Using the Equilator

Why should we use the Equilator?

In this article

• How to use the Equilator
  
• What can one calculate by using the Equilator
  

With the Equilator, one is in a position to quickly and accurately calculate the equity of a hand in a particular situation. The most important use for this is to construct accurate equity charts. The SHC and ORC would not be possible to construct without the Equilator and other similar programs. In addition, by playing around with the program one can get a feeling for various situations so as to help in making the correct decision.

A small example: Lets take the SHC into consideration. For beginners it is optimal, but it has some weaknesses, since there will inevitably arise situations in which the chart simplifies the rather complex preflop game too much.

For this reason, there are also other charts such as the ORC. But even with these two, not every situation is covered. It is extremely difficult, given the wide array of player types, to analyse every situation using only these charts. You'll be better able to take into account these additional unknown factors, once you have internalized a basic understanding of the game. This, however, requires a great deal of study and practice. Nothing will pay off more for you than having a perfect preflop game.

This article will guige you through how to use PokerStrategy's Equilator. If you don't already have the program installed, you can download it here: Equilator

Basics

The equity, or pot equity, refers to the proportion of the pot a player can expect to win when considering the average case in the long run, based on his chances of winning the hand.

If, for instance, there is 10$ in the pot and there is a 50% chance the player will win the hand, then your share of the pot - your equity - is $5, i.e. 50% of the pot. In the long run, if you run this scenario over and over, you can expect the average winnings per hand to be $5.

The average equity is the equity of a player if we assume that every player in the pot has an equal chance of winning. With 2 players, the average equity will hence be 50% of the pot, since we assume each player has the best hand 50% of the time. With 3 players, the average equity is 100%/3=33.3%.

It is the difference between the equity and average equity that provides us a basis for our decisions. Example: we are heads up, the average equit is 50% and our equity is 70%. 20% positive difference means that we can expect to make a profit on average.

Equity of a hand against a range

You are in the CO with QJs. If all the players before you fold, you knoe you can raise QJs according to the ORC. If a player limps before you, you can consult a limp-isolation chart to see whether your hand is sufficient to isolate him. If a player raises before you, you can consult a 3-betting chart to see if your cards are good enough for a 3-bet.

Suppose two players call in front of you, MP2 and MP3. What do you do now? QJs has strength in all 3 key areas. You have two high cards which are both suited and connected. This hand also plays well in multiway pots. A fold is out of the question. The question is whether or not we should raise.

Note: The opponents position is also an important factor when trying to put them on a hand range.

We can use these approximate modifiers to adjust the uppers limit of the PFR stat according to the players' position.

Most opponents on the lower limits are so fishy that you may doubt that they modify their ranges based on position. For this reason, it will play no role is our calculations. For a general approach to this, consider the following examples.

You can now start the equilator and enter these ranges. (You may also wish to consult the Handbook.)

Clicking the hand range selection button in the MP2 row opens up a window with a possible starting hand grid. You can now input all possible starting hands combinations for MP2.

You can also move the sliders below the card matrix to make a "from and to" selection. Next to it you see the selected range. You can also just type these values and the slider automatically adjusts.

MP2s value were:
VPIP: 69,81% ~= 70%
PFR: 13,56% ~= 14%

This means that he will voluntarily play 70% of his hands, but he will only raise 14% of them. The remaining 56% (70%-14%), he will limp or call with.

Since he has only limped in our example, we will set the "from" field to 14 and the "to" field to 70.

Had he raised, we would have given him the range 0 to 14. This covers the best hands he plays, not what he raises with rather than limps.

For the sake of completenes, hands which fall in the 70 to 100 range he is very unlikely to play at all, so we do not include these among his possible hands.

