Parrondo’s paradox appears in game theory which asserts that playing two losing games, A and B (say) randomly or periodically may result in a winning expectation. In the original paradox the strategy of game B was capital-dependent. Some extended versions of the original Parrondo’s game as history dependent game, cooperative Parrondo’s game and others have been introduced. In all of these methods, games are played by two players. In this paper, we introduce a generalized version of this paradox by considering three players. In our extension, two games are played among three players by throwing a three-sided dice. Each player will be in one of three places in the game. We set up the conditions for parameters under which player 1 is in the third place in two games A and B. Then paradoxical property is obtained by combining these two games periodically and chaotically and (s)he will be in the first place when (s)he plays the games in one of the mentioned fashions. Mathematical analysis of the generalized strategy is presented and the results are also justified by computer simulations. A potential application of the model in treatment of type II diabetes is presented. In this theoretical work, we consider two types of treatments as two games which are played among three different players. The player 1 is considered as the treatment success index, the player 2 is the insulin deficiency index and the player 3 is assumed to be the insulin resistance index. It is shown that certain combinations of two losing games for player 1 (unsuccessful treatments) will result in a win (successful treatment).

帕隆多的悖论出现在博弈论中，该论断断言，随机或定期玩两个输掉的游戏A和B（例如）可能会导致获胜期望。在最初的悖论中，游戏B的策略取决于资本。引入了一些原始Parrondo游戏的扩展版本，如历史依赖游戏，合作Parrondo游戏以及其他版本。在所有这些方法中，游戏都是由两个玩家玩的。在本文中，我们通过考虑三个参与者来介绍此悖论的广义版本。在我们的扩展程序中，投掷三边骰子可在三位玩家之间进行两场比赛。每个玩家将位于游戏中的三个位置之一。我们设置了两个游戏A和B中玩家1排在第三位的参数条件。然后通过周期性地和无序地组合这两个游戏来获得矛盾的特性，并且当他以一种提到的方式玩游戏时，他将处于第一位。提出了广义策略的数学分析，并通过计算机仿真证明了结果。介绍了该模型在II型糖尿病治疗中的潜在应用。在这项理论工作中，我们将两种类型的处理视为在三个不同玩家之间进行的两个游戏。玩家1被认为是治疗成功指数，玩家2是胰岛素缺乏指数，玩家3被认为是胰岛素抵抗指数。结果显示，玩家1的两个输掉比赛的某些组合（不成功的治疗）将导致获胜（成功的治疗）。