Two individually losing games combine to produce a winning game. Discovered by Juan Parrondo (1996), it demonstrates how randomness and ratchet-like mechanisms can rectify Brownian motion into directed motion.
Statistics (n=100 players)
Mode:Game A
Mean capital:0
Winning players:-
Steps:0
Parameters
Game A win prob0.495
B mod-3=0 prob0.100
B other prob0.745
Speed5
How it works: Game A: biased coin, P(win)=p_A≈0.495 (slightly losing). Game B: if capital mod 3 = 0, P(win)=0.1 (very bad); otherwise P(win)=0.745 (good). Game B alone is losing because the ratchet keeps landing on the bad state. Combined: Game A's randomness perturbs away from multiples of 3, letting Game B win. This is a Parrondo ratchet — a discrete analogue of a Brownian ratchet (Feynman's ratchet in statistical mechanics).