• Journal of the Korean Data and Information Science Society
• /
• v.27 no.1
• /
• pp.121-130
• /
• 2016

An ansemble of N players arranged in a circle play a spatially dependent Parrondo game B. One player is randomly selected to play game B, which is based on the toss of a biased coin, with the amount of the bias depending on states of the selected player's two nearest neighbors. The player wins one unit with heads and loses one unit with tails. In game A' the randomly chosen player transfers one unit of capital to another player who is randomly chosen among N - 1 players. Game A' is fair with respect to the ensemble's total profit. The games are said to exhibit the Parrondo effect if game B is losing and the random mixture game C is winning and the reverse-Parrondo effect if game B is winning and the random mixture game C is losing. We compute the exact mean profits for games B and C by applying a state space reduction method with lumped Markov chains and we sketch the Parrondo and reverse-Parrondo regions for $3{\leq}N{\leq}6$.