that your returns [would] be statistically no better than break even.”

Now this isn't to say that he would lose a lot of money, or even any money, what it's saying is that he'd be unable to produce enough evidence that to reject null hypothesis that his strategy has positive expectation. Obviously, we'd need to agree on a certain level of significance and I'd certainly have settled for 2 standard deviations above the mean, meaning that if he actually were expected to break even, then strictly by chance we'd see him pass the test 2.275% of the time.

So does that mean he's fairly be a roughly +4,296 dog to win the bet? No. Not even that.

Remember, he's not expected to breakeven he's expected to actually lose (the house edge). And the more stake he were to risk, the more of it he'd expect to lose. That itself would serve as an additional fail-safe mechanism. As the notional size of the bet were to increase so too would the requirement as to how much he'd need to wager in order to complete the meta-bet. In that manner, while he'd only to perform 2 sigmas better than breakeven, he could very well be battling to attain a 2.5, 2.75, 3, or even higher sigma occurrence. While you're certainly correct that the Martingale is effective at transforming small, frequent losses into large infrequent ones, the limiting factor will still be the bankroll.

So in terms of a generic testing structure, it would look something like this: he would need to wager a certain amount (all else being equal, ideally a collar ... rather than a one-sided limit) at a certain table and when he finished the wagering requirement he'd need to have won a certain amount.

But how to determine the wagering requirement?

Put simply, the more he were allowed to bet the higher his requirement would be. If he were playing at an $X max table with an $X bankroll, he'd have a higher wagering requirement than if he were playing at $0.1X max table with an $X bankroll.

So if he were to give me a bankroll and a table limit, then I'd come back to him with a wagering requirement.

Originally Posted by TLD

I assume you would block a strategy like that in the way you specify the details of the “minimum amount of bets” and the “total maximum bankroll,” but how? Could those things be restricted so radically that no strategy would be more likely than not to do better than break even?

Obviously so. Look at a limiting case: you're playing at a table with $1,000 limits and you need to wager $295 centillion dollars. Good luck. The idea here is that while $295 centillion is clearly ridiculous, what about $14 quadrillion? Or $9 trillion? Or $6 million? At some point we get to a figure where the probability of betting through that amount and coming up 2 sigmas ahead of breakeven is right around a 2.5 - 3 sigma event.)

Originally Posted by TLD

And if so, wouldn’t that make just about any strategy people like him believe in unavailable for the challenge, and hence result in him crying foul at your arbitrary rules? (“I just said I can win betting my way. I never said I can win with all these silly restrictions on my bets that no casino in the world places on its customers,” etc.)

Probably. But that's the nature of the beast. Just ask James Randi. You wouldn't believe some of the excuses people to avoid his challenges.

But the truth is that the rules really are rather open. He could bet any way he wanted and could take as many "good luck" breaks as he needed. I'd make every effort to structure the test to meet whatever requirements he had. The only stipulation would be that he come out ahead to a statistically meaningful extent -- and that benchmark would of course vary as function of the test itself. We're not testing whether he can get lucky after all, we're testing whether he can perform in fashion superior to what we might expect through chance alone.