Assume me and a friend of mine both are married. Every morning our wives put to each of us random number of dollars (from 1 to 100) in the wallet. When we meet with friend we open our wallets and the one who has less money takes it all.
Intuition says that in the long term each of us will win and loose the same amount of money. But if you think in terms of probability : probability to loose is 0.5 and probability to win is 0.5 but I win more than I loose. Therefore each day my mathematical expectation is positive???
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