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.
In fact, I misunderstood your proposal—I am incorrect in saying that lying helps. You’d get more bets on the same side as your “good” bets, but at unfavorable payouts so you’d lose too much when you lose.
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.
In fact, I misunderstood your proposal—I am incorrect in saying that lying helps. You’d get more bets on the same side as your “good” bets, but at unfavorable payouts so you’d lose too much when you lose.