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?