Fold Equity

While we've discussed actual hand equity in previous posts, I wanted to dive in a little deeper this time and give some insight on what’s known as “fold equity”. Fold equity is essentially equity that can be added to your hand if you think that your opponent will fold to a bet or a raise. This can be incredibly useful if you’re playing a loose-aggressive style because you’re going to be betting a lot of unmade hands such as straight and flush draws. By utilizing fold equity we actually increase our chances of winning which gives us extra equity in the hand. However, it’s essential to know what the chances of your opponent folding could be, and if you’re playing loose and aggressive you will lose fold equity because your opponent will be more likely to call you knowing that you could be betting with a draw. First we’ll go over what fold equity looks like and then we’ll go through some examples.

In it’s most basic terms, fold equity looks something like this:

• If it is extremely likely that your opponent will fold to a bet or raise, then you have good fold equity.
• If it is unlikely that your opponent will fold to a bet or raise then you have little fold equity.
• If your opponent is never folding to a bet or raise then you have absolutely no fold equity.

An important thing to remember is that if the way you have played the hand doesn't make much sense, your fold equity is diminished considerably. If you check the flop and the turn and then fire a big bluff you’re more likely to get called because you haven’t played the hand like you had anything in the first place.

While the mathematics are pretty straightforward, it’s not important to know that exact numbers at the table, but having an estimation will give you an edge over those who don’t understand or know them. The equation is simple and looks like this:

Fold equity = (chance our opponent will fold) x (our opponent’s hand equity)

Let’s look at an example:

We’re playing a 6-player $1/$2 cash game and we have JT on the button. Our opponent in front of us raises to $6 with KT. We call and both blinds fold so it is heads-up,  we are in position, and the pot is $15. The flop comes KQ6. Although we don’t have a made hand, this is a great flop for us. We have a flush draw and an open-ended straight draw, so any A, 9, or spade with improve our hand. Our hand equity is roughly 55% while our opponent’s is 45%. Now our opponent bets $10. This is a hand that we should be raising, but let’s consider our opponent’s fold equity. Let’s say that our opponent will fold 50% of the time to a big raise here. Looking back at the formula to determine fold equity, it will look like this:

• Fold equity = (chance our opponent will fold) x (our opponent’s hand equity)
• Fold equity = (0.5) x (45)
• Fold equity = 22.5%

Now we would add that fold equity to our hand equity which would look like this:

• Our equity = (hand equity) + (fold equity)
• Our equity = (55) + (22.5)
• Our equity = 77.5%

In this way, we are actually taking away some of our opponent’s equity and giving it to ourselves. Besides having a good drawing hand and considerable hand equity, we have added more equity to our hand because there is the chance that our opponent will fold. However, what if we’re playing against an opponent that will only fold in this spot 20% of the time? Then it will look like this.

• Fold equity = (0.2) x (45) = 9%
• Our equity = (55) + (9) = 64%

As you can see, we still hand considerable equity in the hand, but because our opponent is only folding 20% of the time instead of 50%, it diminishes our equity by 13.5% which is substantial.

Now in the example shown above we were able to know our opponent’s exact two cards which won’t happen in a real-life situation, so the best you can do is to put your opponent on a range and try to determine your fold equity from there.

Hopefully I've helped give some insight into the theory of fold equity and, as always, questions and comments are welcome.

Implied Odds

In previous posts we’ve discussed the ideas of pot odds and equity, but when you think you may be behind in a hand and drawing to hand that may beat your opponent’s there is another factor to consider and that is the idea of implied odds. Implied odds are essentially the odds that you will get paid off in the event that you make the best hand, and playing a loose-aggressive style can help you to get paid off more than a lot of other playing styles would.

Let’s look at a couple of examples of where implied odds would come into play.

Say we’re playing a six-max $1/$2 cash game and we’re on the button (last position). UTG (first to act) opens for a raise of $7 and we look down and see JsTs. This is a great hand for playing in late position because it can flop a lot of drawing-type hands and two-pair hands that may very well have your opponents drawing to a better hand that can be very profitable if played correctly. We call the $7 and both blinds fold. We see a flop with $17 in the pot and it comes 9sQh6d. We’ve flopped an open-ended straight draw and our opponent bets $12. If our opponent has a Q then we’re only look for an 8 or a K to make the better hand giving us eight outs or approximately 36% equity. Now our opponent has bet so much that it doesn’t make mathematical sense to call here and see a turn card, but what if he has something like KQ? In this respect our implied odds improve because a K would give our opponent two-pair, but it would give us the best possible hand. Depending on the type of person you’re playing here, it may very well be worth paying to see the next turn card because the chances of you winning a big pot are very good.

