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Pair Hand
The Gordon Pair Principle Applied
What is the likelihood that when you have a pocket pair your opponent has a higher pair? Let's say, for example, you hold JJ in the cutoff and the player to your immediate right, a loose-aggressive player, shoves. You have him covered. Your jacks are good against any hand other than QQ, KK or AA. Your opponent's range includes pairs as small as 66, AK, AQ, AJ, AT and suited connectors TJ or larger. What do you do? Well, don't fret. Phil Gordon provides us with an answer, the Gordon Pair Principle.
The Gordon Pair Principle Explained
The formula C=(nr)/2 where C represents the percent chance that your opponent has a pair larger than yours, n represents the number of opponents you face and r is the number of higher ranks than your pocket pair. JJ has three ranks higher, 22 has 12 higher ranks and so on. Now you have a rather simple, 4th grade math problem to solve. Using the example above, your JJ has 3 ranks higher, if you call it is likely that the button and blinds will fold leaving you with one opponent so do the math. C=(nr)/2; C=(1 x 3)/2; C=3/2; C=1.5. So there is a 1.5% chance that your opponent holds a hand larger than JJ. Given his range from late position and the fact that he loves to bully his opponents, coupled with the old adage that when you act strong you are likely to be weak, the correct thing would be to call in this situation.
Variations on a Theme
Okay, so you call based on your calculation and the likelihood of a fold from the button and the blinds leaving you heads up. The button, however, doesn't accommodate and also calls. Not terrible, but not great either. Now your percent chance of having top pair is reduced to 3% with the addition of just one more player.
Let's say you are in a loose game of no-limit hold'em. You are on the button. The player under the gun raises, UTG+1 calls and the cutoff calls. You look down and see snowmen (88). Using the Gordon Pair Principle you make a quick calculation. 3 (the number of opponents) x 6 (the number of ranks above your pair) / 2 = 9, thus there is a 9% chance of one of your opponents holding a pair higher than yours. Since you are only being asked to call a 3 bet in this case a call is the correct action. If you hit the flop with a set or quads you most likely have the nuts, if not you are through with the hand.
Taking the example above, say UTG shoves. He is an ultra tight player seeing only 12% of flops out of the blinds or about 1 in 9 hands dealt. He only plays premium hands. The table folds to the cutoff and he raises. This raise looks a lot like a raise to isolate from a solid player. You look down at snowmen. Now there are two opponents. A quick calculation suggests there is a 6% chance that one of your two opponents has a pair better than your 88. On a purely mathematical basis you might want to risk a call here but the intangibles such as the fact that one of your opponents, the initial raiser, is a rock and the re-raiser is a solid player suggests that your hand is likely to be second or third best unless it improves significantly. Given that the rock is likely to play only premium hands like AA, KK, QQ, JJ and AK suited or offsuit, it is likely he has you beaten. The cutoff has a wider range but unless you hit the flop you would likely be in a race with him as only a 55% favorite, perhaps this is the time to simply give it up and wait for a better opportunity. The correct move here would be to muck your hand.
A Chart of the Relevant Calculations
Below is a chart where the calculations are already done for you.
When deciding whether or not to bet a word of caution is in order. Using this chart is not, I repeat, is not the end of your decision making process. Rather it is a good beginning. The likelihood of an opponent holding a larger pair is good information but you also must consider the kind of player that bet in front of you and the likelihood that someone will bet behind. You also must consider whether or not your pair is likely to be the best hand at the moment or if it will only be best if you hit the flop. Stack sizes also must play a part in your decision making process. If you are short stacked then a hyper-aggressive move might just be in order. If you have a deep stack then you can afford to play a bit more cautiously with a hand that is not yet a decent made hand. All that being said, the Gordon Pair Principle does give you an important piece of information to place in your arsenal of decision making tools.
About the Author
Roger Fischel began playing poker with his friends in high school. Seven Card Stud and Five Card Draw were the games of choice back then. Over the years, Roger turned to Texas Hold 'em as his game of choice. He plays both limit and no-limit hold 'em regularly. During a long career as a teacher, Roger learned the value of sharing what he knows with others as a way to give back to the community in which he shares, thus, Rags to the River Poker was born. Roger recommends online poker tracking software for improving one's game. He also offers a listing of online poker sites which welcome US players.
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