> Again, Kelly gives us terrible advice. If you have a trillion to one payout on a coin flip, you want to bet less, not more! Why would you risk half your money, and have a 1/4 chance of losing all your money, when you can bet 1 cent at a time and just wait to win one time so you can buy half of the stock market with your winnings?
So you're just going to throw away the criterion because you think the results are unintuitive? That's the argument you're making here.
To take your reasoning seriously, the reason why you might not want to bet 1 cent at a time is because the Kelly bet is guaranteed to eventually overtake your 1-cent-bet-strategy. Furthermore, it is completely incorrect to say that the Kelly bet has a 1/4 chance of losing all your money in the given situation. If you lose your first bet, the Kelly criterion tells you not to bet the whole house on the next bet.
Nothing you have written so far suggests that you actually understand the sense in which the Kelly criterion is optimal, which I attempted to explain in my other reply to you.
You keep writing as though it only maximizes the expectation of log-utility.
In fact it's not clear that you even understand what the Kelly criterion is telling you to do.
So you're just going to throw away the criterion because you think the results are unintuitive? That's the argument you're making here.
To take your reasoning seriously, the reason why you might not want to bet 1 cent at a time is because the Kelly bet is guaranteed to eventually overtake your 1-cent-bet-strategy. Furthermore, it is completely incorrect to say that the Kelly bet has a 1/4 chance of losing all your money in the given situation. If you lose your first bet, the Kelly criterion tells you not to bet the whole house on the next bet.
Nothing you have written so far suggests that you actually understand the sense in which the Kelly criterion is optimal, which I attempted to explain in my other reply to you. You keep writing as though it only maximizes the expectation of log-utility. In fact it's not clear that you even understand what the Kelly criterion is telling you to do.