If you’re going to be betting based on what you think is less likely, then I would like to play with you too.
OK, telegraphic writing and reading is failing me. I’m looking for the meaning behind this and I get stuck on the idea that P_MoreLikely = 1 - P_LessLikely at least if there are only two choices, so I can’t figure out the important difference between betting on what is more likely and betting on what is less likely.
The point of my post is that probability is hardly just what you think it is. And that there are plenty of ways that people actually think about the probability of poker hands that turn out to be quite consistent with their losing money. Far be it from me to infer publicly that that means they were “wrong” about such a subjective thing as probability. But I am happy to collect their money.
Probability is in the mind. If you know a coin is biased, but you don’t know which way it’s biased, then the first flip is fair. If you suspect that it’s biased towards heads, then it’s biased towards heads.
You could also think of yourself as a coin. Nobody is stupid enough to be biased towards wrong. You’d have to be smart to manage that. You might have biases in each individual decision that make you consistently wrong, but if you have a bucket of coins, and you know that they all are biased but more are biased towards landing on heads then landing on tails, then if you take a coin out of the bucket and flip it, it’s biased towards heads.
If you know you’re not logically omniscient, the correct action isn’t to set all probabilities to 50%. It’s to try and find your biases and correct for them, but use whatever you have at your disposal until then.
I read the probability post you referenced. The question is WHAT is in your mind. If one person has a whole hell of a lot more correctly determined Bayesian conclusions about poker hands than another, and the two of them play poker, they will both bet based on what is in their heads. The one with the better refined knowledge about poker hands will take money, on average, from the one with the worser knowledge. If the game is fixed that might change things, but if the game is fixed and neither of them has prior knowledge of this, it is still more likely the knowledgable player will figure out how the game is fixed, and how to exploit that, than the less knowledgable player.
So if we disagree about the probability of something, do you just agree that for you the probability is p and for me it is p’? I don’t. The frequentist interpretation of probability doesn’t exist because people are idiots, rather it exists because for a very broad range of things it provides an excellent map of the world. If I think I am going to be just as good at poker because me and my opponent both have heads and probability is just in our heads, and my opponent simply knows more about the odds of poker, I will lose. We both just had probabilties in our heads, though. And if my opponent had known LESS about poker, it would have appeared that mine were at least as good as his. But someone who thinks probabilities are whatever he thinks they are is precisely the kind of person you want to bet against. Not being a frequentist does not excuse you from the very real distributions of outcomes the world will give you in dealing out cards from a shuffled deck.
If you know a coin is biased, but you don’t know which way it’s biased, then the first flip is fair.
By that you mean you would not expect to do better betting on heads vs tails. OK.
If you suspect that it’s biased towards heads, then it’s biased towards heads.
No, your suspicions can not bend reality. If it comes up heads first, then you would think it more probable that it is biased towards heads than that it is biased towards tails. You can’t even assign a numerical probability other than >50% to it coming up heads a 2nd time without knowing more about how it might be biased. Is it biased in a way which gives it runs (more likely to hit heads a 2nd time after hitting it the first?) Is it biased in a way that gives it at most a 5% deviation from fair? Even having access to a very long sequence of results from the biased coin doesn’t let you easily determine what the bias is. What if it is biased in a way so that every 67th flip is heads? How long before you notice that?
Yes detecting bias is important, but so is figuring the odds when games are fair, when things are as they seem to be. There is a tremendous amount of money to be made and lost playing fair games.
OK, telegraphic writing and reading is failing me. I’m looking for the meaning behind this and I get stuck on the idea that P_MoreLikely = 1 - P_LessLikely at least if there are only two choices, so I can’t figure out the important difference between betting on what is more likely and betting on what is less likely.
The point of my post is that probability is hardly just what you think it is. And that there are plenty of ways that people actually think about the probability of poker hands that turn out to be quite consistent with their losing money. Far be it from me to infer publicly that that means they were “wrong” about such a subjective thing as probability. But I am happy to collect their money.
Probability is in the mind. If you know a coin is biased, but you don’t know which way it’s biased, then the first flip is fair. If you suspect that it’s biased towards heads, then it’s biased towards heads.
You could also think of yourself as a coin. Nobody is stupid enough to be biased towards wrong. You’d have to be smart to manage that. You might have biases in each individual decision that make you consistently wrong, but if you have a bucket of coins, and you know that they all are biased but more are biased towards landing on heads then landing on tails, then if you take a coin out of the bucket and flip it, it’s biased towards heads.
If you know you’re not logically omniscient, the correct action isn’t to set all probabilities to 50%. It’s to try and find your biases and correct for them, but use whatever you have at your disposal until then.
I read the probability post you referenced. The question is WHAT is in your mind. If one person has a whole hell of a lot more correctly determined Bayesian conclusions about poker hands than another, and the two of them play poker, they will both bet based on what is in their heads. The one with the better refined knowledge about poker hands will take money, on average, from the one with the worser knowledge. If the game is fixed that might change things, but if the game is fixed and neither of them has prior knowledge of this, it is still more likely the knowledgable player will figure out how the game is fixed, and how to exploit that, than the less knowledgable player.
So if we disagree about the probability of something, do you just agree that for you the probability is p and for me it is p’? I don’t. The frequentist interpretation of probability doesn’t exist because people are idiots, rather it exists because for a very broad range of things it provides an excellent map of the world. If I think I am going to be just as good at poker because me and my opponent both have heads and probability is just in our heads, and my opponent simply knows more about the odds of poker, I will lose. We both just had probabilties in our heads, though. And if my opponent had known LESS about poker, it would have appeared that mine were at least as good as his. But someone who thinks probabilities are whatever he thinks they are is precisely the kind of person you want to bet against. Not being a frequentist does not excuse you from the very real distributions of outcomes the world will give you in dealing out cards from a shuffled deck.
By that you mean you would not expect to do better betting on heads vs tails. OK.
No, your suspicions can not bend reality. If it comes up heads first, then you would think it more probable that it is biased towards heads than that it is biased towards tails. You can’t even assign a numerical probability other than >50% to it coming up heads a 2nd time without knowing more about how it might be biased. Is it biased in a way which gives it runs (more likely to hit heads a 2nd time after hitting it the first?) Is it biased in a way that gives it at most a 5% deviation from fair? Even having access to a very long sequence of results from the biased coin doesn’t let you easily determine what the bias is. What if it is biased in a way so that every 67th flip is heads? How long before you notice that?
Yes detecting bias is important, but so is figuring the odds when games are fair, when things are as they seem to be. There is a tremendous amount of money to be made and lost playing fair games.