How to boost your skills with the PokerStrategy.com Equilab

Introduction

In this article

• How to make in-depth hand evaluations using Equilab
• How to use the Scenario Analyser
• How to further enhance your skills with the Equity Trainer

Download the PokerStrategy.com Equilab now for free

It’s not unusual for a poker player to face tough decisions; you may even have to face one on every street throughout a hand. In order to master these situations, it’s crucial to have a good understanding of hand ranges and hand combinations, and how they influence what is probably the single most important factor to consider for every decision made in poker: equity.

Most decisions initially appear to be tougher than they actually are because there’s too much information accumulated across several streets of play, making it almost impossible to find the correct line to take with only a few seconds left in the timebank.

This article will show you how to use the Equilab to break down scenarios to a level where they can be evaluated properly. It will also show you how you can use the information you gain during the process to become a better poker player and make better decisions at the table.

Basic features

Below we have a sample hand that was taken from the hand evaluation forums. We’ll use this hand as an example to help introduce you to the basic features of Equilab.

PokerStars - €0.05 NL (6 max) – Hold'em - 6-players

Stacks &Stats
UTG: €5.00
MP: €5.00
CO: €5.64
Hero (BU): €5.00
SB: €5.00
BB: €9.75

Preflop: (€0.07) Hero is BU with
3 folds, Hero raises to €0.20, fold, BB calls €0.15

Flop: (€0.42) (2 players)
BB checks, Hero bets €0.30, BB calls €0.30

Turn: (€1.02) (2 players)
BB bets €0.50, Hero...

Hero’s hand

The first thing you need to do is to enter your hand in Equilab. To do this, click the button marked with the green circle in image 1 below. You can easily select Hero’s holecards () from the pop-up window.

Villain’s range

The next thing to do is to select a range for Villain. To do this, click the button circled in blue (image 1).

Now you can easily mark the hands you think he will call in the BB against our BU open raise. Here, you've given him some small to medium pocket pairs (22-TT) as well as some suited connectors and broadways. Let’s assume he will 3-bet JJ+ and AQs as well as AK, therefore you don’t put them in his call range.

If you think he will call looser or tighter you can of course select either more hands or fewer hands. You can see the range selection in image 2.

Predefined ranges

There’s also the possibility to choose from predefined ranges (this option is indicated by the green circle in image 2). However, these are mostly based on fixed limit charts. If you play No Limit, you should only use the "Pokerstrategy.com - No Limit" ranges. The other ranges are in most cases much too loose – even most loose-passive players would not call that many hands.

The range slider

Finally, there’s a very useful feature that allows you to quickly make rough estimations about an opponent’s range: the range slider (blue circle, image 2).

If you have stats from your opponent you can use them easily to assign a range to him:

The right part of the slider symbolises the opponents VPIP, the left part of the slider symbolises the PFR.

So if, for example, an opponent has a VPIP of 20 in the big blind and a 3-bet percentage of 10% (the 3-bet percentage equals the PFR in this situation), you can set the right slider to 20% and the left slider to 10%. The Equilab will automatically take the 10% range of hands in between and select them so you can proceed with the evaluation quickly.

Notice that this is a very quick way to analyse a spot, but at the same time it’s not as accurate as if you had put all the data in yourself.

It’s worthwhile playing around with the ranges for a while, to see how big each range actually is in terms of the percentage of total hands (see value in orange circle, image 2) and to get a better understanding of what certain statistics actually mean.

In image 2 you can see the range you have given him here. It contains 12.22% of all the hands.

Image 1: Equilab main window

Image 2: Hand selection window

When you have assigned a range for your opponent and put in a hand for Hero, you can click the "Evaluate" button and the Equilator will show you that preflop, you have 76.81% equity against his range.

Entering the flop cards

The next thing you have to do is enter the flop. Take the cards "6h2s8d" as an example. You can either enter them manually into the orange-circled box (image 1), or click the button next to this box and select the cards.

After we have entered the flop cards and clicked “Evaluate”, Equilab shows that your equity has in fact increased; you now have 81.13% equity against his range.

Adjusting the ranges

However, if the opponent checks and calls your bet, we have to alter his range, as he doesn’t usually call with all hands – in this case if he has something like or he will almost certainly only play check/fold.

To adjust his range you need to open the hand selection window again (blue circle, image 1) and deselect the hands which you would expect him to fold.

As you can see in image 3, it is assumed here he folds some overcards without draws as well as hands like 33, 44 and 55.

