Percentages of player holding overcards vs pairs
Join Date: Apr 2005
Posts: 32
Say a player opens for a raise with 1010+,AQs+, AKo+
What are the percentages of him holding a pair 10+ vs just holding those overcards?
Also, could you please show me how to calculate this so I can try it for other ranges and not have to ask dumb questions. Thanks!
Adam
Join Date: Sep 2006
Posts: 3,655
There are 4c2*5 combos of pocket pairs from 1010+ and 4+4 + 4*3 = 20 hands that belong to AQs+ and AKo.
So the probability that he holds a pocket pair is 30/(30+20) = 60%
4c2 is the number of ways to select a pair from any fixed rank since we are selecting 2 cards from a total of 4 cards. There are 5 ranks of hands we're interested so we multiply the two numbers together. Now notice that there are 4 AQs hands , 4 AKs hands and 4*3 = 12 off-suit AK hands.
