Probability of dealer having a same-value card as me in Black Jack In a game of Black Jack, before any additional cards are given out (so everyone has exactly two cards), what are the chances that the dealer has, say, a King, given that one of my cards is a King ? Secondly, what is the probability that _someone_ at the table has a King given that one of my cards is a King?

Single deck of cards? Are we assuming that one of your cards is a king and the other one _isn't_?

After your king, there are 50 cards and 3 kings. The probability of that the dealer has at least one king is 1 - Probability of no kings. Probability of no kings is 47*46/50*49. So probability of at least one king is is 1 - 46*47/49*50.

If there are n people, including the dealer but not you and we assume you have a king and I non-king, then the probability of at least one player having at least one king is 1 - (47!/(47 - 2n)!)*(50!/(50 - 2n)!)

If you don't know what your second card is the probabilities are: 1 - 48*47/51*50, and 1 - (48!/(48 - 2n)!)*(51!/(51 - 2n)!)