'The Gordon Pair Principle'

by Phil Gordon

Abstract:  When you hold a pocket-pair 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.

Poker Player - Phil GordonI was playing in a sit and go tournament at Full Tilt a few days ago with my fiancée looking on. We were down to three-handed, 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 2-2 on the button. I raised all-in and was called by 6-6. I went broke.

"That was a really bad play, Phil. How can you go all-in 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 all-in 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 Q-Q, there are two ranks higher. If you have 8-8, there are six ranks higher)

Then, C = (N x R) / 2

  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 10-handed 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 2-2 is the best hand there 88 percent of the time.

Good luck at the tables. Better luck arguing the subtleties of no-limit with your significant other.

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