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 bet at even odds:
EV_A(YES) = .4 * -.5 + .6 * .5 = .1
EV_A(NO) = .6 * -.5 + .4 * .5 = -.1
From A’s perspective the no position on the 50⁄50 bet (or any bet where the no position costs more than 40 cents on the dollar) is negative EV. So if A submitted 0% odds, they’d be forcing themselves to take a lot of negative EV bets.
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.