Poker Math: Deciphering Bets

Poker Math: Deciphering Bets
by Martell

A couple of weeks back, I analyzed the play of an online single-table tournament. One of the recurring themes in that article was the concept of having a purpose for every bet. Whether the goal is to isolate your hand against one opponent, to force an opponent to fold, or to get as much money into the pot as possible, it is important to have a clear objective behind any bet. Without that, it will simply be random chance that will determine whether your bet works in your favor or not. Solid players understand this concept and apply it consistently, as it is one of the foundations of winning poker.

The more difficult (though no less valuable) skill to master has its application when the roles are reversed; it is the ability to correctly decipher the purpose behind an opponent’s bet. That is how the pros figure out when to make a tough call and when to make a big laydown. The basis of this decision lies in the combination of mathematics and the relative skill of the bettor. Since a player’s skill is ultimately defined by the logic behind his actions, deciphering these actions requires accounting for the player’s skill level. Here is how I use that information for a variety of players:

Solid Player

The solid player’s bet is understandably the most difficult to decipher. This is because the best players account for their opponent’s frame of mind when making a bet. Though the solid player is always trying to get you to make a mistake, he is capable of thinking multiple steps ahead to do so. You cannot assume that a small bet is one that he wants called and a large bet is an effort to get you to fold. He will try and “get inside your head” in an attempt to figure out what you are thinking, and then tailor his bet to take advantage of that information. That means he will remember that you caught him bluffing that last time he bet, that you struggled with a fold the last time someone placed a pot-sized bet, or that you made a seemingly innocuous comment a dozen hands ago.

With this type of player, don’t try to guess what he has. Just play solid poker. Play your hands like top pair/good kicker or better strong and the rest of your hands cautiously. Sometimes you will end up getting trapped—that is unavoidable if you regularly play against solid opponents—but sometimes you will have your opponent dominated. Breaking even against the solid players is usually good enough.

Average Player

This type of player typically struggles with the concept of making one’s bet size proportionate to the pot size. He will usually either a) bet very small when he has a pair or a flush draw, b) bet way too much when he has a big hand, or c) bet way too much when he’s bluffing. If I see a small bet, I usually call if I have top pair/top kicker or better, then raise if the turn looks like a safe card. That way, I am able to apply enough pressure such that I either win the pot right there, or if my opponent calls, he is making a serious mistake.

If I’m facing a large bet, I tend to play more conservatively—I like to have two big pairs or better to call. I don’t mind laying down top pair to a big bluff, because it not only keeps me out of trouble, but it also reinforces in my opponent’s mind that bluffing is a successful strategy. Over the course of a session, I am likely to have an opportunity to take advantage of that pattern, as long as he isn’t discouraged from continuing to bluff. How do I know when I’m facing an opponent that bluffs a lot? I look at his betting frequency. If he tends to bet a majority of the time, he is likely to have a weak hand or a draw in some of those instances. Not always, mind you, just some of the time. That’s why I choose not to call with top pair; I would rather wait for a better opportunity to try and take all his chips.

One important note: as the game gets shorthanded (six players or fewer) or as I get short-stacked, I tend to call those big bets with as little as top pair/good kicker. In these instances, though, I strongly prefer to be the one initiating the betting. Then my opponent is the one with the difficult task of deciphering a bet.

Bad Player

Of course, bad players are the opponents you want to be playing against the most. They make the most incorrect bets and calls, and thus are the most likely to give away their money. The biggest problem with them is that, since there isn’t much logic to their decisions, they tend to be tremendously unpredictable.

Here I find it to be even more important to wait until the turn to apply pressure. Take for example a hand like King Queen offsuit versus Ace Five suited. The flop comes Queen Ten Three, with a flush draw for your opponent, and he bets. Presently you have the best hand, and you are also the favorite to win the hand, so it might seem like it would make sense to put in a large raise here. But the bad player will often call with his flush draw, and depending on the size of the pot, he is probably not wrong to do so! Remember, your objective is always to force your opponent to make a mistake—that is where your profit comes from.

To make the point more clear, let’s add some number to the above example. Let’s say the blinds are $25/$50, Bad Player calls, you call, and the big blind checks. The pot has $175 in it when the flop comes. You have $800 remaining in your stack (and position), Bad Player has $1200, and the big blind has $1000. The big blind checks and Bad Player bets $100. From looking at the big blind, you are fairly confident that he is going to fold no matter what you do.

Here are your two most extreme choices (assuming you wouldn’t fold): call the $100 bet, or raise all-in for $700 more. Since instinct may say to raise all-in (in an effort to either win the pot right there or force your opponent to pay the maximum for a bad call), let’s examine that one first. Once you go all-in, your opponent will need to call $700 more, and the pot will have $1075 in it. Considering Bad Player’s tendency to call, what is his expectation in this hand? With two cards to come, he will win 45.6% of the time. That means he expects to win 45.6% of $1075 (which equals $490.20) and lose 54.4% of $700 (which equals $380.80), for a net expected profit of $109.40. In this instance, you are not able to raise enough to make his call a mistake.

Now let’s look at calling the $100 bet, and then raising all-in on the turn if you still have top pair and the flush doesn’t get there. If he checks to you and you bet your remaining $700, he will still be faced with a $700 call to win $1075—but there will only be one card to come. That decreases his chances of winning down to 27.3%. If he chooses to call, his net expectation will be to lose $215.42. By waiting until the turn to bet, you have now put your opponent in a position to make a mistake with his call.

Even if Bad Player puts another $100 bet in on the turn, you still can put him in a position where a call would be a mistake. In that case, you could raise $600, and he would need to call that $600 to win $1175. In that case, his net expected loss goes down to $115.42, but it is still a negative number. Since you are the only other person in the hand, his negative expectation translates directly into positive expectation for you.

Here we have seen three different ways to play a hand like top pair/good kicker, based on the size of the bet one is facing and the skill level of the opponent placing the bet. There is no one right way to play a hand; rather, a top player will incorporate both critical thinking and flexibility into his strategy. That is because making good poker decisions involves more than just processing information correctly. It also involves recognizing what information should be processed.

Martell can be reached at martell@babblog.com.