‘Tout vainqueur insolent à sa perte travaille.’ –Jean de La Fontaine
The Parrondo’s paradox, has been described as: A combination of losing strategies becomes a winning strategy. […]
Consider two games Game A and Game B, this time with the following rules:
1. In Game A, you simply lose $1 every time you play.
2. In Game B, you count how much money you have left. If it is an even number, you win $3. Otherwise you lose $5.Say you begin with $100 in your pocket. If you start playing Game A exclusively, you will obviously lose all your money in 100 rounds. Similarly, if you decide to play Game B exclusively, you will also lose all your money in 100 rounds.
However, consider playing the games alternatively, starting with Game B, followed by A, then by B, and so on (BABABA…). It should be easy to see that you will steadily earn a total of $2 for every two games.
Thus, even though each game is a losing proposition if played alone, because the results of Game B are affected by Game A, the sequence in which the games are played can affect how often Game B earns you money, and subsequently the result is different from the case where either game is played by itself.
