Probability
Two losing games with a memory
Parrondo's first paradox needed a game that watched the player's capital. This one watches nothing but the last two results: a coin that wins nine times in ten after two losses, one time in four after a loss and a win, seven times in ten after two wins. Alone it loses, and so does a slightly unfair coin; played at random together they win. The walk treats every position alike, and the paradox survives — because it was never about position.
