Professional risk takers such as gamblers, insurance companies and banks are good at using counter intuitive situations like this to put you on the "wrong side" of a bet or contract. It seems like you are being offered a very reasonable proposition but in fact you are extremely unlikely to benefit from the risk you are taking:
"23 people. In a room of just 23 people there’s a 50-50 chance of two people having the same birthday. In a room of 75 there’s a 99.9% chance of two people matching."
http://betterexplained.com/articles/understanding-the-birthday-paradox/
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