'The Gordon Pair Principle'
by Phil GordonAbstract:
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.
 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 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
| 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 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.
Additional Articles:
-Beating Up on Weak Players
-Go Big or Go Home
-Conditional Probability
-Mixing It Up
-Sit-and-Go 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 Pre-Flop Raises in No Limit Tournaments |
