[BruceZ]

I just noticed one issue with this article. Since we are taking the probability of winning a coin flip to be h > 0.5, it is not exactly true that the standard deviation is 1 chip, as would be the case if h = 0.5. Instead the standard deviation in chips is sqrt[1 - (2h-1)^2]. This means that if the standard deviation is S, then S = sqrt(b^2 - W^2) where b is the value of 1 chip (bet size), so the value of 1 chip is not S as stated in the article, but instead b = sqrt(S^2 + W^2). The result of this is that the final formula for risk of ruin

R($nS) = ((S-W)/(S+W))^n

should be replaced with

R($nS) = ((b-W)/(b+W))^n

where b = sqrt(W^2 + S^2), and b is the value of 1 chip (bet size). This is the form of the equation that appears in my derivation that I linked to above. The difference is small for h fairly close to 0.5, so the formula in the article is usually a sufficient approximation for the games we are interested in modeling. In fact, you can see that this same error is made in the paper by Patrick Sileo which I reference.