Suppose I come to you with a fair coin and say that I’ll give you $50 if it comes up heads and take $40 if it comes up tails. Good deal, right? Now I change the

Suppose I come to you with a fair coin and say that I’ll give you $50 if it comes up heads and take $40 if it comes up tails. Good deal, right? Now I change the deal to 40% of your money with 5:4 odds and you can play as much as you like. You have $100 so it’s the same deal. There’s never a point where this looks like a bad deal, but you will eventually lose everything if you keep playing. On the other hand you will do well if you don’t adjust the amounts. There is a way to adjust the amounts safely, depending on a set acceptable probability of ruin (pr). Consider betting cash/log2(1/pr) at every turn. That reduces the gulf between the expectation of the log and the log of the expectation, but the probability of ruin still increases toward unity. As the timeline increases to infinity, the safe bet drops to zero.