fairness · paradox · traps

Parrondo's paradox

Each game loses. Switching between them can win.

Each machine, played alone, drifts down. What happens if you switch between them?

A coral coin count is a multiple of 3. That is when machine B uses its worse coin. One short walk can go either way.

After 80 plays, the average result Lock a direction, then run the walks.

Walks

—This walk's ending coins

—Average change after 80 plays

—Walks that finished up

Machine A wins 49.5% of plays. Left on its own, the coins drift down.

Machine B wins 9.5% of plays when your coins are a multiple of 3, and 74.5% otherwise. Left on its own, it drifts down too.