Symmetric inverse formula for a matrix-game equilibrium

If a symmetric invertible payoff matrix satisfies $A^{-1}e\ge 0$, both players may useand the game value is $(e^T{A}^{-1}e{)}^{-1}$.

Forboth players optimally choose cards $1,2,3$ with probabilities $41/50,2/25,1/10$, and the row player's expected payoff is $57/25$.