The choices we made result in the following range of hands, which is displayed underneath the selection bar: 22-44, A6s-A2s, K9s-K2s, QTs-Q2s, J2s+, T2s+, 94s+, 85s+, 76s, A8o-A2o, KTo-K2o, Q2o+, J2o+, T5o+, 96o+, 87o

He has a very wide range. It seems illoigical that such a player would play hands such as 85s, but not 75s. For our approximation we can therefore add some additional hands to his range using the card matrix, such as 75s, 65s, 76o.

This will, of course, increase the hand range to over 57% of all hands, however we'll also need to remove some hands such as J2o, Q2o, for instance.

This results in the following range: 22-44, A6s-A2s, K9s-K2s, QTs-Q2s, J2s+, T2s+, 94s+, 85s+, 75s+, 65s, A8o-A2o, KTo-K2o, Q3o+, J3o+, T5o+, 96o+, 87o, 76o

We now do the same for MP3.

MP3s values were:
VPIP: 66,67% ~= 67
PFR: 10,46% ~= 10

He only limped, so we can write the value 10 in the "from" field and 67 in the "to" field.

The choice now gives the following range: 22-55, A7s-A2s, KTs-K2s, Q2s+, J2s+, T2s+, 95s+, 85s+, 76s, A9o-A2o, K2o+, Q2o+, J3o+, T6o+, 97o+, 87o

Even though it would be useful to make some small modifications to the range, we won't do so in this case, to keep things simple.

Now that you've entered the relevent situation and conditions we can start the experiment. What's missing is your own hand which you need to enter in the CO row by using the card selection button. After doing this, click the "Equilate" button.

Tip: Right next to the Equilate button you have a chooice between two calculation methods, Monte Carlo and Enumerate. Under normal circumstances, the "Monte Carlo" variant is recommended. It is very fast and is accurate enough for our uses. The "Enumerate" varient delivers more accurate results and so requires more time.

The result window gives the following:

We are mainly interested in the equity column. This is your average equity for all the scenarios. Notice that your equity is significantly higher than that of any other player. We can therefore raise, since we have the edge (as long as QJs is in listed in the ORC for the position MP1).

Equity of different hands against ranges

After your first calculation, you can now take the opportunity to see with which other hands you should also make this move. In addition, we can take a look at the Equilator's "Hand Range" calculator function.

Before, we simply calculated our average equity. There are three players in this situation. This means that the average equity is 100%/3 = 33,3%. If we have a hand with at least 34% equity, we have an edge.

What we are now interested in knowing, is with what range of hands do we have such an edge against MP2 and MP3. You can delete the QJs-hand now from the CO line. Now select the "Hand Range" option next to the Equilate button.

Using the "Minimum-Equity" slider, you now put in whatever minimum equity value you require, in this case 34%.

Now click on "Equilate" to start the calculation. This can sometimes take quite some time. You'll find your result in the right-hand part of the main window (Overview). You can also find it in text at the bottom of the main window (Result window).

The Equilator's approximate calculations will end up producing some marginal hands which will be highlighted in yellow. You can check out the results individually to examine these hands. Let's look at the equity analysis for the hand, 33, for instance:

You see that with an equity of 34.235% you are only slightly above the required 34%. In such cases the difference is so small that there is little strategic advantage of using a raise. With 33, in particular, there's no advantages in raising - we hope with this hand that we see a third 3 and then get some action.

If you raise this hand, then a) you'll have less opponents on the flop and b) these opponents will be more afraid of you and are less likely to give action postflop. Additionally, it makes the preflop round more expensive for you, which is not what we want with such a hand, since it will usually have good implied odds, but if it goes unimproved, it's difficult to play. A call is better with this hand, but with 44 and better, you can raise.

The bare result tells us that we could raise with the following hands, since we'll have more than 34% equity against the ranges of the limpers (leaving out the marginal hands): 44+, A2s+, K3s+, Q8s+, J9s+, T9s, A2o+, K7o+, Q9o+, JTo

We have a huge isolating range against these opponents. A large part of this range won't be of much use to us however, since we'll still have to deal with our opponents in the later betting round, so we should restrict our raising range to those hands of this range which also appear in the ORC for our position (see Article).

