"To understand this paradox, we need to imagine a situation in which you play two games with some very specific parameters. For instance, let's imagine that the first game, A, involves a coin toss. The coin in this case has a weight distribution has been slightly altered so that it lands preferentially on one side with a probability of 50.5 percent."
"Then there is a second, more complicated game, B, that involves spinning two wheels of fortune. For this game, you will get to spin one or the other based on how much money you currently have. If your available capital for the game (based on how you've been playing A) is evenly divisible by 3, then you spin a wheel of fortune that gives you a chance of winning of only 9.5 percent."
Juan Parrondo discovered that two games that individually cause losses can be combined into a winning strategy. The paradox arises when alternating between a slightly biased losing coin-toss game (Game A) and a capital-dependent game with different win probabilities (Game B). Game A gives a 49.5% chance of winning, producing an average loss of one cent per play. Game B uses two wheels chosen depending on capital divisibility by three, with one wheel offering only a 9.5% win chance when capital is divisible by three. Alternating or combining these games can reverse expected outcomes, with implications for slime mold life histories and cancer therapy strategies.
Read at www.scientificamerican.com
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