On the walk home I remembered the following. You play a game with a friend. The friend deals from a pack of cards, turning each card face up one by one. After each card, you have the opportinity to say "STOP" (and after the 51st card has been turned over you have to say "STOP"). The next card is then turned over, and you win if it's red. Can you devise a strategy which enables you to win on average with probability over 50 percent?
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