Now let’s look at the same situation with a slightly different flop. We still have JsTs and the flop comes KsQd2s. Here we’ve flopped another open-ender, but this time we have a flush to go with it so if we are behind to a K or Q we have about 52% of making the best hand. However, there are a number of scare cards for our opponent such as any A, which would be a higher card than his pair of Ks or Qs, and any spade brings in a flush. While we should never be folding here, our implied odds are significantly decreased because of the way the board is coordinated. If our opponent puts out even a pot-sized bet we should be ready to call here, but a lot of cards that make our hand will stop any betting from our opponent and we probably won’t make nearly as much money. While the A of spades is a good card for us because it completes our flush, our opponent will be very weary of this card and may not be willing to put any more money into the pot. An 9 of hearts, clubs, or diamonds is going to give us our best chance of getting paid off because our straight is more disguised.

Implied odds are based more on the player than the cards, so it’s important to keep track of who is playing which kind of style. You may get paid off by looser opponents, especially if you’re playing loose as well, but tighter opponents won’t be so quick to put money in the pot when they could potentially be behind. In the next post we’ll talk about how to take advantage of these tighter players using a loose-aggressive style.

As always, questions and comments are welcome.

The Rule of Four and Two

To be a good poker player it is not absolutely necessary to know every single mathematical approach to the game, but there are some very valuable and relatively simple equations that you can do while sitting at the table which could very well give you an edge over your opponents. One example of this is the mathematical principle of the “rule of four and two”. The rule of four and two allows you to estimate the amount of equity you have with a certain hand as long as you can put your opponent on some kind of range. The amount of equity you have is relative to the size of the pot and the two should never deviate too far from one another. Let’s say we have a 48% chance of winning the hand after the flop then we can call most bets that are up to the size of the pot which would give us two-to-one odds which is 50%. Here you can see how the two are related, but how do we find out what our estimated equity in a certain situation is? This is where the rule of four and two comes into play. Let’s look at an example.

Let’s say we’re playing in a six-max $1/$2 cash game and we are on the button with Ac7c. Our opponent raises from early position to $6 and we decide to call. Everyone else folds their hands so it is just us and our single opponent. The flop comes out Kc7h4c. Now here we have made a pair of 7s, but we could be already beat by a K. However, we also have a flush draw to the best hand with two clubs in our hand and two on the board and if we hit an A then our hand may be good as well. There is $15 in the pot (small blind-$1, big blind-$2, opponent’s raise-$6, and our call-$6). Before the fourth card we can multiply our number of outs, which are cards that would more than likely give us the best hand, by four and come up with our estimated equity. There are three 7s left in the deck, 3 As, and nine clubs, which would give us three-of-a-kind, a higher pair, or a flush respectively. If we multiply those outs (3 7s + 9 clubs + 3As = 15 outs) then we come up with an estimated equity of 60% of winning the hand. Now let’s say our opponent bets $10. That brings the pot up to $25. We would need to call $10 to win $25 which gives us pot odds of 2.5:1. Math indicates that we should call and see another card here. Let’s say that the turn card is the 8d. This doesn’t help our hand at all and though we still have the same amount of cards that will help us, our equity has dropped substantially because there is only one card left to come. So we take our 15 outs and multiply them by two now which gives us an estimated equity of 30%. This means that if our opponent were to bet more than 30% of the pot then we should be folding because, in the long run, this is a call that will cost you money.

Now let’s look at another example:

We’re playing in the same game and we’re on the button with the same hand: Ac4c. Our opponent again raises to $6 in early position. We call and every one else folds. This time the flop comes out Qd2h5s. Now our outs are severely diminished as is our equity. The cards that we would need to catch to make the best hand (assuming our opponent is holding one Q in his hand) are the three remaining As and the four 3s to give us the straight. We take those seven cards and multiply them by four to give us an estimated equity of 28%. But what if our opponent is holding exactly AQ? That takes away our A outs and leaves us with only the four 3s, giving us a 12% chance of winning the hand. Now unless our opponent bets roughly 1/10 the size of the pot, which would be incredibly uncommon, we should not be calling here because the math dictates it.

