And it’s not a zero-sum game then, either.

Well, per-game, I suppose. But wealth is conserved in the economy, unless there’s depreciation (or appreciation) of the currency. The “economy graph” question then is about the distribution of finite wealth.

And it’s not “squandering” — it’s aiding in the redistribution….

And it’s not a zero-sum game then, either.

What happens if players start with an initial wealth of 1000 quatloos, and their wealth cannot drop below 0? That is, if a round won against a bankrupt player results in no exchange of funds.

What happens if a bankrupt player wins against a moneyed opponent? Do they get the stake, even if they offer no ante? If so, then I’d suspect strategies that were bad at RPS would learn to call “raise” as much as possible, and those that were good at RPS would be conservative with their bets.

I’ll amend it to address what I actually meant to say, which is about the higher-order moments of the distribution of scores an individual should expect vs. all opponents of equal memory.

First, notice that for any strategy A, there is a corresponding strategy A* which, playing against A, will always make the same moves. (Essentially, A* flips the “my move - opponent’s move” distinction around, then computes its move using exactly the same tables as A.) If we then take all of A*’s moves and shift them “up” (to the moves that would beat them — rock to paper to scissors to rock), we get another strategy A+, which will *always* beat A; if we shift A*’s moves “down” we get A-, which is *always* beaten by A. Note that A-, A*, and A+ have identical memory to A. Thus, there is always at least one strategy of identical memory which will *tie* with A; one which will beat A by T quatloos; and one which will be beaten by A by T quatloos.

Since the average score of two randomly chosen competitors will not be higher than +T (or lower than -T), then, no strategy A can do worse than this against *every* opponent.