Poker’s Endless Lesson; or, In Todd We Trust

Have been playing more and more Stud-Eight-or-Better lately. Doing okay, actually. Also have noticed my variance is quite low when compared to other games, especially when I play on Stars where the antes are lower than on Full Tilt or Bodog.

I’ve read up a bit, having worked through the Stud/8 half of Ray Zee’s book, High-Low-Split Poker for Advanced Players, as well as Todd Brunson’s chapter in Super/System 2. Am feeling increasingly comfortable gauging starting hands, remembering upcards, figuring out when to apply pressure, and keeping in mind the importance of scooping (what Brunson calls the “platinum rule” of the game).

Like any game, intuition plays a big role in Stud/8, I think, insofar as one has to have a “feel” (so to speak) for what others have and are gunning for, as well as whether or not the situation is right to pursue one’s own hand. Of course, moving from flop games like Hold ’em & Omaha to stud games introduces some different situations that can have a tendency to screw with one’s “feel,” making intuition less reliable as a result.

Keeping track of upcards, for instance, is a very alien-seeming obligation to Hold ’em & Omaha players. And while that can be hard enough to do, knowing what those upcards actually signify isn’t always as easy as it might appear.

Here’s just one example of how our intuition -- esp. among us players of flop games who haven’t a lot of experience with keeping track of upcards -- can potentially fail us. I had a hand a couple of days ago in which I was dealt Q-5-Q rainbow with one of my queens showing. I instinctively glanced around to see if any other queens were out, then waited for the action to come around to me.

Might be a playable hand in Stud high, but in Stud/8 this is a fairly crummy starter. Even a relative novice like me knows better than to get in too deep with a high-only hand like this. Making me even less likely to play the hand was the fact that to my right I saw two players each of whom had a king showing. There were a couple of limpers, the first king folded, then the second one -- the one to my immediate right -- completed.

Like I said, I had already decided I’d probably be letting go of my queens. But tell me this. What do you think are the chances the fellow who completed has a king underneath?

This is exactly one of those intuition-defying situations, I think. Todd Brunson writes about it specifically in his Super/System 2 chapter. His entry is divided into a list of concepts, and included is one titled “Dispelling a Long-Held Misconception.” His point there is to explain a mathematical truth that frankly seems counterintuitive until one really concentrates on the explanation. For those who haven’t read it, let me try to summarize. Brunson is making a point here about making assumptions about what our opponents might have underneath on the basis of what cards are showing on third street.

Let’s say (says Brunson) we look around the table and see one player with an ace showing. A certain percentage of the time that player will also have at least one ace as a downcard as well. Brunson goes through the math to show that there is exactly a 13.94% chance that player has at least one ace underneath (if we don’t hold one of them, that is). So if that player completes or raises on third, we keep that possibility in mind as we proceed.

Now let’s say we look around and see two players have aces showing as their door cards. What percentage of the time will one of them have an ace underneath as well? Without doing the calculations, we might be tempted to say the percentage must be less than in the previous scenario. After all, there are only two aces left, right?

That is the long-held misconception, explains Brunson. In fact, there is a higher chance one of the two players has an ace underneath. Significantly higher, actually. As Brunson shows, in this case one of the two players will have at least one ace underneath 18.35% of the time.

Going back to my hand, if I weren’t aware of Brunson’s tip, it might have seemed like there would be less chance the fellow who completed had a king underneath. Perhaps if I were a bit looser (or thick-headed), I’d have talked myself into playing my queens based on that assumption.

But no. I let ‘em go. I knew better than to pursue a high-only hand like this. (The idea that it is worth going for half the pot -- except in certain cases -- is itself a misconception a lot of players have trouble dispelling.) And I’d also read Todd Brunson’s chapter and so had an idea my neighbor might have split kings after all. The hand played to the end, with my neighbor ending up sharing the pot with a low hand across the table. Sure enough, he’d had a king underneath. Full Tilt does reorder the downcards after the hand is done, but I’m reasonably sure he had that king under there to start out.

How long would it have taken me to learned that bit about upcards and stud games? If you hadn’t known already, how long would it have taken you?

A lot about poker I don’t know. One thing I do know, however. There’s always something new to learn.