This is just a basic introduction to the idea of estimating equity and while the numbers are not exactly precise, they’ll only be off be a couple percent at most, so you can get a pretty good understanding of where you stand. However, there are other variables to consider such as reverse implied odds and card ratios, but we’ll cover that later. For now I just wanted to give you a general idea of how to calculate equity and how it relates to the size of the pot.

As always, questions and comments are welcome.

Building an Image

Image at the table is one of the most important things at the poker table. It will play a incredibly large part of how people perceive you and whether or not they pay you off on your big hands. The entire idea behind the game is to make as much money as possible from your good hands, and lose as little as possible with your second-best hands. Playing a loose-aggressive style, as we’ve been talking about, can allow for some huge paydays. If your opponents think that you could be betting with any two cards, they’re more likely to call you down when you have a huge hand. Let’s look at some key factors in building an image at the table:

Firstly, we’ve covered the idea of balancing your range. This, if done correctly, can let your opponents walk right into the traps that you set for them that don’t look like a traditional trapping play. Traditionally if a player makes a huge hand they want to check to appear weak and let the other players put the money in for them. In our case however, a trap would look much differently. We want to represent at all times that we have a made hand so that when we do our opponents think we could very well be bluffing. Let’s look at an example:

We’re playing a 6-max $1/$2 cash game and we’re in first position. We find ourselves with KhKd and we raise it to $6. We get a caller on the button (last position) and a caller in the big blind. The flop comes KsQc7s. This is a great board for us as it’s likely to hit a lot of our opponents’ ranges. Right now we have the best possible hand and we want to make them pay to draw to a better one. If someone is holding two spades or a hand like JT, they’ll likely come along. KQ is absolutely calling every time, as they should. The great thing about having a loose image here is that WE could very well be the ones holding two spades or JT. There are some scare cards for you that could come such as an A or a 9, but your opponent would have to be holding exactly JT to have us beat.

Poker is all about long-term results, so we shouldn’t be afraid to show our bluffs or second-best hands when necessary (only at showdown) and we certainly shouldn’t let a picked-off bluff slow us down. Everyone gets bluffed in this game, but not everyone gets right back into the game afterwards.

As always, questions and comments are welcome.

Floating

In today's poker world, the continuation bet, or C-bet, is incredibly common. The continuation bet is when a player raises before the flop and then continues to bet after the flop is dealt. We talked about having a balanced range is the previous post, and this is an essential part of that balance. Statistically speaking, a player will only connect with the flop about one out of three times. However, if you were to look at your opponents' stats, you would notice that they are betting post-flop much more than 1/3 of the time. They're basically betting on the fact that you didn't connect with the flop in any way, and that you will fold to another bet. So how do we counter this move? How do we defend ourselves against a player who is c-betting 70% of their hands? We can utilize a technique called the "float".

The float is a more advanced play which helps to counter the continuation bet by calling your opponent with nothing. If your opponent is c-betting a vast majority of the time then they obviously can't always have a hand. If your opponent c-bets and you call behind them, this is going to get their attention. If they don't have anything, they may very well shut down the betting on the turn and we can bet here and take down the pot. It's basically announcing to your opponent that you have some piece of the board and that they should continue with caution. Floating is a play best used when you have position on your opponent and the pot is heads-up between the two of you. Let's look at a couple of examples:

Let's say that you're playing a six-max $1/$2 cash game and you have JhTh on the button (last position) and the player in front of you raises to $6. You call and both of the blinds fold. The flop comes 8d5hKd. Now this doesn't help our hand whatsoever, but this is also a  pretty dry board meaning there isn't a lot in the way of straight draws. There is a flush draw with two diamonds out. Your opponent continuation bets $10 into a pot of $15 and you call. There are some cards that could potentially help you on the turn such as a queen or nine, which would give you a straight draw, and any heart will give you a flush draw. This is considered to be "backdoor equity" meaning that if one of these cards comes then you may have a chance of making the best hand by the river and won't have to bluff anymore. However, there are other cards that could potentially help us as well. Another diamond puts a flush on the board and may be a scare card for your opponent, so we could use a diamond as a "bluff out". Now the turn comes the 6d and your opponent shuts down the betting and checks. This is a good opportunity for us to lead at the pot and try to take it away. In order to do so, you should bet like you would with any made hand, so since the pot is $35, you should be betting somewhere around $22-$28. If your opponent folds then you've just taken a pot without making any kind of hand. The float is an effective way to bluff in position and take down pots that you would have otherwise had no chance of winning.

