Probability pair over bigger pair?
 

Does anyone here know the probability that someone in a full table (ten players) will have a bigger pair when you hold:

1, KK
2, QQ
3, JJ
4, TT
5, 99
6, 88
7, 77
6, 66
7, 55
8, 44
9, 33
10, 22

Harrington says 4,2% with KK and 10% with QQ. If anyone knows the probability for the rest of the pairs, it would be very helpful. Thx.

Re: Probability pair over bigger pair?
 

Figuring this out isn't very difficult, but thinking about stuff like this isn't usually very important. When someone reraises your reraise by pushing all and you hold JJ, you don't say to yourself "There's a twelve percent chance that I am up against an overpair, so I call"

Re: Probability pair over bigger pair?
 

I wrote an excel spread sheet awhile ago that figures this. The probability that one or more of your nine opponents holds a higher pair when you hold xx is:

K 4.4%
Q 8.6%
J 12.6%
T 16.5%
9 20.2%
8 23.7%
7 27.1%
6 30.3%
5 33.5%
4 36.5%
3 39.3%
2 42.1%

This uses three terms of inclusion and exclusion and should be relatively accurate.

Cobra

Re: Probability pair over bigger pair?
 

Thx.
I found the math here: http://www.math.sfu.ca/%7Ealspach/comp35/
The figures seem to deviate a little bit from yours.