Poker Articles

Understanding The Nature Of Poker By Playing Against Everyone In the World - Part 1
By Mike Caro

Let's think together. Today's column is going to be a little tougher on our brains than most. But, it won't hurt much, and we can use the exercise. What we're going to think about is important, and I want to make sure that we understand.

Someone died a few months ago. His name was Andy Morton, and he had contributed greatly to an Internet newsgroup called rec.gambling.poker. RGP is a place where I hang out a lot and participate in the discussions, and it's a place you should learn to visit - whether just to read messages or to add to the discussions. You'll need newsreader software like Forte's Agent, or you can use facilities built into America Online, Netscape Navigator, or Internet Explorer. Anyway, ask around if you don't know how to access the newsgroups. It will be worth your trouble.

Back to Andy. He was young and died tragically in a motorcycle accident. He was a rising star among poker theorists, and he offered us something that has come to be known as Morton's Theorem that was eloquently stated and brilliantly explained.

He had once contacted me to say that he agreed with 90 percent of what I said. But after Andy died, a friend of his posted something he had written - something I had never seen before. In it, Andy says he had totally agreed with a column I had written, then changed his mind. He goes on to partially challenge David Sklansky's Fundamental Theory of Poker and to describe and explain the foundation that makes up Morton's Theorem.

Who's right?

I want to talk about these things today. First of all, I don't disagree with Andy's theory. But it simply doesn't dispute what I said. And I think Sklansky's theory stands as gallantly as ever. But, more than anything else, I'm going to show you today how a simple example I used for teaching poker 20 years ago really goes a long way toward bringing all these thoughts - and more - together.

First, here is Sklansky's Fundamental Theorem of Poker, from the book Sklansky on Poker Theory, page 30. "Anytime you are playing an opponent who makes a mistake by playing his hand incorrectly based on what you have, you have gained. Anytime he plays his hand correctly based on what you have, you have lost." (David has stated that this is intended to apply to head-to-head situations, which involve only two players.)

The dispute began with a publicly posted message from Abdul Jalib (who is himself a great asset to the RGP community) to rec.gambling.poker. He said he was saddened by the loss of Andy Morton, who had once stayed at his residence and shared many powerful insights about poker. He included the words of Morton.

And these are Morton's words:

I usually enjoy reading Mike Caro's column. One from last June made a big impression on me. In it he says:

The real low-limit secret for today

The most important thing I can teach you about playing the lower limits is that you usually should *not* raise from early positions, no matter what you have... because all of those theories of thinning the field and driving out opponents who might draw out on you don't hold true in these smaller games [where] you're usually surrounded by players who often call with nearly hopeless hands.... Which is better, playing against a few strong and semi strong players with possibly a small advantage for double stakes, or playing against a whole herd of players, mostly weak, for single stakes? Clearly, when you're not likely to win the pot outright by chasing everyone out, you want to play against weak opponents, and the more the merrier. So, why raise? There, I've just described one of the costliest mistakes in low-limit poker. The mistake is raising when many potential callers remain behind you, thus chasing away your profit. Don't do that.

Until recently, this made a lot of sense to me. After all, the Fundamental Theorem of Poker states (roughly) that when your opponents make mistakes, you gain, and when they play correctly, you lose. In holdem, if all of those calling stations in the low-limit games want to chase me with their 5 out draws to make trips or 2 pair when I flop top pair best kicker, and they don't have the pot odds to correctly do so, that sounds like a good situation for me.

Yet, it seems like these players are drawing out so often that something must be wrong. Hang around the mid-limits, holdem or stud, for any length of time and you're sure to hear players complain that the lower limit games can't be beat. You can't fight the huge number of callers, they say. You can't protect your hand once the pot has grown so big, they say.

