  An optical model of classical photons propagating through array of many beam
splitters is developed to give a physical analogy of Parrondo's game and
Parrondo-Harmer-Abbott game. We showed both the two games are reasonable game
without so-called game paradox and they are essentially the same. We designed
the games with long-term memory on loop lattice and history-entangled game. The
strong correlation between nearest two rounds of game can make the combination
of two losing game win, lose or oscillate between win and loss. The periodic
potential in Brownian ratchet is analogous to a long chain of beam splitters.
The coupling between two neighboring potential wells is equivalent to two
coupled beam splitters. This correspondence may help us to understand the
anomalous motion of exceptional Brownian particles moving in the opposite
direction to the majority. We designed the capital wave for a game by
introducing correlations into independent capitals instead of sub-games.
Playing entangled quantum states in many coupled classical games obey the same
rules for manipulating quantum states in many body physics.
