Rock-paper-scissors-lizard-Spock is a five-action extension of rock-paper-scissors. Each action defeats two others and loses to the remaining two: rock defeats scissors and lizard; paper defeats rock and Spock; scissors defeats paper and lizard; lizard defeats paper and Spock; and Spock defeats rock and scissors. Identical actions tie.
Assigning payoff 1 to a win, 
to a loss, and 0 to a tie gives the row player's payoff
matrix
![A=[0 -1 1 1 -1; 1 0 -1 -1 1; -1 1 0 1 -1; -1 1 -1 0 1; 1 -1 1 -1 0],](/images/equations/Rock-Paper-Scissors-Lizard-Spock/NumberedEquation1.svg) |
with rows and columns ordered as rock, paper, scissors, lizard, and Spock.
This zero-sum game has no Nash equilibrium in pure strategies. Its unique mixed-strategy Nash
equilibrium assigns probability 
to each action, and its game value
is 0. When both players choose independently and uniformly, the probability
of a tie is 
, compared with 
for rock-paper-scissors.