Notice that some strong hands are also excluded from the range, such as sets, because you would expect him to check/raise them on the flop – so once he check/calls they are not in his range anymore.

Image 3: Hand selection window for the check/call range on the flop

A further thing to bear in mind is that the selected range now contains 66 hand combinations, or 4.98% of all the hands.

This can be important if you want to see how often he folds on the flop.

He had a 12.22% range on the flop, now he only has 4.98% of all hands. This means he folded 12.22%-4.98% = 7.24%. Or, as a percentage of his flop range: 7.24/12.22 = ~59%.

What this means is that if the assumptions hold true, we have about 59% fold equity on the flop.

Therefore, as you invested €0.30 in a €0.42 pot, you can make a profitable contibet with any two cards.

You risk €0.30 to win a total of €0.72, so you need €0.3/€0.72=41.6% fold equity – and you've already seen that he folds more than that on this board.

The next question you need to ask is: which hands is he donk betting on the turn with?

This is the hardest part when you evaluate hands because there is no definite answer. From now on, all assumptions will directly influence the results of your evaluations.

It is also the part in which people make the biggest mistakes. For instance they say something like ”his donk bet doesn't make any sense, he has to be bluffing!”. While this might be correct in a vacuum, something should jump out at you.

After he check/called on the flop, there aren't many bad hands in his range anymore. You can assume he’s not doing this with unimproved overcards, so you can deselect AT, AJ and AQ.

With the rest of his range he might very well bet first: he could bet TT and 99 for value as well as straights and 2 pairs. So his range should look something like this: {TT-99,77,T9s,98s,87s,76s}.

When you enter the turn card and click “Evaluate”, you’ll see you have 48.69% equity against this range. You have to call €0.50 with a pot size of €1.02. Therefore you need €0.5/(€1.02 + €0.5 + €0.5) = €0.5/€2.02 = ~24.75% equity. As you have over 48%, you should definitely call a bet.

So the key concept to take with you is that you should only reduce the opponents range and never add hands that weren't in the range on previous streets.

If he folds a hand on the flop, he cannot have it in his range on a later street. Of course we can go back to the flop and assume he’s calling some more hands to see how this influences the results for the entire hand. However, once we assume he folds a hand on one street we should stick with the assumption.

A good way to quickly improve your understanding and knowledge of the game is to take a hand, evaluate it and then alter the parameters.

It’s nice to know that we should fold in the sample hand above, but what if next time the board isn’t next time, but ? What effect does this have on his range and on the equity you have against it?

A few more suggestions of aspects to to investigate:

• (1) How does a affect his range and your equity against it?
• (2) What do you do if the board is ?
• (3) What do you do against a check/raise on the flop (i.e. what’s his range for check/raising and what’s your equity against it)?
• (4) What if you had 99 instead of QQ?
• (5) Would you still want to call the turn bet with A8s?
• (6) What if he checks the turn to you, should you bet?
• (7) Let’s say you call and the river is a K. Do you want to call another bet? Should you bet yourself if he checks to you?
• (8) If he check/calls the turn and the river is a 2, should we value bet?

You should try to work out the answers to the possibilities above by yourself. At the end of the article you can see what the answers should look like.

Suit selection

Sometimes we assign certain suited hands to Villain’s range, but actually we only want to hands in one suit (for example not 65s-T9s but only - ).

You can either put all of these hands in manually, or you can use the suit selection tool. To do this, simply click the "Suit selection" button in the range selection window (blue circle, image 5) and then mark the hands you want to assign to the range. Click "Suit selection" again and a window will pop up in which you can select which suits you actually want to have in his range (blue rectangle, image 5).

Image 4: range selection window with Suit selection option

Image 5: suit selection window

Below is an example to illustrate what happens when cards are removed:

Let's say you're in a spot preflop where you give your opponent a range of {AA, KK, AK}. So he has 6 combinations of AA, 6 of KK and 16 of AK.

His range doesn’t change whether we hold 65s or A5s (for example) - he still has {AA, KK, AK}.

However, the distribution of the cards changed. When he have A5s there's one A less in the deck, so the number of combinations of AK and AA is reduced – AA from 6 to 3 and AK from 16 to 12.

You can make Equilab to take this effect into account by checking the "Display card removal" box on the bottom left of the range selection window (image 6, blue box). If the card removal has an effect in your current hand, you’ll immediately see a difference in the number of hands the range contains.

If you do this for the flop range in sample hand 1, you’ll see that the number of hands decreases from 162 to 126 (12.22% -> 9.50%). You can immediately see which hands are influenced by the card removal as the squares of the affected hands will appear in a slightly darker blue.

