As rationalists, we don’t want to be playing negative expectation value games, so I suppose it’s time to give up on the martingale…
There are many plausible scenarios in which playing games with superficially negative outcomes is wise. The businessman who is facing bankruptcy unless he can deliver a million dollars to his creditors is rational to put his half-million on black.
Sure, one can always embed a game inside another one and so alter the overall expectation values how one likes. That said, we still only want to play the meta-game if it had positive expectation value, no?
Minor semantic quibble: I would say we always want positive expected utility, but how that translates into money/time/various intangibles can vary tremendously both situationally and from person to person.
There are many plausible scenarios in which playing games with superficially negative outcomes is wise. The businessman who is facing bankruptcy unless he can deliver a million dollars to his creditors is rational to put his half-million on black.
Sure, one can always embed a game inside another one and so alter the overall expectation values how one likes. That said, we still only want to play the meta-game if it had positive expectation value, no?
Minor semantic quibble: I would say we always want positive expected utility, but how that translates into money/time/various intangibles can vary tremendously both situationally and from person to person.