What are the odds?

Can you tell me what the odds would be if: you had two decks of cards (each with 52 playing cards and 2 jokers), and you shuffled both decks, set them on a table, then had two seperate people each cut their deck and select one card from their deck, - - - and have both cards be the same card? For example; each person took their deck of cards, cut the cards, took one card out, layed it face down on the table, and then when each card was revealed - - it turned out to both be the 5 of hearts.!!! Can anyone tell me what the odds of that happening are - - - (without the cards being forced by a magician) ?
Thank you for whoever responds to my question.

I would suggest you not publicize your email address online...
I think the odds are 1//54 x 1/54 or 1 in 2,916.
2,915 to 1
But this would assume you can differentiate between the two jokers.

Thank you for your help and the advice. I won't publicize it again.

I disagree with these findings. If you specify beforehand that it MUST be the 5 of hearts or specify some other card with rank and suit, then I would agree with WongBo. However, if you take two 54 card decks and you simply want to know what are the odds that the two cards chosen are exactly the same (and that they could be any card) then the odds are 1 in 107.

The reason is that the first card chosen does not matter. It could be any card in the deck and it will have exactly 1 other card which matches it. After the 1st card is chosen, there are 107 remaining cards in the deck and one of these is the matching card. Thus, the odds will be 1 in 107 that you will choose the exact matching card.

WongBo gave the correct answer based upon your wording.

I think you really wanted to know, what were the odds that they picked the same card, without regard to what the card actually was.

In that case, the odds are 1/54.

duckmankilla gave the correct answer, assuming the two decks were shuffled into one pile of 108 cards. That is not what was indicated in the wording.

Quote: DJTeddyBear

WongBo gave the correct answer based upon your wording.

I think you really wanted to know, what were the odds that they picked the same card, withont regard to what the card actually was.

In that case, the odds are 1/54.

I am in agreement with this figure if the decks are kept separate. From the OP's question, I was under the impression that when he said "both decks are shuffled", that they were "shuffled together". If they are shuffled together I stand by my 1 in 107. If they are kept separate, I agree with 1 in 54, provided that one card is chosen from each deck.

I don't think the OP meant the two decks are shuffled together. I think they're still separate, in which case the odds are simply 1 in 54 that the card drawn from the 2nd deck will match whatever card is drawn from the first.

Edit: at least three people were replying to this simultaneously...

Quote: gandcgiese

then had two seperate people each cut their deck and select one card from their deck

I should learn to read better. Yes you are correct. 1/54 is the answer he is looking for.

Quote: WongBo

But this would assume you can differentiate between the two jokers.

I've never seen a deck that included two identical jokers. I've always seen some type of difference, usually colorization of the jester's clothing.