You have two standard 52 card decks that have been shuffled randomly. You turn over the top card from each dec

Question

What is the probabliity that the two cards match? You keep turning over the top cars on each deck until you have gone through the two decks. How many matches do you expect to find?

Answer 1

I do not know the odds on this but they are great enough to make this a classic bar bet. Basically, you have the setup that you described. The claim is that for each card that matches the person who started the bet(the scammer) will be paid $5. For each time that no cards match up out of the entire deck the scammer will pay the dupe $10. The dupe thinks that the odds of a card matching are astronomical and that $10 is guaranteed. However, a few cards will match up.

Here is a site that gives a brief discussion of it.
http://scams.wikispaces.com/Two+Deck+Snap+

Answer 2

The first question sounds too easy. The probability of matching the top card in deck 1 to deck 2 is 1-in-52. For the sake of argument deck 1 could have any card on top. The odds are 100% that "some" card shows up there, right? So then the only question is the odds of matching a particular card with the second deck, therefore 1 in 52.

The second question sounds harder to me. I was thinking of a series like: (1 in 52) added 52 times. But that can't be right. I'll be looking to see if someone else has a good idea.