# Beware of pairs!

Dec 19, 2005 12:29 AM

Analyzing Texas Hold’em from a mathematical perspective is a tricky proposition. This is because, unlike video poker, table poker is NOT just about math.

For those who saw the movie "Rounders," you’ll recall Matt Damon’s character commenting that he could beat most players without ever looking at his cards. To him, it was all psychological and recognizing tells.

I think that today’s game of Texas Hold’em is a combination of both. As such, there must be a mathematical component that has to be realized, and quantifying it in someway for the masses becomes critical.

One way that I like to do this is by defining how a particular hand would do against what I call a "random hand" or RH. For all practical purposes, every other player’s hand at a poker table is a random hand because we have no way of knowing what that player’s hand contains.

In reality, we recognize that most hands that get played are actually BETTER than a blind random hand and thus the value of knowing how a hand will do against an RH only has value for comparison purposes. That is to say, would you rather a suited K-9 or an unsuited J-10?

When we look at these two hands against a random hand, we find that the suited K-9 will win the hand 58.5% of the time. The unsuited J-10 will win about 53.6% of the time. This in NOT to say that you can expect to win these hands over 50% of the time when playing Texas Hold’em, as these percentage are against a completely random hand and assume playing against only ONE other player. In reality, you will likely at least start against multiple players, and their hands will be stronger than a random hand. But, we do get a sense of which hand has a higher value. We will make more straights from the J-10, but we will make more flushes from the K-9 AND the king in that hand will help us win the many hands that wind up as pairs, two pairs and three of a kinds.

Many novice Texas Hold’em players’ eyes light up when they are dealt a pocket pair. Obviously, there are no hands better than a pair of aces, and it’s tough to beat a pair of kings, but players should be very careful as the rank declines from there. You also need to be very careful how you play these high pairs. If you are in a no limit game, it’s very tempting to want to immediately go all in, but it is also very possible that you will scare everyone off and your reward for your pair of aces will be to win the blinds. Do you really want the hand that you’re going to get about once in 220 hands to net you only the blinds?

As the rank of your pair decreases, you have to be mindful that for each flop card that is HIGHER than your pair, the odds that you are no longer in the lead increases greatly. A pair of pocket kings when the flop is a 2-7-10 is a very powerful hand (especially if the flop consists of three suits and doesn’t have a lot of straight possibilities).

If the flop contains an ace, the likelihood that one of your opponents has a pocket ace is fairly high and you need to proceed with a bit more caution.

If you start with a pair of jacks, the likelihood that one of the flop cards will be a queen, king OR ace is very high, about 57%. On the other hand, the likelihood of picking up a third jack is only 11.5%. If you have a pair of 9s, the chances of a flop card being higher than your 9s increases to 75%, while the probability of coming up with trips or better is still only 11.5%.

From this, we learn that starting with a pair is not the guaranteed winner that many players think it is. Many of them can be an all or nothing situation. You have little chance at a straight or a flush, and really need to hit the trips to win with a mid-pair or less. But, if you do hit it on the flop, you can really take a big pot from your opponents. The lesson is to proceed with caution until you’re sure you’re in the driver’s seat.