At first, I thought these players were wrong. They just don't understand the increased variance of playing in such situations, I told myself. In one sense, these players are right, of course. The large number of calling stations combined with a raise or two early in a hand make the pots in these games very large relative to the bet size. This has the effect of reducing the magnitude of the errors made by each individual caller at each individual decision. Heck, the pot might get so big from all that calling that the callers _ought_ to chase. For lack of a better term, I call this behavior on the fishes' part _schooling_.

Still, tight-aggressive players are on average wading into these pots with better than average hands, and in holdem when they flop top pair best kicker, for example, they should be taking the best of it against each of these long-shot draws (like second pair random kicker). In holdem, the schooling phenomenon increases the variance of the player who flops top pair holding AK, but probably also _increases_ his expectation in the long run, I thought, relative to a game where these players are correctly folding their weak draws.

Thinking this way, I was delighted to follow Caro's advice, and not try to run players with weak draws out of the pots where I thought I held the best hand on the flop or turn. This is contrary to a lot of advice from other poker strategists, as Caro points out, and I found myself (successfully, I think) trying to convince some of my poker playing buddies of Caro's point of view in a discussion last week.

Well, some more thinking, rereading some old r.g.p. posts (thank you, dejanews), a long discussion with Abdul Jalib, and a little algebra have changed my mind: I think Caro's advice is dead wrong (at least in many situations) and I think I can convince you of this, if you'll follow me for a bit longer...

End of Morton post.

Andy's post goes on and becomes quite compelling. You should not be satisfied with the way I'm summarizing his thoughts. Instead, if you have access to the web, you should go to DejaNews.com and search for his article. In general, he says that I am wrong because there is a point in very many multi-way hands at which every additional caller gives you the worst of it. By making incorrect decisions, they are costing you money.

And, Andy is right! I just wish we'd had the chance to discuss this, because I've actually said that - although I haven't set forth a proof as elaborate or as example-filled and as thought-provoking as he did.

David Sklansky's theorem comes under question in the same post, because - although he pointed out specifically (right under the theorem itself) that his concept may not always apply to multi-way pots, Morton thought that the theorem seldom applies to multi-way pots. I don't know which way David believes in this regard, but I think that for most situations, even in multi-way pots, you will profit when an opponent makes a bad decision. True, the error can sometimes help another opponent more than you, and can even cost you money, but - in general - I still believe that loose callers are to your benefit in real poker games, with eight or fewer opponents.

Fine. I have said all these things previously:

1. That when you raise with a strong hand with the intention of "thinning the field" of opponents, you are usually employing the wrong strategy. Why? First, because you'll usually make more money if everyone calls (this is what's in dispute). Second, if you do succeed in thinning the field, you are most likely going to chase away the players you would most likely like to have call you and be isolated against the players you wanted to fold. In other words, thinning the field usually results in you chasing out the weaker hands and failing to chase out the stronger ones. That's a problem with the strategy.

2. There really are some hands that play better against fewer opponents.

3. If you have the second-best hand possible and people are drawing to beat it, there comes a point when there are too many callers and your profit dwindles.

4. There comes a point beyond that when you hand is not profitable at all.

5. There comes a point beyond that when your hand is almost worthless.

At a seminar in the late eighties, I explained that, in a real-life, eight-handed poker game, some hands play best against an exact number of opponents. More opponents and these hands fare worse. Fewer opponents and these hands fare worse. (Of course, the exact number of opponents that most hands - in fact, all but the very strongest hands - play best against is zero! This means that you will usually make more instant profit by winning the ante or blinds outright than you will make, on average, if you are pursued by opponents.)

In discussions on RGP, people have surmised that you can have too many pathetically loose callers - that you should prefer a game where there are one or two sensible opponents to one where all opponents are out to play every hand and destroy their bankrolls. This is, perhaps, a way of applying Morton's Theorem, but it's wrong. I guarantee you that in most ring games, consisting of the usual number of opponents - you will make more money if you are surrounded by the weakest foes you can find - and the more the better. Still, I'm about to show you why this isn't so for large groups of opponents.

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