[MikeBandy]

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Golden: It seems like I get pockets a lot more than 1 in 220. Am I missing something

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FeNeF: He means any particular wired pair.

So it's 220-1 to get dealt Aces, 220-1 for Kings, 220-1 for deuces etc.

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Right. Perhaps the following is too simplistic, but we may take it one step further. The odds against getting a pair are 16:1.

As Rufus demonstrated, there is one chance in 221 of getting a pair of a certain rank. There are thirteen ranks, so there is one chance in seventeen (221/13) of getting a pair.

We can arrive at the same conclusion using the algorithm Rufus provided:

There are 52 choose 2 = (52*51) / 2 = 1326 possible pairs of hole cards.
There are 4 choose 2 = (4*3) / 2 = 6 possible pairs of a particular value.
There are 6*13 = 78 possible pairs.
1326 / 78 = 17

Which corresponds to odds of 16:1 against.