The Interrupted Game's Fair Split
Two people wager equal stakes on a fair coin-flip game, first to 6 points wins the whole pot. They're forced to quit early, with the score at 5 to 3. Splitting the pot 5:3 (by points won) feels natural, and splitting it evenly feels fair too — but a judge insists both are wrong. How should the money really be divided?
Reveal the answer
The pot should be split 7:1 in the leader's favor: the trailing player can only still win by winning the next three flips in a row (odds 1/8), so the leader's true winning chance is 7/8. Fra Luca Pacioli posed this 'problem of points' in 1494 and got it wrong; Cardano criticized him but also erred. Pascal and Fermat's 1654 letters solving it correctly are usually cited as the birth of mathematical probability theory.