Parrondo's Paradox

Below is my simulator for Parrondo's paradox, an interesting set of games that were discovered by Juan Parrondo.  The paradox consists of two coin flip games, both of which are losing games when played consecutively.  When these games are played together, alternating back and forth between them with a common capital, they can become winning games.  The games are:

-Game A: A simulated coin flip with a winning probablity of (.50 - epsilon).
-Game B: Two coins; if the player's capital is multiple of the modulus, then a coin with a winning probability of (.10 - epsilon) is flipped, otherwise a coin with a winning probablity of (.75 - epsilon) is flipped.

The paradox can be shown to exist when using epsilon = .005, modulus = 3, and, for the alternating game, alternating every other game.  These are the default values on the simulator, but you can experiment with other values.  However, the graph layout is designed for these values, and more extreme values may make the graphs run off the page.

Keep in mind that the more trials you select, the longer it will take.  You can run up to 50,000 trials at a time, but if you do so, be prepared to wait.

Also, this applet does not work properly under some versions of Netscape 4.x, particularly on Macs and Unix/Linux.  For information about these browser problems, click here.

Downloadable Java source and byte-code are available here.  If you have any problems with the simulator, please email me.

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 The graph displays the average score for each of the 100 plays of each game.