The flawed poker concept of limiting the field


Note: Not at the old Poker1 site. Originally published  published (2006) in Bluff magazine.


There exists a favorite poker concept shared only at the highest levels. It’s hush-hush. It’s a guiding force. It’s believed to be fully understood only by poker masters. It’s clever. It’s mysterious. It’s fascinating. It’s intuitive. It’s wrong.

I’m talking about thinning the field — the notion that driving opponents out of pots reduces your chances of being beaten. Makes sense so far, right?

They claim some big hands make more profit when a whole herd of opponents aren’t chasing them to the river. They’re right. When too many players try to draw out, the profit expectation can be reduced. Many hands earn more money on average when targeted by a few opponents than when targeted by a lot of them.

But such arguments for thinning the field are illusion. Let me tell you how it really is…

Reality

More than 30 years ago, I started explaining that any hand, except an unbeatable one, loses value when the number of opponents passes a certain point. I used a five-card poker example. Suppose you’re dealt a king-high straight flush from an infinite deck of cards. We’re playing showdown for the antes and there is no draw. Whatever you’re dealt at first is what you end up with, except duplicate cards are exchanged. (Remember, we’re imagining an infinite deck.) The best hand is a traditional royal flush.

Well, you have a hand that’s second-best to a royal, and the chances against any specific player having you beat are almost 650,000 to 1. Obviously, against just one opponent, you’re in a profitable situation. Do you want two opponents? Of course! Twenty? Sure. A thousand? Yes, again. Each added opponent adds to your profit expectation – up to a point. Strangely, each additional opponent is a little less valuable than the one added before.

Now it gets weirder. If you played against six billion people, your king-high straight flush would be unprofitable. In fact, it would be almost worthless. You’d be an enormous favorite against each opponent independently. But put six billion opponents together and you’re likely to face at least 9,000 royal flushes superior to your hand. Because poker is played so that there can only be one winner, your king-high flush would have to encounter no royals to win. What are the chances that there are no royals when you’re predicting over 9,000 of them? Effectively (though not mathematically) impossible.

Best number of opponents

That shows that there can be a cap on the number of opponents a hand can face and still be profitable. There is also a range within the possible number of opponents for which a hand remains profitable, but the profit is reduced. Does this have real-world application in poker, where practicality limits the number of players at a table to 10 or fewer?

Yes. And you should remember that many hands have a best-number of opponents. Too many or too few, and the expectation of profit is reduced. Let’s take aces before the flop in hold ’em as an example. The most profitable number of opponents for a pair of aces in a limit hold ’em game is four or five, depending on conditions. (I could argue for six, in some cases, but I won’t.)

The most-profitable number of opponents for a starting pair of kings or queens is even fewer. This is why many pros recommend thinning the field with big pairs. They hate the thought of letting opponents draw out, when an extra raise could have saved the day.

Now it seems as if everything I’ve said adds weight to the argument in favor of thinning the field, doesn’t it? Well, here’s why the concept is wrong. Indeed, it would benefit you to right-size the number of your poker customers and discourage too many calls. But there’s a problem.

When you make an extra raise (typically a reraise) to thin the field and keep players out, you’re more likely to scare away the weaker hands that would have been the most profitable to you had they called. Stronger hands are apt to play anyway. Often, the unwanted effect is that acting to thin the field backfires. You have a better chance of facing the right number of opponents, but they’re frequently the wrong opponents. And that’s why making extra raises to thin the field frequently fails.

When to thin

But sometimes you may want to thin the field, anyway. You should try it when players acting behind you are strong and players already committed to the pot are weak. That way, you often end up chasing away sophisticated opponents and playing a strong hand only against weak ones. Conversely, if strong players are already committed and weak players remain to act behind you, it’s often better to call and invite these usually looser opponents in. Raising just chases away the weak action and leaves you stranded with stronger foes.

Get it now? Thinning the field is a noble ambition, but it often backfires. If you try it, choose situations in which weak players are already in the pot and strong players can be chased out – not the reverse. — MC

Published by

Mike Caro

Twitter: http://www.twitter.com/mikecaro FaceBook: http://www.facebook.com/caro.mike Known as the "Mad Genius of Poker," Mike Caro is generally regarded as today's foremost authority of poker strategy, psychology, and statistics. He is founder of Mike Caro University of Poker, Gaming, and Life Strategy (MCU). See full biography at Poker1.com.

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