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by mynameisme 4677 days ago
Say there is a game at a casino, that has a 1/100 chance of winning, and if you win, you get a payout of 100.01(original bet). You have $100. How would you play without it being extremely dangerous?
1 comments

By the Kelly criterion, you should bet edge/odds of your bankroll. Your edge here is 0.01 * 0.0001 = 0.000001. Your odds are 0.01. Therefore you should bet 0.0001 of your net worth. So if you had a million dollars, that $100 bet would be a sensible investment. If you've only got, say, $100k then you should only bet for entertainment value.

The investment rule that underlies Kelly is to maximize the log of your net worth. Why? Bets multiply your net worth by a random factor, take logs and you're adding a random factor. In the long run a sum of independent random factors tends to converge to the expected value, so maximizing the expected log of your net worth will result in a strategy that with 100% odds will, in the long run, beat any other.

Sorry, I was being rhetorical, I guess it wasn't obvious. My point to the parent was that no need to bet your entire life savings on one company, you can split it among hundreds and take advantage of your edge.