By $2 bet at 66% odds, I mean that the Yes position costs $2*66% and the No position costs $2*34%.
You're right that "max wager" is meant to be maximum loss. I think you're picking up on the fact that I made a mistake in calculating loss for each player. I was calculating the potential loss for "$2 bet at 66%" as 2 dollars for both players, but that's obviously wrong, and no reason afaik that the players should have the same maximum loss. Thanks for the observation.
I don't understand your observation about the incentive to overstate.
Let's say A gives event E 60% odds and B gives E 90% odds. For a... (read more)
I like your summary of the method. Good point as well. Perhaps you would want a norm that players don't discuss their maximum bets before entering them.
I'm not familiar with the Kelly Criterion so I'll check that out.
Alice and Bob are talking about the odds of some event E. Alice's odd's of E are 55% and Bob's are 90%. It becomes clear to them that they have different odds, and being good (and competitive) rationalists they decide to make a bet.
Essentially, bet construction can be seen as a bargaining problem, with the gap in odds as surplus value. Alice has positive EV on the "No" position for bets at >55% odds. Bob has neutral or better EV on the "Yes" position for bets at <90% odds.
Naive bet construction strategy: bet with 50/50 odds. Negative EV for Alice, so this bet doesn't work.
Less naive bet construction strategy: Alice... (read 387 more words →)
Good point.