Card Game with Bluffing is Completely Mixed Game

Theorem

The game of cards with bluffing is a completely mixed game.

Proof

From Solution to Card Game with Bluffing, the optimum strategy for the [[Definition:Card Game with Bluffing|card game with bluffing, is:

For $A$, to use both pure strategies but favour $A_1$ by $2/3$ to $1/3$.

For $B$, to use both pure strategies but favour $B_1$ by $2/3$ to $1/3$.

Hence the result by definition of completely mixed game.

Sources

• 1956: Steven Vajda: The Theory of Games and Linear Programming ... (previous) ... (next): Chapter $\text{I}$: An Outline of the Theory of Games: $3$