Parrondo's paradox is a surprising statement about the
combination of certain probabilistic events. We start with two
games A and B that, individually, are losing games. But we
define game C as follows: Flip a fair coin and play A if the
coin comes up heads and B if it comes up tails. Then C can be a
winning game. The details: Game A is simply the flip of a coin
that comes up heads with probability 0.495. Since heads win, the
expected value of game A is clearly negative: a bettor who
stakes $1 on each flip would have an expected long-term loss of
1¢ per game. Game B is a bit more complicated: Consider two
coins, W and L, with W coming up heads with probability 0.745
and L coming up heads with probability 0.095. Clearly W is a
winning coin and L is a losing coin. For game B, if the player's
stake (it is assumed the player starts with $0 and wins or loses
$1 on each throw) is divisible by 3, then coin L is used on the
next flip; otherwise coin W is used. Some computation shows that
the expected return from game