Of the examples given, game A was always a losing game, and game B was basically two games (I'm calling these sub-games) duct taped together, where one is a winning game, and the other is a game that loses very badly. This causes negative expected value across all of game B.
The important parts here are that in game A you lose slower than in game B's losing sub-game, and game B's sub-games switch depending on the resources you win/lose in game A.
The strategy is to play game A until you hit the conditions for game B's winning sub-game to kick in, then play game B until it swaps back over again, then go back to A and repeat the process.
Thus two games where each have negative expected value, can be daisy chained to produce positive expected value.
Sometimes Wikipedia reads like it is written by that math teacher who “just gets math” and teaches in a way that the only people who will understand … are people who already do.
Granted maybe this article is good and just beyond me, but it is disappointing how much Wikipedia is like that.
In my experience almost in every topic it is way better textbook than any textbook. Simply because Wikipedia has the right scope, and the right amount of content. Wikipedia can, and almost always do talk about anything in math in 3 different levels, and tell everything related (including history) about everything. Textbooks can't do that.
To be said, this article is not graspable at first for me either. There is the "even simpler example"[0], but I am not even sure if it is a right example (different games can share a state, the amount of money), or just an analogy.
Unrelated, but I always want to link permanent wiki articles, but there is no culture for it, and I am afraid it would annoy people because it is uncommon.
> 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.
