Waldegrave problem

In game theory, the Waldegrave problem is a problem first described in the second edition of Pierre Raymond de Montmort`s Essay d'analyse sur les jeux de hazard, which is the first discussion of a mixed strategy to derive a solution in game theory.

He provides a minimax mixed strategy solution to a two-person version of the card game le her.

The loser of each game puts one unit into the pot.

The original problem, stated in a letter dated 10 April 1711, from Montmort to Nicholas Bernoulli is for n = 2 and is attributed to M. de Waldegrave.

The problem, according to Montmort, is to find the expectation of each player and the probability that the pool will be won within a specified number of games.