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H. G. Muller wrote on Tue, Jun 15, 2010 08:01 PM UTC:
I am not even sure which betting scheme ou are analyzing here. You bet on one
number, and when you lose, (the typical result), you do what? Increase the
bet?

Gamblng is ill advised, even if the odds are in your favor (such as in the stock market). Even in games that are obviously rigged in your favor (like 50% probabiliy on a 3x payout), it requires very careful handling to extract the gains. Paradoxically, when you are not careful enough, this game will bankrupt you with probability 1! So I'd rather not be the house at roulette either...

Very interesting is the following game, which I named 'Goose with the Golden Eggs': you can pick a number N and an amount to bet X. With probability 1/N you will then get N*N*X; otherwise you get nothing. (The betted amount always goes to the house). For any N>1, the odds are heavily in your favor, growing with N. What N and X (the latter as a fraction of your total capital) would you pick?