Game theory, as applied to poker, is complicated and confusing. It's easy to feel disoriented when reading books with a mathematical focus,... The Mathematics of Poker. Therefore, it is important to note that you do not need to be a master of theory nor do you need to memorize every detail of solutions to specific situations to use game theory to your advantage. The point of studying game theory is not to memorize the specifics, but to learn to understand the general principles, such as bluffing.
One of the most important lessons I've learned from game theory is that bluff-catching hands are overrated. This doesn't mean that these hands shouldn't have a place in your game, just that they should rarely be your Plan A.
In an ideal equilibrium situation, catch-bluff plays tend to be breakeven. That is, unless you can actually beat some portion of your opponent's value range (in which case the term catch-bluff may no longer be appropriate to use), or you have some blocking cards for that range, the only way to make money with catch-bluff hands is if your opponent obviously bluffs. And not occasionally, he needs to bluff a lot to make the play profitable. With the right hands it's safe to try, but it's not a particularly profitable or desirable situation to be in very often.
When facing a bet, the value of your pure bluff-catching hands, that is, those that beat all bluffs but lose to all value hands, is entirely dependent on how often your opponent bluffs. Against a villain who has an optimal bluffing frequency, the value of calling with these hands is $0, the same as if you had chosen to fold.
If both calling and folding have an EV of $0, you may ask, why call?
Why try to catch bluffs?
Remember that an opponent theoretically bluffing optimally in a game is, well, a theory. It’s an assumption we make in the absence of better estimates of his strategy. If the villain has a particularly bad strategy, where he ends up bluffing with hands that are too strong to turn into bluffs, then your previously breakeven bluff catches now become profitable plays. So calling with these hands is a great opportunity to make money, as long as you don’t start calling with so many hands that you encourage your opponent to stop bluffing altogether.
It is true that if you believe that your opponent will bluff very often in a given situation, playing bluff-catching hands becomes profitable. However, many people tend to misjudge these situations, which leads them to overemphasize this type of play in their strategy.
For example, “a good opportunity to catch bluffs” isn’t necessarily when your opponent seems inclined to bluff. I hear a lot of justified calls with statements like “I thought he was just bluffing the scary card” or “That was a good spot for him to bluff.”
Generally, the reason scary cards are scary is that they are legitimately good for your opponent's range. While it is true that they do induce your opponent to bluff, what is left out of this analysis is that they also open up a lot of value betting opportunities, since what matters is not simply how many bluffs your opponent makes, but rather the ratio of bluffs to value bets. Thus, so-called "scary cards" are not, in and of themselves, a better or worse reason than any other card for influencing your decision to try to catch a bluff or not.
The reverse is also a common mistake. Many players will mistakenly conclude that an opponent who bets a harmless card on the turn is not bluffing simply because that card “doesn’t change anything on the board.” Since it’s not a “scary card,” it seems like the opponent would never bluff and therefore must have a value hand.
For many of the same reasons the argument doesn't hold water. It may be the case that your opponent will bluff less often on a particular card or another, but there is no reason in principle that we can assume that he or she will never bluff with a particular card; it all depends on the situation.
Even in cases where you have either a blocker or a read that allows you to play bluff-catching hands profitably, these calls still tend to be only marginally +EV. In other words, you would generally be better off just folding the hand.
When you take bluff-catching hands to showdown, your EV is equal to the chance that you have the best hand, which is usually a value much higher than $0. When your opponent bets, the chance that you have the best hand usually decreases, and in addition, you must put extra money into the pot to see showdown, which means your Expected Value (EV) decreases. Turning your hand into a bluff-catcher is something your opponent tricks you into doing, not something you should try to do to yourself.
The biggest mistake when turning a hand into a “bluff catcher”
The biggest mistake I have in mind when I say “turning your hand into a bluff catcher” is when a player takes a hand that is strong enough to bet for value and instead chooses to check, claiming that he wants to give his opponent “a chance to bet.” What we’ve just seen, however, is that your hand usually doesn’t gain value when faced with a bet. If it does win, it will be the result of a mistake on your opponent’s part, which isn’t something you can always count on.
Most opponents, when they stick to the usual loose-passive fish profile, are more likely to make loose mistakes (calling) than aggressive mistakes (betting). By checking strong hands, you not only give your opponent the chance to bet, but also the chance to check.
Often, both betting and checking cost you money. When your opponent bets, your hand loses value because it is reduced to a bluff catcher, even if it is a slightly profitable one. When he or she checks, your hand loses value because his or her checking range usually consists of hands weaker than yours, including some that may have zero chance of improving by the river. You lose value both by letting these hands see a free card and by letting weak hands that would likely not call a bet get closer to showdown. In other words, you have lost the opportunity to extract value from your opponent by turning too many of your hands into bluff catchers.
This mistake is particularly dangerous when made with very strong hands, since playing “bluff catchers” with these hands also gives you the highest possible EV. This is because they are ahead, and far ahead, of even hands in the villain’s value range. It’s no surprise that premium hands have the highest value compared to other bluff catchers: nut or near-nut hands have high EV no matter how you play them (as long as you don’t fold). The question is not whether they are profitable bluff catchers or not, but whether playing them this way is the most profitable strategy or not.
The answer is that it is rarely the best strategy. Yes, if you check a strong hand, your opponent may mistakenly assume that he has the best hand and value bet hands that are much worse than yours. It is important to realize, however, that these hands would also have called a bet if you had made one.
Think about two sets of hands: those that will bet but not call a bet (bluffs) and those that will call but not bet (bluff catchers). If you try to extract value from the former, you are at the mercy of your opponent's bluffing frequency. Even if he or she does bluff often, the bluffing needs to occur often enough to make up for all the value you are losing when he or she checks a hand that would have called a bet from you.
Betting with strong hands leaves you less reliant on chance. The only thing you need to worry about here is your opponent folding too conservatively. This is a much less common mistake, since, again, most players fall into the loose-passive category. Furthermore, the type of player who will fold very often is not usually the type you want to exploit with this play anyway.
Sometimes calling with a pure bluff catch will be profitable, however, you should not look for these situations, let them come to you. Look for profitable opportunities and they will come naturally.
Suppose you raised with :As :5s from early position and got called by the button. The flop comes :Ad :8c :2h . I suggest you check the flop, as you are unlikely to get called by worse hands than yours. You are not exactly expecting a bet, which could represent a bluff or a hand that could beat yours.
What you should really expect is a check, so that you can extract value on future streets. Once you check the flop, many of the strongest hands become less possible for both of you. This means that if he or she also checked the flop, your hand will become stronger on the turn. This is true no matter what card comes on the turn.
In the process of trying to create this situation you may end up with bluff-catching hands, but this should not be your main goal.
Article translated and adapted from the original: To Catch a Bluff
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