what are the odds of getting 2 of the same cards in a row after shuffling a deck?

Answer 1

A single deck only has 1 of each card. That is, once you've drawn one card, if you don't replace it, you will never draw that card again. There is only one 3 of hearts, for example, so after you draw a 3 of hearts, there is a 0 percent chance of getting a 3 of hearts again.

So right now the answer to your question is 0.

Now, let's say you actually wanted to know what are the odds of getting two cards of the same suit in a row. Are you replacing your card after drawing it? That is, are you putting it back in the deck? Let's assume that you are NOT.

In that case, the first card you draw just fixes the suit. Since there are 13 cards in a suit, after drawing the first card, there are 12 more cards of that suit left in the deck and 51 cards total left in the deck. Thus, your odds of drawing another card of the same suit is 12/51.

Now, maybe you want to know what are the odds that you get two 2's in a row (or 2 3's or 2 4's or whatever). In this case, your first card just fixes the face of the card. After that, there are 3 more cards that have that same face (because there are 4 suits). Yet, there are still 51 cards. Thus, the odds of you getting another of the same face (yet a different suit) are 3/51.

So, in other words, if you kept drawing two cards and reshuffling over and over again, then on average 12 of every 51 times you would draw two cards of the same suit and 3 of every 51 times you would draw two cards of the same face. (and 0 of every 51 times you would draw two of the exact same card, face and suit)

Answer 2

Do you mean two of the same suit, or two of the same value? There are 13 cards of each suit and 4 of each value, and of course 52 total (assuming no jokers). If you mean two cards of the same suit, your chances are 12/51 = 4/17, and if you mean the same value, your chances are 3/51 = 1/17. This is because, after you take one card, 51 cards are left. 12 have the same suit as your card, and 3 have the same value. Obviously, if you really mean "the same card," the chances are zero because there is only one of each card in the deck.

Answer 3

If you mean you take a card from the deck, then shuffle then take another and see if it's the same, see the top of this page:

http://weblogs.asp.net/justin_rogers/archive/2004/09/13/228656.aspx

Answer 4

Getting the same card is impossible, unless someone has been cheating and added more cards to the deck.

Answer 5

The very same card?

Impossible

Answer 6

Same card?? Zero

Answer 7

[(1/52)*(1/51)]^2