Playing pairs in Limit Texas Hold’em

I caught a cold over the weekend and had just about enough energy to lay in bed, but not to get up.  (Not entirely true, since on day one of the cold I painted four rooms of the house, but that's probably why I was bed-ridden the next two days…)

While laid up in bed I took some time to go over the stats for the last 25,000 hands I've played since the beginning of the year.  I wanted to see what the numbers said about my winning hands empirically, versus what the a priori statistics say should have won.

One of the graphs I generated was a particularly interesting one.  For pocket pairs, this is my win rate when the pair makes one of the following hands: unimproved single pair, two pair, or a set.

Now it doesn't take a poker genius to tell you that you'll win more if your pocket pair hits a set than if it hits two pair.  But when you're sitting on a pair of 66's or 77's, and you're trying to decide when you whiff the flop and a big bluffer bets if you should call it to the river, this graph provides a little guidance.  Though every situation is different, those 66's are going to win unimproved about 25% of the time.

If you're comfortable with that, perhaps because one or two other passive calling station players are in the pot with you, then go for it.  But since your odds of hitting one of the two remaining sixes is not compensated by the size of the pot, your sixes aren't likely to survive.

This graph also illustrates the fallacy of the on board two pair, and shows that it makes no difference in your win rate since it's a community two pair, EVERYBODY has it.  In fact you can see that sometimes it just gives you two pair and others three of a kind.  (That's where that red line dips below the blue)

This exercise of building out a poker game empirically from a base of 25k hands played is a fun one, and probably what I'll do for October and November.  I've build out hand standards, both preflop and postflop, based upon what I saw in my own results.  Here's another great example:

I win, very rarely, with high card and one pair that I show down.  A lot of those situations are AK, AQ, or KQ.  With the giant caveat that all poker situations depend on the context, as a general rule I need to slow down or fold hands that aren't well on their way to two pair or better on the flop.

Again, I'm sure a million people have uttered this poker wisdom in one of the 200 books I have on my bookshelf, but that's not my game.  My game is in the PokerTracker database I keep, and when I study my game and drop the things that cost me money, my game improves.

(This exercise is called "lopping off your C game", and as far as I know it was first coined by Tommy Angelo, the Boddhisattva of Poker.)

When I looked at my graph yesterday, the money I had lost calling down with 1 pair or a high card entirely offset the money I had made with the better hands.  On a more positive note, I'm just about break even for the year.

I'll post another update in 5k hands or so after I've played my new empirical hand strategy for a while.   Before that, though, I'll probably post stuff from my Vegas trip in late October.