Assume the average payoff is 103% (allowing for economic growth) and that the payoff distribution extends down to 0% (ruin).

Assume the agents can place more distinct bets the more money they have. (Assuming a nonzero smallest bet size suffices)

Then the wealthier players can diversify their variance away and capture the 103%. The less wealthy players cannot and are more likely to go bust.

If the average payoff is less than 100% so the game is a loss to players, and you must play, it is known that diversification doesn't work because you want to have sufficient variance to be able to have payoffs about 100% some of the time.

Is that it? The proofs are left as an exercise for the (bored) reader.

A vivid image of what should exist acts as a surrogate for reality. Pursuit of the image then prevents pursuit of the reality -- John K. Galbraith