This applet implements a simplified version of the card game Le Her as presented in the article Analysis of N-Card Le Her of Arthur T. Benjamin. The original version was studied by Bernoulli and Montmort, but it was Waldegrave who gave a solution using the concept of mixed strategies.

Game description: 13 cards of a single suit are shuffled. In the beginning of the game, the player 1 receives a card X (only he sees this card), the player 2 receives a card Y (only he sees this card) and a card Z is put over the table (nobody sees this card). The player 1 plays first: he must decide if he will keep or swap its card X with the card Y of the player 2 (in the last case, the player 2 cannot deny the swap). After player 1's decision, the player 2 must decide if he will keep or swap its card with Z. The winner is those who has the card with the highest value (J > Q).

In the applet below, the computer assumes the role of player 1. If the game is played several times, who will have the highest score in the long-run?

You may use this applet offline downloading the file leher.zip (71 Kb). The source code is also included in this file.