Two games that each lose in the long run can be alternated to produce a winning sequence.
Parrondo demonstrated it in 1996 with a pair of simple gambling games whose rules depend on the player's current capital. Switching between them, at random or in a fixed pattern, keeps the capital in states where the second game is favourable, which neither game can do alone. It is not a way to beat a casino: the games have to be coupled through a shared state, and ordinary bets are not.
In practice
- A gambler told that two losing games make a winning one reads the rules and finds that the trick is the shared bankroll rather than the games.
- A manager alternates two unpopular policies and gets a result neither produces alone, because the second works only on the state the first leaves behind.
- Standing
- Often quoted loosely as proof that two bad strategies can make a good one. Without the coupling, losing games stay losing. Compare Simpson's paradox, whose arithmetic it resembles.
- Further reading
- Wikipedia
- Subject
- Games & Strategic Interaction
- Essay
- The recurring shapes of conflict and cooperation