Tuesday, August 31, 2010

Your Range Or His?

When deciding whether or not to call a possible bluff, there is a method used commonly by high stakes players that many casual or low stakes players are not aware of. To put it simply, you can analyze your own range rather than your opponent’s range.

Before I get into things, I need to offer a disclaimer. The reason this method is used in high stakes games is because it’s primarily only useful in high stakes games. Against someone that bluffs too much, you should virtually always call with your bluff-catchers, and against someone that doesn’t bluff enough, you should almost always fold with your bluff-catchers. The approach in this article is primarily useful against players that are very good, players that don’t telegraph the strength of their hand and, ideally, against players that you have played a bunch in the past, and plan on playing again in the future.

The standard method of deciding whether or not to call against a possible bluff is very simple in nature. That’s not to say there isn’t much depth to these decisions, because there is seemingly boundless depth to these decisions. I’m simply saying that the general overlying principal is very simple: Analyze your opponent’s range and general tendencies. If he’s likely to be bluffing, you should call. If he’s not likely to be bluffing, you should fold.

The problem arises when you are playing against a player with very balanced tendencies. To put it another way, the above strategy is useless against someone that bluffs with optimal frequency. In general, optimal bluff frequencies are balanced such that you do not care what your opponent does with his hands that can only beat a bluff. He will break even with those hands regardless of whether he calls or folds.

This is not always true. For example, say you bet the turn with a combination of made hands, flush draws and straight draws. If the river completes both the flush and the straight, you now have so few bluffs in your range that your optimal bluffing frequency is to bluff with all of your bluffs, and your range is so strong that your opponent still can never call. I digress.

So what is the method many high stakes players use on a regular basis to decide whether or not to bluffcatch? It’s simple in its elegance.
Instead of analyzing your opponent’s range, analyze your own range! If you have the strongest possible hand you can ever have in a single instance, you should probably call. If you fold, you are just inviting your opponent to run you over. The opposite of course is true, too. If you have the weakest hand you can possibly have, you should probably fold, otherwise you run the risk of calling until you have no chips left.

Let’s look at a hypothetical example. Pretend you’re sitting in a really tough online $25/$50 cash game. It folds to you on the button, and you raise to $150. The small blind, who is a very intelligent aggressive player, reraises to $550. You call. The flop comes T-3-2 rainbow. Your opponent bets $700. You call. The turn is a queen. Your opponent bets $1,500. You call. The river is a five. Your opponent moves all-in for $4,000.

What’s the worst hand you would call with?

If at all possible, you should analyze your opponent’s bluff frequency first. If he bluffs too much, you should call a lot, and if he doesn’t bluff enough, you should fold a lot. That much should be obvious. Let’s say for the sake of argument that you think he bluffs just the right amount to put you in a really tough spot. How do you take that scary piece of information into something that helps you make a decision?
Instead of analyzing his range in this spot, analyze your own range.

Take pocket deuces for example. If you have bottom set, that is one of the strongest possible hands you can have. If you fold hands this strong, your opponents are sure to catch on and start bluffing you. You just can’t beat an aggressive player if you are folding every river where you don’t have the nuts. This much should be obvious.

Let’s say instead you have 5-4♠. You flopped a straight draw, and missed your straight, but hit a pair on the end. A pair of fives is just about the worst possible hand you can have on this river in this situation. If you are calling in this spot, that means you are basically always calling the river. This is an obvious recipe for disaster. Your opponents will stop bluffing you and rake in the money every time they have a hand.

As always, some basic math can be applied to this situation. There is $5,550 in the pot, and your opponent is risking $4,000 to win it. If you fold 50% of the time, your opponent is showing a large profit on his bluffs (-$4,000 for a failed attempt, +$5,550 for a successful attempt = profit). Naturally, if you fold only 33% of the time, your opponent is losing a ton of money on his bluffs. (-$8,000 for two failed attempts, +$5,550 for one successful attempt = loss). Some not-too-complicated algebra can determine the exact equilibrium point at which your opponent will break even on his bluffs, but this math is not really what the article is about.

