The bit that helped me was here: > The role of M now comes into sharp focus. It serves solely to induce a dependence between Games A and B, so that a player is

The bit that helped me was here: > The role of M now comes into sharp focus. It serves solely to induce a dependence between Games A and B, so that a player is more likely to enter states in which Game B has a positive expectation, allowing it to overcome the losses from Game A. With this understanding, the paradox resolves itself: The individual games are losing only under a distribution that differs from that which is actually encountered when playing the compound game. In summary, Parrondo's paradox is an example of how dependence can wreak havoc with probabilistic computations made under a naive assumption of independence. Trying to rephrase: if you combine systems in a way that the rules of the combination itself serves to "manipulate" the individual conditions of the two systems, then you can get positive outcomes from two things that, individually, would give negative outcomes if not otherwise manipulated. The example with the even simpler "In Game B, you count how much money you have left — if it is an even number you win $3, otherwise you lose $5." (compared to the game where the above quote came from) really sums that up - if you know your starting point you can set up the sequence of those two games to steadily win.