Parrondo Mixed Game Stationary Drift
Two losing coin games can combine into a winning game because mixing changes which capital states are visited.
Free theory articleTwo losing coin games can combine into a winning game because mixing changes which capital states are visited.
Concept & interpretation
The Parrondo Paradox is a fascinating result in probability where two games, each having a negative expected return (losing games) when played individually, can be combined (either by random mixing or a periodic schedule) to create a game with a positive expected return (a winning game). This module explores this phenomenon using a Markov chain on the capital modulo three.
Experiment
In this experiment, you can interact with the mixed game to see how different parameters affect the stationary drift.
- Open the interactive module at https://riano.app/module/parrondo-mixed-game-stationary-drift.
- Set Epsilon to 0.005 and Mix A probability to 0.5.
- Observe that while both Game A and Game B individual drifts are negative, the Mixed Drift is positive (~0.0157).
- Change Mix A probability to 0 or 1 to see the individual losing games. The stationary residues shift, explaining the paradox.