How Wide Are Your Ranges?

We poker wonks tend to like to analyze individual hands. I had this and did this. Then my opponent did that. Then I did this, but actually I think doing this other thing might have been more profitable.

Then we write a thousand-word column about the merits of doing this versus doing the other thing.

Analyzing individual hands has value, but if you do it too much, you can fall into a bit of a trap. You begin to think of poker as a series of independently played hands. There's a "right" way to play this hand, then a "right" way to play the next, and so on.

Poker doesn't quite work that way. The hands aren't independent. What happens on one hand can affect the outcome of a future hand. It won't affect the actual cards dealt, of course, but it will affect how your opponents read your hand and react to your plays.

In other words, your goal isn't to make sure that every hand you play is as profitable individually as it can be. Your goal is to have the most profitable overall strategy. You'd happily give up a penny on this hand if that would mean winning a dime on another.

When you think about poker this way, you soon come upon a key insight: From your opponent's perspective, you don't hold a specific hand; you hold a range of hands. Here's a quick example: Let's say you raise preflop and get called. The flop brings three low cards, and you bet and get called. Another low card comes, and you bet and get called. The river is another low card. Your opponent checks, and you move all in.

Your opponent can't know exactly what hand you hold. But he can think of all of the possible hands you could have that you'd play this way. You could have pocket aces. You also could have pocket kings. You also could have any pocket pair that would form a set with any of the cards on board.

Let's say those hands are the only hands you would play specifically this way. They would comprise your entire possible range of hands. This is a very narrow range. You have only a few possible holdings, and they're all fairly strong.

If I had watched you play for a while and knew you well enough to know that this was your entire hand range, I would never call that final river bet with less than two pair. Calling with top pair is futile, because every hand in your range beats it.

So, narrow hand ranges have a problem: The narrower your range, the more perfectly your opponent can play against you. I'm never going to pay you off with top pair if, when you raise preflop and bet all three streets, you never hold a hand weaker than top pair. I'm going to call only with hands that I think will make money, and since your range is so narrow, I'll have a good idea of exactly which hands those are.

So, for the most part, it pays to have wide hand ranges. Generally speaking, the wider your hand ranges, the more uncertainty your opponents will have about how to react to you, and the more mistakes they'll make. (Obviously, if your ranges are too wide, you'll be shoving money in all the time with terrible hands and your opponents can just attack you as if you're playing blind.) When you have the opportunity to widen your hand ranges, generally, you should do it.

What does that mean? Let's say a loose and aggressive player opens for $30 in a $5-$10 no-limit game. A weak player calls from the button. Everyone folds to you in the big blind, and you have the 10 6. You consider three options: folding, calling, and reraising. Let's say, for the sake of argument, that you're blessed with infinite mathematical prowess for this particular decision. You can mystically calculate perfectly how each option will perform, on average, over every possible outcome.

Folding nets you $0 (if you consider the $10 big blind already part of the pot). Coincidentally, reraising to $120 nets you $0, on average, also. Calling does a little worse at -$2, on average. (I just made these numbers up to demonstrate a principle. How the hand will actually perform obviously depends on your opponents.)

So, folding and reraising both average $0. From an individual hand profit perspective, you're indifferent to either option. So, which one should you choose? Some people would say that you should fold because it reduces your variance. After all, why gamble money when you don't have an edge?

I disagree strongly, however. I think, for sure, you should reraise. Why? It widens your range. Think about what hands you'll be reraising here. You'll reraise pocket aces and kings, and perhaps queens, jacks, and A-K. You should probably reraise a number of other strong hands, as well (depending on the stack sizes and opponents).

If you reraise only good hands, your range will be narrow and weighted toward strong hands. As a result, your opponent will find your reraises fairly easy to play against. But when you add weak hands to your reraising range, you become much trickier to play against. If you can add those hands "for free," because reraising averages the same as folding, adding the hands is a no-brainer. You won't make any profit directly on the weak hands, but widening your range will net you significantly more profit when you hold aces or kings. The individual hand may not be profitable, but reraising it makes your overall strategy more profitable by getting you more action on your good hands.

I wrote a couple of issues back about the squeeze play. Your opponent raises, someone calls, and you put in a bluff-reraise. It's a good bluff to throw in against players who raise preflop with lots of weak hands in an attempt to control the table. They won't be able to call your bluff with most of their hands, and the individual play will show a profit.

But even when the individual squeeze play is, on its own, break-even or even slightly unprofitable, adding it to your game can improve the profitability of your overall strategy by widening your range, confusing your opponents, and encouraging them to make mistakes.

Aggression pays in poker. Everyone knows that. But sometimes when people sit down to analyze specific aggressive plays such as squeezing, they don't look quite so strong on paper. "Sure, you're attacking weakness, but your bluff has to work 65 percent of the time to break even, and that's a tall order."

But aggression does pay. It makes you hard to read and encourages your opponents to play badly against you. One day you'll reraise preflop with pocket aces and get called by J-10 because your opponent saw you squeeze before. You'll shove a 10-high flop and get paid. That's when you'll see the dividends.

Ed is a featured coach at StoxPoker.com. Also check out his online poker advice column, NotedPokerAuthority.com. He has authored four books on poker, most recently Professional No-Limit Hold'em: Volume 1.