Parrondo's Paradox

Started reading the examples and my eyes glazed over. Someone have a better example?

Further down the article there's a simpler example: https://en.wikipedia.org/wiki/Parrondo%27s_paradox#A_simplif...

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.

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.

This seems like such a pointless semantic flex to me...

In this case has the game not become Game A + Game B ?

It's just a larger game with a distinct winning strategy because the ruleset is expanded right?

What's the significance?