There is an old proposition bet in which you wager that two people, who each turn cards face up at the same time from two randomly shuffled face down decks, will at some point turn over the identical card. The probability of turning over two cards that match from two honestly shuffled decks is much higher than 50%, but can you explain why mathematically?

The problem: Two people shuffle two decks of 52 cards. When they finish, they each flip over the top card of each deck. If the two cards match exactly, then the proposition has occurred. In the very likely event that the two cards do not match, they continue turning over cards at the same time until two cards match exactly as to suit and number. If no two cards match after each person has dealt through all 52, then the proposition has not occurred.

Most people would assume this is a 50/50 proposition since they think the chances of two cards matching at any turnover is 1 in 52 and there are 52 chances to match the cards. However, the odds are far better than 50/50.

Can you say why mathematically?

DK

I found the answer to my own question: http://www.themagiccafe.com/forums/viewt......forum=99

Thanks,
DK

This together with the birthday bet have definately helped my lifestyle.