Game Development Reference
But RPSLS gains nothing in terms of decision interest over RPS. No
Nash equilibrium means no Nash equilibrium. Adding more symbols
does nothing to enrich the mind game of anticipation and deception. More
options may add fictional interest, but it's probably not worth the extra
So far, I've described 1games like rock-paper-scissors as having no Nash
equilibrium. This wasn't entirely accurate. Rock-paper-scissors has no
pure Nash equilibrium. It does, however, have a mixed Nash equilibrium.
A MIXED NASH EQUILIBRIUM is a Nash equilibrium where each player
randomly chooses from a set of strategies with some given set of
In rock-paper-scissors, for example, there is no pure Nash equilib-
rium, but there is one mixed Nash equilibrium. It calls for both players to
throw each move 33.3% of the time. This is a Nash equilibrium since there
is no way one player can gain by deviating from this configuration (since
when the opponent is throwing with perfect randomness, it doesn't matter
what you do; you'll always win half the games).
Other strategy mixes in rock-paper-scissors are not in equilibrium.
For example, imagine you were to choose rock 35% of the time and scissors
and paper 32.5% of the time. Now your opponent can beat you by changing
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