discuss Russell's paradox, at least some of my students seem to gain a greater appreciation for the intricacies of set theory (the others just give me a baffled look). I can now add another paradox to my repertoire of paradoxes that I can use to try to get students interested in mathematics. This paradox is one that has only recently come to light and is being called Parrondo's paradox, after physicist Juan Parrondo [2]. The paradox involves the playing of two games, both of which are losing games (i.e., if played repeatedly, one should expect to lose more often than win). The paradox, however, is this: if we play a third game, which consists of randomly switching between playing the two losing games, we actually end up with a winning game (i.e., if we randomly play the two losing games repeatedly, switching between the two games, one can expect to win more often than lose). In this article, I will demonstrate how Parrondo's paradox works, and provide an explanation of the mathematics underlying it. I will first describe how each of the three games is played. Each of the games involves flipping a coin, with heads a win and tails a loss. We will assume that we start each game with $0 and the gain or loss in a round is $1. Game 1 Game 1 consists of flipping a biased coin one time. The coin is weighted so that the probability of winning is slightly less than 0.5, say 0.5 - a. Then the probability of losing is 0.5 + a. Clearly, this is a losing game.