Recently, I read this article on expected value. The author cites the example of a poker player. If he has a hand that gives him a 1 in 5 chance of winning the pot, would you take the chance? The answer of the majority of people would be to say ''Are you crazy!!? I would never do that!” The answer should be “It depends!?”. For example, if I have a 1 in 5 chance of winning the $500 pot or a 4 in 5 chance of losing my 100 dollars bet, then the answer would be different if you know a bit about probability theory. In this specific case, I would win an average of 20 dollars on each hand. In my perspective, I think I would take the bet, but I am still confused! Does it depend of a certain variance? If I bet everything I have on a certain hand even though on average I am positive, there's still a risk I would lose everything. How should I demystify my questions?
2026-04-08 00:21:41.1775607701
Should I bet everything even though my expected value is positive?
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Working with expected value is sufficient when the value is small compared to your economy or you can play enough times for the law of large numbers to kick in. It fails when enough is at stake that losing is worse than winning even if the expected value is positive. Expected value assumes that every dollar is the same value to you. At large stakes that fails and generally you should be more conservative.
In this answer I talk about an extreme case-you are offered very nice odds, so by expected value you should bet all your money each time. The chance you wind up broke is very high, but if you don't you are so rich that the expected value is also very high.