The REM Process, Part Two: Range

While all three parts of using the REM process are important, possibly the most important is the first and that is to put your opponent on a range of hands. Many players, especially novice players, believe that they should be putting their opponent on two specific cards out of the over 1,300 combinations of hands. Now, if you can do that it's all well and good, but many get caught up in this line of thinking, get set on the idea that they have a dead read on an opponent's hand, and lose money because of it. Therefore, it is much more valuable to be able to put your opponent on a range of possible holdings and gather information as the hand progresses. A lot of times it's much easier, with the information at hand, to eliminate possible hands from your opponent's range than it is to narrow that range down or define it. Let's look at an example:

If a tight player raises from first position, you can take hands like Q♦4♦ and hands like it out of their range. In fact they’re not going to play basically any trashy hands in first position. So how can we narrow down this person’s range? We look for their tendencies. We look for physical tells, what we’ve seen them show down with in the past, and betting patterns and sizes. One thing that many players are not aware of is that they will reveal the strength of their hand by the amount that they raise before the flop. Say for example that a weak-tight player is raising three times the amount of the big blind with hands like KQ, KJ, AJ, AT, but they’re coming in for five times the size of the big blind with hands like AA, KK, or QQ. This person essentially just told you what they had, so you can make the best decision based on those types of patterns. One of the keys to playing a loose-aggressive style is that you should keep your raise sizes the same amount no matter what two cards you hold. If you’re going to raise with AA, you should raise it the same way you would with something like 8♣9♣. By doing this you are able to make it much more difficult for your opponents to put you on a specific range of hands from the very beginning.

One thing that you should be doing is reassessing your opponent’s range with each card that is dealt. What if your opponent likes to slowplay big hands such as flopped sets or top two pair? Let’s say a tight player has raised from first position. We can likely put his range around AA, KK, QQ, AK, or maybe even JJ or TT. Then the flop comes K♥7♦3♣. Your opponent checks, and you check. Now we’re thinking that we can eliminate KK or AK from his range. We see a turn card of J♠ and we put in a bet and without hardly thinking, our opponent puts in a raise. As stated before it’s unlikely that our opponent would raise with something like KJ, so now we can pretty easily put our opponent on either KK or AK. If our opponent likes to slowplay, it’s more than likely KK, which is the best possible hand right now. Your evaluations will change with each new card and action and will give you more information and allow you to narrow down your opponent’s range.

In the next section we will take a look at the second part of the REM process: equity and how you can make the best decisions possible after you have put your opponent on a range of hands.

As always, questions and comments are welcome. 

The REM Process, Part One: Introduction

This will be the first of a four-part post focused on the REM process. First we’ll look at an introduction to the process. REM stands for:

• Range
• Equity
• Maximize

Many novice players believe that the goal of playing against an opponent is to be able to put that opponent on their exact two cards. Since there are 1,326 possible starting hands in Hold’Em, this can be a daunting task. Instead we want to focus on a particular range of hands that our opponent could be playing. With the action that our opponents takes, we should be able to narrow down their range significantly.

Equity, as we’ve mentioned before, is your stake in the pot or your chances of winning the pot against the range that you have assigned to your opponent. We’ll look at an example shortly.

Finally, we look at maximize. This is the idea of making the best possible play against your opponent given the prior information you have gather (range and equity).

In this article we’ll touch briefly on these three topics and later articles will be dedicated to each process respectively.

Let’s say we’re playing in a $1/$2 cash game with six players. The player who is first to act is a very tight player who only raises to $7 with maybe top 1-2% hands such as AA, KK, QQ, or AK. It folds around to us and we look down at A♦J♦. Knowing our opponent’s range, we can then calculate our perceived equity against their hand which is, at best, around 33%. The pot is $10 and we would have to call $7 to play giving us odds of about 1.4:1 to call. By using the maximum amount of information at hand we know that we are getting bad odds to call, so our best play here is to fold.

While there is much more to the REM process, we’ll touch on that next week.

As always, questions and comments are welcome.

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.