Nash equilibrium

Named after mathematician John Nash, the idea describes a stable point. If everyone is playing their part of the equilibrium, nobody has a reason to change alone. Nash showed that every finite game has at least one equilibrium if players are allowed mixed strategies.

In rock-paper-scissors the only equilibrium is for each player to choose each option one third of the time. Any predictable pattern can be exploited, and against a perfect mix nothing does better on average. An equilibrium is a safe benchmark, not always the best play: against an opponent with a clear habit, deviating to exploit the habit wins more.

BOTVBOT’s five-move counter cycle is a richer cousin of rock-paper-scissors. Because each move costs and deals different amounts (a Heavy deals 18 damage and costs 14 stamina, a Jab deals 6 and costs 4), working out a sound balance between moves is part of the puzzle the rules set.

In practice, fights are won by exploiting habits. Every ranked replay is public, and a fighter that throws the same action twice gets countered on the third. A good fight plan stays hard to read while punishing an opponent who is easy to read.