So what should you call with? Unfortunately, like all complicated poker decisions, this one requires some more analysis. Think back to previous streets. Would you just call the flop and turn with A-T? What about T-9? A-Q? A-A? 9-9? What you do with all of these hands determines what makes up your range on the river. If you have a tendency to slowplay all of your big hands, that pushes some of the weaker hands like T-9 into the bottom of your range. On the other hand, if you tend to raise every time you have top pair or better, all of the sudden 9-9 is the best hand you can have. Naturally, this is a concept you need to be aware of on the flop. If your range to get to the river is too weak or too strong, you are probably making a mistake somewhere along the line before the river.

So how would I play in this spot? Preflop, I’d call with a wide range of hands. This would roughly include hands like 5-5, A-9o, K-To, T-9o, A-4♠, K-8♠, Q-9♠, 8-6♠, and all hands better of course. My exact tendencies depend heavily on the small blind’s 3-betting range, but let’s say it’s a range that makes me want to call with all those hands listed and all hands better. We’ll assume that I never reraise anything in this spot (which is often, but not always, how I would actually play).

What hands would I continue with on the flop? I would call with any pair. Good overcard hands like K-Q, and A-J (especially with a backdoor flush draw), and any hand that has a gutshot, which basically means only A-4♠ and A-5♠.

On the turn, my range gets a lot more narrow. I might continue with only hands that have a ten or better. This would basically narrow my range down to T-8♠, T-9, J-T, K-T, A-T, Q-T, K-Q, A-Q, A-A, K-K, Q-Q, J-J, T-T. This range is actually so strong that, against a really aggressive player, I might balance it by adding in a few hands that I can float to bluff the river if checked to. The best hands for this are generally the strongest draws – in this case, gutshots like A-Jo, and A-4♠. There’s also an argument to be had for calling with hands like 9-9 and 8-8 instead, or just arguments for calling the gutshots to check the river rather than bluff, but those are beyond the scope of this article.

Let’s get back to the river. With what hands should I call his all-in? Just from eye balling, the hands that make a pair of tens or worse account for a bit under half our range. That’s approximately the cut-off point we want, based on the earlier quick math. Given our flop and turn plans, our borderline hands on the river are roughly A-T and J-J. Any hands worse are close enough to the bottom of our range that we should fold to avoid calling too much. Any hands better are close enough to the top of our range that we need to call to avoid being bluffed too much.

This, of course, is just a made-up range for a made-up situation. Don’t dwell too much on these hands I actually listed. They might be designed for an opponent that is much more aggressive than the ones you are used to.

Instead, focus on why this line of thinking is often useful for high stakes players. If you are calling with the appropriate portion of your range (or some approximation thereof), you are basically making it impossible for your opponent to “own you.” If he bluffs too much, you only suffer when you fold the worst hands you can have. If he only value bets, you only suffer when you have the best possible hands you can have. If he bets hands like K-T that make no sense to bet, then you get to own your opponent by almost always making a perfect decision! Your strategy will be nearly unexploitable.

Regardless of whether or not you are up against expert aggressive players, you should try thinking about some of the concepts in this article. Next time you are in a similar spot on the river, think to yourself, Am I letting my opponent exploit me by folding too much of my range? or, Am I letting my opponent exploit me because I’m calling with virtually everything? If the answers to either of these questions are yes, it’s possible you need to reevaluate where your hand ranks among your overall range.

Before I sign off, I need to finish with the same disclaimer I started with. Even if the answer to those questions is yes, it is possible that you are playing perfectly. If your opponent is simply incapable of bluffing you, it doesn’t matter that you are letting him exploit you by folding too much. There is no downside to playing exploitively against someone that is incapable of taking advantage of it. Above all else, you should always be aware of what type of opponent you are playing against and what level of analysis is appropriate for him.

Happy Bluffcatching!

Source: http://www.bluffmagazine.com/magazine/Your-Range-Or-His%3F-Justin-Bonomo-1996.htm

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