I think I've reached an understanding, but do correct me if I'm wrong. lim players -> inf mean wealth -> starting_wealth * (win_chance * (1 + win_gain)

I think I've reached an understanding, but do correct me if I'm wrong. lim players -> inf mean wealth -> starting_wealth * (win_chance * (1 + win_gain) + lose_chance * (1 - lose_loss)^rounds) So in their example case win_change = lose_change = 0.5 win_gain = 1.5 lose_loss = 0.4 (0.5 * (1 + 0.5) + 0.5 * (1 - 0.4)) = 1.05 so on average the mean wealth increases as the number of rounds increases. Yet at the same time for a single player lim rounds -> inf wealth -> 0 As others have mentioned, this is because the win multiplier is 1 + win_gain = 1.5 whereas the loss multiplier is 1 - lose_loss = 0.6. This is more easily seen by comparing the log of the multiplier ln(1.5) = 0.41 ln(0.6) = -0.51 For the game to be profitable, it must satisfy ln(1 + win_gain) > -ln(1 - lose_loss) <=> 1 + win_gain > 1/(1 - lose_loss) So for a gain of 50% the loss must be less than 33.3%.