Simulation of A Three Player Game

Two player game
The attacker will be called Abe.
The defender is Dan.
Abe is dealt card from [0,1].
Dan is dealt 2 cards from [0,1].
Dan plays his better card.
Abe may bet or check.
Abe checks, showdown.
Dan may call or fold to a bet.
Dan is playing his best card from an unit square.

Dan is like two players. Abe is one player.
With no betting Abe should win 1/3 of the time.

The pot is S and the bet is b.



The above is the image of the Abe's payoff cube.
His strategy options are cut into three sections.
A is Abe betting for value. B is Abe checking.
C is Abe bluffing. Abe's payoffs are color
coded. The legion is in the image box.

On the first play of the game, the pot is 30 and the
bet is 10. Abe's EV is 10 with no betting.
Abe optimizes at .231 bet for value.
His EV is 11.622.
On the second play, the pot is 90 and the bet is 10.
This is similiar to a fixed limit game ratio. Abe's
EV is 30 with no betting.
Abe optimizes at .28 bet for value.
His EV is 32.304.