This relates to the card removal effect. By checking the "Display # combos" checkbox on the bottom left of the hand range selection window (image 6, blue box), the Equilab will show you how many combinations of each hand Villain has in his range. You can see this by the small numbers in the bottom right corner of every hand you've selected (image 6, orange circles).

Generally, it's easy to remember the number of combinations: offsuited hands have 12, suited hands have 4 and pocket pairs have 6 combinations (this is only true if no card is removed).

Note that you can select the "Display card removal" and "Display # combos" features simultaneously.

Image 6: card removal and number of combinations

Image 6a: card removal and number of combinations

This is a useful tool to make future hand evaluations easier and enable you to go through hands more quickly. You can use this to save hand ranges for spots that re-occur on a regular basis.

For example: we can save the range we gave Villain for calling our preflop open raise in sample hand 1, as this is a scenario that occurs frequently. Next time, analyse a hand where you play BU vs BB, you can just select your user-defined range instead of having to go through all the hands again.

To do this you have to select the range as shown in image 2 and then simply click the "Save" button (image 7, blue box). A small window will pop up where you can enter any name (image 7, orange box). I recommend using a descriptive name, as it will be a lot easier to find the scenarios you’re looking for later than if you just number them, for example. As you can see, here it's labeled it "BU vs BB reg flatcall".

Once you confirm by clicking "OK", ’the range will appear under "user-defined ranges" (image 7, green box). To use one of your predefined ranges, proceed as described in 1.2 – predefined ranges.

You also have the option to organise your user-defined ranges by creating folders. You do this in the same way as you would when saving ranges. Just click "Create folder", label it and save it. After that you can organise everything simply per drag&drop.

Image 7: user-defined ranges

The Scenario Analyser

The Scenario Analyser is a very powerful tool that allows you to quickly look at a lot of different scenarios depicting how a hand can and will play out in terms of your equity.

To evaluate the current hand into the Scenario Analyser, simply enter the hands and hand ranges into Equilab and click "Scenario Analyser" tab on the top bar.

Let’s have another look at Example 1:

As previously established, you should definitely call the opponent's turn bet in sample hand 1 because you have the equity to do so.

However, there are scenarios in which you will not be able to continue - for example, if a scare card comes on the river and the opponent bets again. So now you need to figure out which river cards are good for you.

To do this, put the opponents range at {TT-99,77,T9s,98s,87s,76s}, as well as your own hand and the board in the Equilab and open the Scenario Analyser.

Image 8: Scenario Analyser main window

Now we can quickly look at how the hand will perform on different river cards by clicking the "Analyse river cards" button.

Several bars have appeared in the main graph, they symbolise the equity we have on each river card. You can see the cards on the right, in ascending equity order.

In image 8 you can see a slider circled in orange (bottom right). With this you can set the minimum amount of equity want to have against the opponent's range. The Scenario Analyser will automatically filter out the cards on which you have less than the desired amount of equity. They appear grey.

This is a particularly useful feature if you are trying to determine with which cards you can call a bet from Villain.

Let’s say for example you expect Villain to bet two thirds of the pot on the river with his entire range. So you get odds of 5:2, or in other words you need roughly 28.6% equity. By setting the slider to 29% (image 9, circled orange), you can see that, in this case, you could call a river bet on all cards except for 5, T or 9 (image 9, circled blue).

Image 9: Scenario Analyser - equity slider

Notice that you can play around with the parameters of the hand without having to leave the Scenario Analyser window.

The Equity Trainer

The Equity Trainer is another powerful tool that enables you to train your understanding and knowledge of equity in a lot of different situations.

To open the Equity Trainer, simply click "Equity Trainer" on the top bar of the Equilab main window. Now you can choose from predefined scenarios or define your own ones.

To work with a predefined scenario, click the dropdown menu, select one of the situations you want to train in and click the "Start Training" button.

The Equity Trainer now presents you with different selections of flops by taking cards from the predefined range for Hero, so you can estimate how much equity this hand has versus Villain's range.

You can either type in the amount of equity you expect to have per hand, or use the slider to adjust the number. By clicking the "Result" button you can see how much equity you actually have and move on to the next scenario.

If you want to end the training, you can do so by clicking the "Final results" button. The Equity Trainer will give you a summary of your performance and allow you to export each of the scenarios you have encountered for further evaluation.

You also have the option of define your own scenarios so you can target specific spots in which you want to train your knowledge of equity. For example let’s take the preflop scenario of sample hand 1 and enter it into the Equity Trainer.

