An optical model for implementing Parrondo's game and designing stochastic game with long-term memory

Highlights: ► Using a photon propagating through a designed array of beam splitters to simulate Parrondo's game paradox. ► Design the optical flowchart for implementing Parrondo history-dependent game paradox. ► Design new game with long-term memory on a designed tree lattice and loop lattice. - Abstract: An optical model for a photon propagating through a designed array of beam splitters is developed to give a physical implementation of Parrondo's game and Parrondo's history-dependent game. The winner in this optical model is a photon passed the beam splitter. The loser is a photon being reflected by the beam splitter. The optical beam splitter is the coin-tosser. We designed new games with long-term memory by using this optical diagram method. The optical output of the combined game of two losing games could be a win, or a loss, or an oscillation between win and loss. The modern technology to implement this optical model is well developed. A circularly polarized photon is a possible candidate for this physical implementation in laboratory.