AK: Pair by the river?

[sandycove]

So I know that with AK, the odds of one pair on the flop are 2.1:1 (32.4%).

And, having missed the flop, my odds of pairing one hole card are 3.2:1 (24%).

But what are my preflop odds of pairing one card by the river? And what is the calculation?

Also, what are the preflop odds of a pocket pair making trips by the river?

[jay_shark]

1)There are 44 cards that are non aces or kings . We wish to select 5 of these cards from 44 since it's easier if we work the complement case . The probability is 44c5/50c5 . Therefore , 1 - 44c5/50c5 = 48.74..%.

2)2*48c4/50c5 =18.36% . This may also include some flushes and some straights as well as a full house . If you want an exact calculation , where a set is the highest hand , then you have to specify the pocket pair .