Question

A game between two equally skilled players is ended before a winner is declared. Player A needs 3 more points to win, and player B needs 2 more points to win. How many possible outcomes of the rest of the game would Pierre de Fermat have considered in order to determine how to divide the stakes?

Answer 1

Plater A gets 40% of the price and player B gets 60% of the stakes

Explanation:

Pierre de Fermat would take into account every possible outcome, considered who it would benefitted and divide the price accordingly.

We will enumerate the possible points and assingning a winner for each case:

A-A-A: A

A-A-B-A:A

A-A-B-B:B

A-B-A-A:A

A-B-A-B:B

A-B-B:B

B-A-A-A:A

B-A-A-B

B-A-B:B

B-B:B

There are 10 possible outcomes of which A wins 4 and B wins 6.

This would mean A gets 40% of the stakes and B gets 60%.