All together I would say the odds are fifty-two to four.

The "Dead Man's Hand" is not just Aces and Eights; it is Black Aces and Black Eights. You did not specify how many players there are so I am assuming that there is just one player. Therefore, what you are asking is how many ways can you be dealt 4 specific cards out of 52 or 4 specific cards out of 51 (because the "Kicker" can be any card) and then divide that into the only two desired outcomes. To obtain the number of ways that M specific things can chosen from N things you need to use the Binomial Coefficient: http://en.wikipedia.org/wiki/Binomial_coefficient On your calculator, the key that computes the binomial coefficient is probably marked (nCr) and you must give the calculator two numbers. If you give the calculator 52 and 4 you get: 270725 If you give the calculator 51 and 4 you get: 249900 You must do both because you don't care what the 5th card is (though legend has it that it was a Queen of Diamonds in the hand held by Bill Hicock when he was shot). The odds of one person being dealt a pair of Black Aces and Black eights is: 1 in 1/{(1/270725)+(1/249900)} = 1 in 22803 If you have more than one person sitting at the table, the problem becomes much more complicated.