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But "streaks" are irrelevant. Reversion to the mean doesn't tell you things across trials, it tells you things about individual trials. Try this on: What i

But "streaks" are irrelevant. Reversion to the mean doesn't tell you things across trials, it tells you things about individual trials. Try this on: What is the "mean" red-black on the roulette wheel? There isn't one. The only way you can reasonably expect the past streak to have an impact on the next spin, is if you've concluded the streaks are sufficiently unlikely to cause you to judge the wheel not to be fair. If it's random, then you have no recourse but to post-hoc description. There is -no- predictive weight. ... And editing your comment to refer to groups of throws is disingenuous. It would have been more honest to modify your case in a reply.

gexla 5y ago
Right, I have never heard "mean" being used in the context of casino games. I get what they are trying to say though, at some point the variance should start evening out to reflect the odds of the game. But we should be practical and remember we're in a casino. A red/black bet on roulette is one of the few games where you're going to get that low of variance. With slots, you have to play a ton of games before you can get an idea of what the variance is just from your game play. In poker, the rule of thumb is 10,000 hands before the player can be confident of having an idea of how effective a change of strategy is. Overall, whoever wrote this article is out of their element. Like this bit... > So we think we can use our amazing powers of pattern recognition to determine that black is “due” and use that power to win big. Casinos love this delusion, because they know that math wins out in the end. This is contradictory. They're saying the player is wrong, because of math. By that line of thinking, the casino would also be wrong to love it, because of math. In a typical casino game, gambler's fallacy won't make your choice more or less correct, unless the choice is to keep playing or to walk away. The author doesn't specify why the casinos would love this though. As an aside, gambler's fallacy could affect more decision making in poker, but poker is a game of skill and the casino doesn't have a house edge on poker (they take a rake.)
coldtea 5y ago
>If it's random, then you have no recourse but to post-hoc description. There is -no- predictive weight. Well, a "post-hoc description" of empirical observations is how we make predictions. We gather cases (and their probabilities) post hoc, and predict future results based on that. Why shouldn't it be applied in this case, especially when here not only we can calculate the probabilities post-hoc, but even use probability to pre-calculate those post-hoc probabilities for every series of streaks? >The only way you can reasonably expect the past streak to have an impact on the next spin Regression to the mean is a reason to expect past streaks to have an impact on future spins. Doesn't have to be some force that specifically affects the individual next spin, but it's a probability that affects (and moves toward the mean) the outcome of next spins. Intuitively speaking, why shouldn't the gambler use it? If they shouldn't, "because spins are independent" seems too hollow as an answer, because we have independent spins but also a statistical property for their aggregation. I guess we could test it empirically: in a fair sequence of coin tosses, would a gambler always betting on tails after seeing N (for e.g. N > 4) consequtive heads have an advantage, over one always betting randomly on the same N+1 toss? But regardless of that, my point is that intuitively is quite justified, and the explanations why it's not seem more hand-wavy. >Try this on: What is the "mean" red-black on the roulette wheel? There isn't one. Well, (ignoring non red-black case), there's not a mean value, but for the distribution there's an expected long term tendency of a balanced red and black outcomes. >... And editing your comment to refer to groups of throws is disingenuous. It would have been more honest to modify your case in a reply. I didn't modify my case, I expressed it more clearly. What exactly was disingenuous? I more often than not post a quick comment (HN habbit, as sometimes old edit forms expire), and then re-read it and quickly improve it as I re-read it, find typos, better wording, etc. Didn't even think anybody would read it and answer in the time it took me to refine it. And, how about it, you can always answer to my final, improved, formulation. Does it have any historical interest if you answer to a worse worded case?

gexla 5y ago

Right, I have never heard "mean" being used in the context of casino games. I get what they are trying to say though, at some point the variance should start evening out to reflect the odds of the game. But we should be practical and remember we're in a casino. A red/black bet on roulette is one of the few games where you're going to get that low of variance. With slots, you have to play a ton of games before you can get an idea of what the variance is just from your game play. In poker, the rule of thumb is 10,000 hands before the player can be confident of having an idea of how effective a change of strategy is. Overall, whoever wrote this article is out of their element. Like this bit... > So we think we can use our amazing powers of pattern recognition to determine that black is “due” and use that power to win big. Casinos love this delusion, because they know that math wins out in the end. This is contradictory. They're saying the player is wrong, because of math. By that line of thinking, the casino would also be wrong to love it, because of math. In a typical casino game, gambler's fallacy won't make your choice more or less correct, unless the choice is to keep playing or to walk away. The author doesn't specify why the casinos would love this though. As an aside, gambler's fallacy could affect more decision making in poker, but poker is a game of skill and the casino doesn't have a house edge on poker (they take a rake.)

coldtea 5y ago

>If it's random, then you have no recourse but to post-hoc description. There is -no- predictive weight. Well, a "post-hoc description" of empirical observations is how we make predictions. We gather cases (and their probabilities) post hoc, and predict future results based on that. Why shouldn't it be applied in this case, especially when here not only we can calculate the probabilities post-hoc, but even use probability to pre-calculate those post-hoc probabilities for every series of streaks? >The only way you can reasonably expect the past streak to have an impact on the next spin Regression to the mean is a reason to expect past streaks to have an impact on future spins. Doesn't have to be some force that specifically affects the individual next spin, but it's a probability that affects (and moves toward the mean) the outcome of next spins. Intuitively speaking, why shouldn't the gambler use it? If they shouldn't, "because spins are independent" seems too hollow as an answer, because we have independent spins but also a statistical property for their aggregation. I guess we could test it empirically: in a fair sequence of coin tosses, would a gambler always betting on tails after seeing N (for e.g. N > 4) consequtive heads have an advantage, over one always betting randomly on the same N+1 toss? But regardless of that, my point is that intuitively is quite justified, and the explanations why it's not seem more hand-wavy. >Try this on: What is the "mean" red-black on the roulette wheel? There isn't one. Well, (ignoring non red-black case), there's not a mean value, but for the distribution there's an expected long term tendency of a balanced red and black outcomes. >... And editing your comment to refer to groups of throws is disingenuous. It would have been more honest to modify your case in a reply. I didn't modify my case, I expressed it more clearly. What exactly was disingenuous? I more often than not post a quick comment (HN habbit, as sometimes old edit forms expire), and then re-read it and quickly improve it as I re-read it, find typos, better wording, etc. Didn't even think anybody would read it and answer in the time it took me to refine it. And, how about it, you can always answer to my final, improved, formulation. Does it have any historical interest if you answer to a worse worded case?