Solution to Card Game with Bluffing

Proof
From the payoff table:

The solution is:
 * $A$ takes strategy $A_1$ for $2/3$ of the time, and $A_2$ for $1/3$ of the time.
 * $B$ takes strategy $B_1$ for $2/3$ of the time, and $B_2$ for $1/3$ of the time.