As mentioned before, this is a play best used in position against your opponent. However, it's also important to have a read on your opponent and be sure that they can be c-betting with nothing some of the time. It's equally as important to pick your spots with this play and not overuse it or your opponents will pick up on it and you may find yourself in some sticky spots later in the game. If overused, you may find your opponents checking on the turn so you can bet and then they can raise. Any type of bluff is essential to the game, but should never be overused. Otherwise you will find that you have become an easy target for the other players at the table.

As always, questions and comments are welcome.

Balancing Your Range

Now that we’ve talked a little bit about finding your range of starting hands, I’d like to talk a little bit about how to balance that range. This is a relatively simple concept which is meant to keep your opponents from being able to put you on a certain range of hands. For example: say you raised three times the big blind with hands like 77, 88, 99, AT, AJ, but you raised four times the big blind with premium hands like AA, KK, AK, QQ, it will be much easier for other players to pick up on those tendencies. In its simplest terms, range balancing is where you play the exact same way with a wide range of hands in certain situations. Much of this is going to depend on how often you are continuation betting, or betting after the flop after you’ve raised pre-flop.

Let’s say you’re playing a 6-max 1/2 cash game online and you are in late position with JhTh. You raise it to six dollars and get called by the big blind. The flop comes out JdTc4d. With the big blind having only called, you can be pretty sure that you’ve got the best hand. You have a made hand and should bet it for value here. However, any hands like KQ, Q9, or any two diamonds are drawing to a better hand than yours. You want to keep up the betting and give them bad odds to draw to a better hand.

Now let’s look at a different example with the same hand and pre-flop action. You raise $6 in late position with JhTh and get called by the big blind. This time the flop comes out Qh9c4h. This time you don’t have a made hand, but you should be betting it like you do. This is called a semi-bluff because, although you don’t have a hand yet, you have considerable equity (~52%) to make the best hand. You hand an open-ended straight draw and a flush draw. Any K, 8, or heart will make your hand and more than likely give you the best of it. Of course, in situations like this, there are implied odds to think about, but we’ll talk about that later.

Now we’ll look at one last example. Same game, same hand, same situation. You raise to $6 in late position with JhTh and get called by the big blind. This time the flop comes out Ah6d5c. This flop in no way helps your hand, but because you raised before the flop, you can bluff and represent an ace here. Sometimes by just keeping the pressure on and betting the flop you can take down the pot then and there. This obviously won’t always be the case, but this is why a balanced range is so important to have in your arsenal. If your range is balanced then your opponents will know that sometimes you’ll have a made hand here and sometimes you won’t. The idea is to bet it the same way you would if the ace did help you.

Essentially, having a balanced range will make it much harder for opponents to play against you because you could very well be holding any two cards.

As always, comments and questions are welcome.

Playing Your Range 9/05/2014

In this post I’d like to discuss starting hand ranges for the loose-aggressive player. One of the things that I think appeals to some many players about playing a LAG style is the creativity it allows you to employ in your play. In the world of poker today, it’s not uncommon to see people 3-betting, 4-betting, and even 5-betting light. While the 5-bet bluff can often be incredibly exciting and sometimes lucrative, it’s imperative to know when to pick your spots.

            Let’s say you’re playing a 6-max cash game and you find yourself holding 9T suited in late position with a raise in front of you. This hand has good flopping value for many reasons. Firstly, it’s less likely to run into hands that have you dominated that will call or re-raise you. Secondly, with a hand like this you can flop a lot of good draws that will more than likely hit your opponent’s range, so you can really apply pressure with multi-way draws or make them pay to draw if you flop a hand like two pair.

            Now let’s flip the tables. What if you’re in first position (UTG) with the same hand? While this could certainly be a raising hand, it loses a lot of its value when you no longer have position on your opponent. As the saying goes, “position is power” in poker. Sure you can flop big with it, but as stated above, your opponents could really put the pressure on you with combo draws or make you pay to draw. Playing this hand from out of position (OOP) also may decrease your implied odds of getting paid off. Let’s say that you call with 9hTh and the board come JhQs5h. You’ve flopped a huge draw, but if you call all the way down with this hand you’re much more unlikely to get paid off should you make your hand. However, with a loose-aggressive approach to the game, there is always the option to represent a made hand here and take the betting lead. This is something we’ll get into in later posts.

            Taking a LAG approach to the game will open you up to more variance, as you’ll be playing more hands and your raising range may essentially turn into your 3 and 4-betting range. In the next post about playing marginal hands we’ll cover this topic more extensively. As always, comments are appreciated.