Parrondo's paradox is used extensively in game theory, and its application to financial risk. There exist pairs of games, each with a higher probability of losing than winning, for which it is possible to construct a winning strategy by playing the games alternately or even randomly.

The birthday paradox, also known as the birthday problem, states that in a random group of 23 people, there is about a 50 percent chance that two people have the same birthday. How do we know that?

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