You could now basically write a raising chart for use against these two limpers. All entries must also coincide with those in the ORC for your position.

You could look at the other positions in the ORC and create additional raising charts, for instance, you could have two charts for use against these limpers, one for the CO and one for the BU. K3s, for example, would not be raisable from CO, but it would from the BU.

CO vs. these two limpers: 44+, A2s+, K8s+, Q8s+, J9s+, T9s, A7o+, KTo+, QTo+, JTo

BU vs. these two limpers (Here again the equity results match the requirements of the ORC): 44+, A2s+, K3s+, Q8s+, J9s+, T9s, A2o+, K7o+, Q9o+, JTo

Finally, we must question our ability to play these hands against these limpers in order to construct a good chart. K3s is one hand which we could raise from BU based purely on equity and the ORC. But whether doing so would actually be +EV is another question, one which is beyond the scope of this article.

Equity for completing a hand in the SB

There's more to equity than using it to determine whether we should make an isolation raise, so we'll now take a look at another example where we'll consider whether completing the SB is worth it, even if we do not have the equity edge. We will be looking for an equity of at least 70% of the average equity (see Article).

You are in the SB withT6s. Before you, both the CO and BU, both fairly loose players, have limped (estimate: VPIP 50%, PFR 10%). You do the same as before. You enter the appropriate limp-ranges for CO and BU by putting 10 in their "from" field and 50 in their "to" field.

We find the following range: 22-55, A7s-A2s, KTs-K2s, Q2s+, J6s+, T7s+, 98s, A9o-A2o, K2o+, Q6o+, J7o+, T9o

Do the same for both of them and then enter your own hand, for instance: T6s.

How large is the average equity? 100%/3=33,3% Assume that in the SB you need 70% equity in order to complete the SB. 33,3%*70%=23,3%

If the Equilator yields a value between 23,5% and 33%, then we should complete the SB. If the value is smaller, we fold. If larger, then we raise.

T6s has an equity of 29,1%. This is significantly more than the required 23,5%, but it is not large enough for a raise. Therefore we complete the SB.

Your thinking is as follows:

• Can I fold this hand? 29% > 23,5% -> no.
• Can I raise this hand? 29% < 33,3% -> no.
• Therefore I must call.

Suppose you want to know what the situation is should a similar player in MP3 also call. No problem! Copy the hand-range of either CO or BU into the line for MP3 and press "Equilate".

The average equity will change in this case, however. With 4 players, it is 100%/4=25%. 70% of this is: 70%*25%=17,5%. To complete, you need at least 17,5%.

Now you get 23,2% and once again you confront the same questions:

• fold? 23,2% >17,5% -> no.
• raise? 23,2% < 25% -> no.
• call? (1.= no) and(2. = no) -> yes.

This is still a complete. Finally, we now view an extreme example with six opponents:

Average equity:
100%/7=14,3%
14,3*70%=10%

• fold? 14,8% > 10% -> no.
• raise? 14,8% > 14,3% -> yes.

We note that T6s in all cases where two players limp in front is worth completing the SB. In the SB, T6s is a "call 2" (with the opponents being passive and poor as a prerequisite).

In the last example, theoretically, we even have the equity to raise. The small advantage we have is compensated by the fact that we would have to play a marginal hand out of position postflop against six players. Therefore, despite the edge, we shouldn't raise.

Conclusion

The standard charts and tables that Pokerstrategy provides help you with the lower limits and are a good grounding for the higher limits as well. But at some point you'll want to think for yourself and, using mathematical foundations, incorporate your own strategies into your game.

The Equilator is a valuable tool for doing this. Sometimes it will make sense to play differently against opponents, and you should investigate what alternatives exist. The ability to anticipate your opponents' action and to analyse played hands in detail, is indispensible to the advanced player.

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