Your friend says “It’s totally gonna work this time”. You say “uh, no it’s not”. She says “Okay, maybe not but like 90% yes”. You say “Bet, it’s only like 1 in 4,” putting down $25 (.5625-.0081) = $13.86. She puts down her $25 (0.8281-.0625) = $19.14. She attempts, smug in her expected 0.91 $13.86 − 0.09 $19.14 = $10.89, while you wait arms folded for your expected 0.75 $19.14 − 0.25 $13.86 = $10.89.
Sweet! In practice I would allow any percent estimate, loser gets to keep fractional cents as a humorous consolation prize, and obviously always settle up over PayPal or successive games of zero $EV high card to even up to whatever denominations the loser has on hand, because using pennies lowers both participants $EV to negative infinity.
This doesn’t punish estimates like 99.999% when the estimate should be more like 99%, unless you rescale and allow much higher than $25 bets.
A worked example:
Your friend says “It’s totally gonna work this time”. You say “uh, no it’s not”. She says “Okay, maybe not but like 90% yes”. You say “Bet, it’s only like 1 in 4,” putting down $25 (.5625-.0081) = $13.86. She puts down her $25 (0.8281-.0625) = $19.14. She attempts, smug in her expected 0.91 $13.86 − 0.09 $19.14 = $10.89, while you wait arms folded for your expected 0.75 $19.14 − 0.25 $13.86 = $10.89.
Sweet! In practice I would allow any percent estimate, loser gets to keep fractional cents as a humorous consolation prize, and obviously always settle up over PayPal or successive games of zero $EV high card to even up to whatever denominations the loser has on hand, because using pennies lowers both participants $EV to negative infinity.
This doesn’t punish estimates like 99.999% when the estimate should be more like 99%, unless you rescale and allow much higher than $25 bets.