I just wrote a notebook about game theory, which you find here.

How would you play in the following game?

• Both players put 1$ on the table.
• Both get a random number from 0 to 1, with even distribution in the interval [0,1].
• The first player can another 1$ or pass. If he passes the second player gets all the money on the table (i.e., he wins 1$).
• If the first player has not left the game, the second player can add 1$ or pass. If he passes the first player gets his 1$.
• Otherwise, numbers are compared. The player with the higher number wins the table.