For a class, I have prepared an analysis of a very simple poker game.

The rules are very simple.  It is a game with two cards 1 to m only and two players P1 and P2. The game is like this:

• Each player sets A.
• P1 passes or sets B.
• Then P2 passes or sets B.
• Player with higher card takes stock.
• Stock is shared with equal cards.

For m=2 we have only two card values, which the players get at random. For A=B=1, it is easy to see that both players must set all the time. For B/A>1, things start to get complicated. For more than 2 card values, bluffing occurs.

I computed the optimal strategy (in this case the Nash equilibrium) using optimization. See the notebook. One of the Examples in Euler Math Toolbox contains the same problem, but with a little less explanation.