'The Gordon Pair Principle'
by Phil GordonAbstract:
When you hold a pocketpair preflop, it's nice to know the odds of whether or
not someone behind you holds a bigger pair. This article offers a 'quick
and dirty' method for making that calculation.
I was playing in a sit and go tournament at Full Tilt a few days
ago with my fiancée looking on. We were down to threehanded, all the stacks
were about the same, though I was the short stack. The blinds were very high 
the average stack was about 12 big blinds. I had 22 on the button. I raised
allin and was called by 66. I went broke.
"That was a really bad play, Phil. How can you go allin there?" she said.
I protested vigorously: "Honey, it is well against the odds that either of my
opponents will have a higher pocket pair. With only 12 big blinds, I'm either
allin or I fold in this situation. Doing anything else is just crazy, I think.
Especially because we're already in the money, and the difference between second
and third place isn't very significant."
"Well, I think it's much more likely for them to have a pocket pair. What are
the exact odds?" she asked.
I didn't know off the top of my head, which just seemed to give her more
ammunition for her argument. It is hard to argue odds when you don't know them.
So, I set off to do some math so I could "prove" to her that I was right. In the
process, I "discovered" a general mathematical formula that everyone can use
when arguing with a significant other.
I'm calling this rule the "Gordon Pair Principle" (GPP). I've always wanted a
theorem named after me, and so here it is. A few years back, I got zero credit
for naming the "Rule of 4 and 2," and I'm a little on tilt about it. Now, I'm
not claiming that I discovered the "Rule of 4 and 2," but I do claim naming it
and referring to it in print as such for the first time (see my book "Poker: The
Real Deal").
So, here goes.
The Gordon Pair Principle
Let C = percent chance someone left to act has a bigger pocket pair Let N =
number of players left to act Let R = number of higher ranks than your pocket
pair (i.e., if you have QQ, there are two ranks higher. If you have 88, there
are six ranks higher)
Then, C = (N x R) / 2
NUMBER OF PLAYERS REMAINING 

1 
2 
3 
4 
5 
6 
7 
8 
9 
22 
6 
12 
18 
24 
30 
36 
42 
48 
54 
33 
5.5 
11 
16.5 
22 
27.5 
33 
38.5 
44 
49.5 
44 
5 
10 
15 
20 
25 
30 
35 
40 
45 
55 
4.5 
9 
13.5 
18 
22.5 
27 
31.5 
36 
40.5 
66 
4 
8 
12 
16 
20 
24 
28 
32 
36 
77 
3.5 
7 
10.5 
14 
17.5 
21 
24.5 
28 
31.5 
88 
3 
6 
9 
12 
15 
18 
21 
24 
27 
99 
2.5 
5 
7.5 
10 
12.5 
15 
17.5 
20 
22.5 
TT 
2 
4 
6 
8 
10 
12 
14 
16 
18 
JJ 
1.5 
3 
4.5 
6 
7.5 
9 
10.5 
12 
13.5 
QQ 
1 
2 
3 
4 
5 
6 
7 
8 
9 
KK 
0.5 
1 
1.5 
2 
2.5 
3 
3.5 
4 
4.5 
Some examples:
You have pockets 10s and there are six players left to act. Someone will have a
bigger pocket pair about 12 percent of the time.
You have pocket kings under the gun in a 10handed game. You'll be up against
pocket aces (and probably broke) about 4.5 percent of the time.
Now, this formula isn't exact, but it is a damned close approximation. It's
definitely close enough to use when arguing with your significant other. Of
course, I showed her this calculation after about an hour of work and she still
thinks I made a stupid play despite the fact that my 22 is the best hand there
88 percent of the time.
Good luck at the tables. Better luck arguing the subtleties of nolimit with
your significant other.
Additional Articles:
Beating Up on Weak Players
Go Big or Go Home
Conditional Probability
Mixing It Up
SitandGo Strategy
4 Quick Tips for Better Online Play
The Truth About Tells
Asian Poker Players
Seating in Cash Games: A quick way to increase poker
profits
Lessons From the FBI
The Gordon Pair Principle
Battling with 'The Mouth'
Grinding Out the Borgata
Standard PreFlop Raises in No Limit Tournaments 