Can Two Wrongs Make a Right? Coin-Tossing Games and Parrondo’s Paradox

Background On frequent occasions, a logical oddity comes along, which attracts a sizeable audience. One of the most recent is known as Parrondo's paradox [5, 6]. Briefly, it is the observation that random selection (or merely alternation) of the playing of two asymptotically losing games* can result in a winning game. Conceptually similar situations involving only the processing of statistical data are not novel. What has been referred to as Simpson's paradox [8] is typified by this scenario: Quite different items, say type 1 and type 2, cost dealers the same $10 per unit. Suppose that, dining a given period, dealer A sells 20 and 80 of these two types, charging $13 and $15, respectively, per item. Dealer B, on the other hand, who charges $14 and $16 per item, sells 80 and 20 of the two types. Then the average cost per item to dealer A's customers is (1/5)13 + (4/5)15 = $14.60, while B's on the average only pay (4/5)14 + (1/5)16 = $14.40, a net result that B is delighted to advertise. This despite the fact that A sells both items more cheaply than B does! No surprise, since A sells mainly the more expensively marked