Gordon's Pair Principle
Wednesday, March 07, 2007
While surfing the web (does anyone still use the term surfing?) I stumbled upon an article by Phil Gordon. Sometimes it feels like there is only so much left to discover in poker, and then you experience something or read something and a whole new door opens. For me, this was one of those moments, discoverying the GPP or Gordon Pair Principle.
The Principle basically helps find the odds that a player after you has a higher pocket pair when you are dealt a pocket pair. I suppose it is mostly a tournament aid, but also provides some mathematical insight to those times when your Queens run into Kings or your Kings run into Aces.
The probability (C) that a player acting after you has a higher pocket pair roughly equals the amount of players left to act (N) multiplied by the amount of pocket pairs higher than yours (R) divided by 2. As a formula, it appears like this:
C=(N x R)/2
Admittedly, I am doing nothing here other than reiterating Phil Gordon's concept, but I find it to be an interesting one. So, if you are UTG in a full 10person table of a tournament and have pocket Jacks, what are the chances that your Jacks are dominated by Queens, Kings or Aces? There are 9 players left to act (N), and there are three possible higher pocket pairs (R), so the chances are roughly 13.5% (9 x 3 = 27 / 2 = 13.5%).
Its an interesting concept, especially as I head into the WSOP Circuit even this weekend. Hands like pocket sixes to pocket nines can be tricky to play from middle position, and once shorthanded, it can be very tempting to push and hope for the best. Now, I have a better way to calculate whether such a move is likely to run into trouble. Two overcards are always a possibility, but those are less scary because overcards won't dominate the hand and will have a 50/50 chance of winning at best. On the other hand, those over pairs are the real threat, often giving your opponent an 80/20 lead.
So, you are in MP (5 players left to act, including the blinds) with 88 and you have a stack of about 9x the BB. To me, this is a pushorfold situation, and at first glance, I would likely push, hoping to take the blinds and/or face a race or underpair. Let's do the math. The chance that I am facing a dominating over pair is (5 x 6)/2, or 15%. Okay, let's go for it. If I had 66 there, the chance of facing an overpair becomes (5 x 8)/2, or 20%. Suddenly, I am a little more concerned. If I'm sitting with a lowly pair of 2s, the probability jumps to (5 x 12)/2 or 30%.
Hmmm...interesting information. Practically speaking, I'm not too sure if this would effect a decision too strongly. After all, I am generally playing my table image and my opponents, so a push with 22 in middle position with a stack of 9x the BB could be used to push out slight overpairs like 3366, and suddenly the real range of calling overpairs shrinks. Likewise, if I have a severe shortstack that cannot push anyone out of the hand, I still might have to make my move because of escalating blinds. But still, as theories and deep thought about poker goes, this is an interesting concept.
Until next time, make mine poker!
posted by Jordan @ 12:27 PM,
2 Comments:
 At 1:08 PM, Fuel55 said...

Mike Albert did a much better job of the pair thing:
http://hippocampride.blogspot.com/2006/11/pairunderpair.html  At 4:34 PM, StB said...

You may want to check out Phil Gordon's Expert Insight dvd if you haven't already. Good stuff there as well.