Maximizing the probability of winning does not lead to maximizing the expectation from the game when one’s strategy may include skewness, i.e., a small chance of large loss and a large chance of a small win. If you engaged in a Russian roulette–type strategy with a low probability of large loss, one that bankrupts you every several years, you are likely to show up as the winner in almost all samples—except in the year when you are dead.
