The Parrondo paradox: losing + losing = winning


A and B are both losing games.

A is simple, B is complicated.

In simple game A, you win $1 with probability p (a bit less than 0.5, say 0.495) and lose $1 with probability 1-p (0.505).

Game B is a combination of two games B1 and B2.

In B1, you win $1 with probability p1 (a bit less than 0.1, say 0.095). You lose $1 with probability 1−p1 (0.905).

In B2, you win $1 with probability p2 (a bit less than 0.75, say 0.745). You lose $1 with probability 1−p2 (0.255).

The instructions for B are: play B2 if your stash is a multiple of 3, B1 otherwise.

A is a losing game, B is a losing game, but the combination ABBABABBABABBABABBAB… is winning.

Click here for simulation.

And see the map of the “probability space” below.