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With choices ordered rock, scissors, paper and winner payoff $1$, the row-player payoff matrix is $\left(\begin{smallmatrix}0&1&-1\\-1&0&1\\1&-1&0\end{smallmatrix}\right)$. Both the row and column sums vanish. Thus the uniform <mixed strategy> guarantees expected payoff zero against every opposing strategy; the <value of a zero-sum game> is zero. A player responding to a known nonuniform mixture can instead optimize its linear expected payoff over pure responses and their ties.


 Rock paper scissors (source code)