# Bored with Stripped-Down Poker, Felix and Oscar now make the game more interesting by adding a third

Bored with Stripped-Down Poker, Felix and Oscar now make
the game more interesting by adding a third card type: Jack. Four Jacks are
added to the deck of four Kings and four Queens. All rules remain the same as
before, except for what happens when Felix Bets and Oscar Calls. When Felix
Bets and Oscar Calls, Felix wins the pot if he has a King, they “tie” and each
gets his money back if Felix is holding a Queen, and Oscar wins the pot if the
card is a Jack.

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(a) Show the game in extensive form. (Be careful to label
information sets correctly.)

(b) How many pure strategies does Felix have in this

(c) How many pure strategies does Oscar have in this

(d) Represent this game in strategic form. This should be
a matrix of expected payoffs for each player, given a pair of strategies.

(e) Find the unique pure-strategy Nash equilibrium of
this game.

(f) Would you call this a pooling equilibrium, a
separating equilibrium, or a semi separating equilibrium? (g) In equilibrium,
what is the expected payoff to Felix of playing this game? Is it a fair game?