(odds) Pocket pair vs. pocket Overpair

Case KK: What's the chance of your KK bumping into AA?

- There are 6 kinds of AA.
- 50 cards remaining, 1225 possibilities.

Sample calculation for 9 opponents:
1-((1225-6)/1225)^9 = 0.043 (1 in 23)

9 opponents: 1 in 23
7 opponents: 1 in 30
5 opponents: 1 in 41
3 opponents: 1 in 68
1 opponent: 1 in 204

Case QQ: What's the chance of your QQ bumping into KK or AA?

Sample calculation for 9 opponents:
1-((1225-12)/1225)^9 = 0.0848 (1 in 12)

9 opponents: 1 in 12
7 opponents: 1 in 15
5 opponents: 1 in 21
3 opponents: 1 in 34
1 opponent: 1 in 102

Case JJ: What's the chance of your JJ bumping into QQ, KK or AA?

Sample calculation for 9 opponents:
1-((1225-18)/1225)^9 = 0.124 (1 in 8)

9 opponents: 1 in 8.0
7 opponents: 1 in 10
5 opponents: 1 in 14
3 opponents: 1 in 23
1 opponent: 1 in 68

Case TT: What's the chance of your pocket 10s bumping into JJ, QQ, KK or AA?

Sample calculation for 9 opponents:
1-((1225-24)/1225)^9 = 0.163 (1 in 6.1)

9 opponents: 1 in 6.1
7 opponents: 1 in 7.7
5 opponents: 1 in 11
3 opponents: 1 in 17
1 opponent: 1 in 51

Case 99: What's the chance of your pocket 9s bumping into 10s or above?

Sample calculation for 9 opponents:
1-((1225-30)/1225)^9 = 0.200 (1 in 5.0)

9 opponents: 1 in 5.0
7 opponents: 1 in 6.3
5 opponents: 1 in 8.6
3 opponents: 1 in 14
1 opponent: 1 in 41

Case 88: What's the chance of your pocket 8s bumping into 9s or above?

Sample calculation for 9 opponents:
1-((1225-36)/1225)^9 = 0.235 (1 in 4.2)

9 opponents: 1 in 4.2
7 opponents: 1 in 5.3
5 opponents: 1 in 7.2
3 opponents: 1 in 12
1 opponent: 1 in 34

I guess you have a good idea now. In headsup play it is just very rare to push into an overpair. Even with pocket 2s you are looking into 1 in 17. So does this mean that you should always push pocket dueces? 16/17 of the time you are slightly ahead (usually 55:45), and 1/17 of the time you are doomed.

problem is, lots of those slight edges fold to you while the higher pockets mostly call you all the way. So depending on your stack, pushing heads up with 22 isn't a great move. And to the math, using pokerstove, 22 vs. another non-pocket pair is 52.3% vs. 47.7%. Against a pair, it's 81% vs. 19%. But because of how much more you get the first scenario, you are ahead 50.3% vs. 49.7% according to pokerstove against a random hand. So if you could be guaranteed any hand would call you just go all-in there, you have a slight edge. But almost every hand that has you beat (and if they have you beat they have you dominated) calls here and lots of hands you have beat fold here. Some good thoughts though, very informative overall, just don't agree with your analysis of playing 22 heads up.

I do know that on a 6 handed table , the odds of KK running into AA is about 44 to 1...thats what I heard Gabe say on HSP anyway

gabe is the best announcer.


anyway, cool odds list, good to see what my chances are