A very simple problem

[Lexander]

[ QUOTE ]


This is another question that can be answered with super easy math (read: non-combinations)

It's 1 in 26 that you get a specific card in holdem. Multiply this by itself, and you've got the odds of getting it two hands in a row. 26x26 = 676.

Rob


[/ QUOTE ]

The one problem I have with that is that you are only accounting for one of the two cards. The probability of a repeat from either hole card is the probability that either the first card drawn the second time matches either of the previous hole cards or the second card matches either of the previous.

P(A OR B) = P(A) + P(B) - P(A AND B)

P(A) is the probability the first card matches (2 in 52)
P(B) is the probability the second card matches (2 in 51)
P(A AND B) is the probability both cards match (2 in 52 * 1 in 51)

So,
P(A OR B) = 2/52 + 2/51 - (2/52 * 1/51).

Is there a flaw in this reasoning?