No, one shouldn’t. Playing a game of chance once or a thousand times does not influence the outcome of the next round (aka the gambler’s fallacy). If a bet is a good idea one time, it’s a good idea a thousand times. And if a bet is a good idea a thousand times, it is a good idea the first time. How could you consider betting a thousand times to be a good idea, if you think each individual bet is a bad idea?
Gambler’s ruin. The bets are the same, but you are not. If bets are rare enough or large enough, they do not justify they simplifying assumption of ergodicity (‘adding up to normality’ in this case) and greedy expected-value maximization is not optimal.
Correct. Which is why risk management and diversification are crucial and why you should never bet more than you can afford to lose. I have this as an implicit rule, but I should have mentioned it. Thank you for pointing this out.
Edit: And I should probably read up more on the Gambler’s ruin. I can see how expected value maximization doesn’t hold up in the extreme cases, but it had to be pointed to me first.
The bets are the same, but you are not. If bets are rare enough or large enough, they do not justify they simplifying assumption of ergodicity
Can you expand on this a little? I don’t understand why the number of sequential bets you’re offered makes it easier to assume ergodicity, or indeed changes optimal bet sizing at all. (I strongly agree with the rest of your post fwiw)
Gambler’s ruin. The bets are the same, but you are not. If bets are rare enough or large enough, they do not justify they simplifying assumption of ergodicity (‘adding up to normality’ in this case) and greedy expected-value maximization is not optimal.
Correct. Which is why risk management and diversification are crucial and why you should never bet more than you can afford to lose. I have this as an implicit rule, but I should have mentioned it. Thank you for pointing this out.
Edit: And I should probably read up more on the Gambler’s ruin. I can see how expected value maximization doesn’t hold up in the extreme cases, but it had to be pointed to me first.
Can you expand on this a little? I don’t understand why the number of sequential bets you’re offered makes it easier to assume ergodicity, or indeed changes optimal bet sizing at all. (I strongly agree with the rest of your post fwiw)