Comment by pyrale
1 day ago
The cost/information function of moves exists in poker regardless of whether it's tied to actual money. You put your money in a hand if you believe that you have good ev, whether that ev is labeled in chips or dollars. I don't see how changing the rules of chess (therefore changing the ev - of course if you change the ev that changes players' behaviour. But that would be like changing the poker ruleset, not changing the money value of chips) makes a comparable case.
Let me give you a counter-comparison: if regardless of which chess piece was moved, after both players had made a play, they could bet on the game outcome (therefore not changing the ev of a move), I'm not sure players would want to play differently.
Your chess betting example would play slightly differently than standard chess. Since the goal becomes not just to win, but to win the most cash, you'd be trying to leverage your hidden information in order to improve your outcome, which in chess is just "things you've foreseen but your opponent hasn't", which, due to the nature of chess, you'd weaken by jacking up your bets to try and capitalize. The result would probably be a worse game of chess, since without the chance component the better player will win the chess game far more often than the worse player, and then the optimal move for the worse player would be to forfeit early constantly.