To do this, select user-defined mode by checking the corresponding box in the Equity Trainer main window (image 10, orange circle).

We now need to give Villain a range (image 10, green box). We can use our user-defined range again by opening the range selection window and using the "BU vs BB reg flatcall" range we saved earlier on.

For Hero's hand we’ll use for now (image 10, blue box), but you can also enter an entire range (preferably the one you open raised from the button).

By clicking the "Start Training" button you'll face Villain's calling range on different boards.

Image 10: Equity Trainer main window

There are lots of common scenarios that you can easily practice with the Equity Trainer, for example calling 3-bets in position.

For example let’s say we’re open raising the button and BB 3-bets. We assume he has a fairly wide range of {66+,A8s+,K9s+,Q9s+,JTs,T9s,98s,87s,ATo+,KJo+}.

With AJo we have 49.84% equity against this range, so we decide to call.

Many poker players have a hard time continuing when they don’t hit anything on the flop. Usually, the problem is that they don’t know how much equity they have on certain boards – now, you can easily fix this leak by training for this spot with the Equity Trainer!

Putting it all together

You should now be able to use the basic features of the Equilab to evaluate almost every situation you may encounter at a poker table. However, as always in poker: practice makes perfect. Below are two more sample hands for you to analyse. In section 5 of this article you will find evaluation solutions.

PokerStars No Limit Hold'em, $0,50 BB (5-handed)

Stacks & Stats
UTG: $58
MP: $48.50
Hero (BU): $50
SB: $50
BB: $53.50

Preflop: ($0.75) Hero is BU with
2 folds, Hero raises to $1.50, 1 fold, BB calls $1

Flop: ($3.25) (2 players)
BB checks, Hero checks

Turn: ($3.25) (2 players)
BB bets $1.50, Hero...

Question:

The question on the turn is whether to raise or call the bet.

You should begin by trying to work out your equity against Villain’s range and then use the scenario analyser to find out how many river cards will help your hand.

Hint: How does our check on the flop influence Villain’s hand range for betting the turn?

PokerStars - €0.10 NL (6-max) – Hold'em - 6-players

Stacks & Stats
UTG: €10.00
MP: €10.00
CO: €10.30
Hero (BU): €10.00
SB: €10.00
BB: €18.60

Preflop: (€0.07) Hero is BU with
3 folds, Hero raises to €0.40, 1 fold, BB raises to €1.20, Hero calls

Flop: (€2.45)  (2 players)
BB bets €1.40, Hero...

Questions:

• (1) What’s your equity against either a 6%, a 10% and a 15% range preflop? Do you want to call a 3-bet against all 3 of those ranges?
• (2) What’s your equity against either of the ranges above on the flop and how should you proceed once the opponent bets - should you fold, call or raise?
  Hint 1: What part of his range is Villain folding to a raise? What does that mean in terms of the fold equity you have?
  Hint 2: You can evaluate the call using the Scenario Analyser to simulate different turn cards.
• (3) If Villain 3-bets 10% preflop and cbets 100% on the flop, how would you do with 99 instead of AJo?
• (4) What if you have 99 and the flop is , or (again vs a 10% range that cbets the flop 100% of the time)?

Conclusion

In this article you learned about the basic features (as well as some more advanced ones) of the PokerStrategy.com Equilab. You should now be able to break hands down to a level where they can be evaluated objectively.

On the lookout for leaks

A great way to improve your game is to evaluate hands and post them in the sample hand forums afterwards. In this way, other members and hand judges can have a look at your work and give you tips about how to improve.

They may also find mistakes you’ve made and help you to understand where you made them and why.

Evaluations & answers

For all the answers the opponent’s preflop calling range remains the same:

{TT-22,AJs-ATs,KTs+,QTs+,JTs,T9s,98s,87s,76s,AQo-AJo,KJo+,QJo}

• (1) How does a affect his range and your equity against it?

On the 6 8 J board his range for check/calling will look like this: {TT-99,AJs,KJs,QJs,JTs,T9s,98s,87s,76s,AJo,KJo,QJo}

So you can see due to the different board structure – it’s J high instead of 8 high – he has more top pair hands in his range against which we have much better equity than against the lowcard-hands that connect well with the on the turn. So we’re still an underdog against the 2 pairs, but against his range we do much better because he has so many Jx hands.

Equity analysis
Board
	Equity	Win	Split	Loss	Hand
Player 1	75.08%	75.08%	0%	24.92%
Player 2	24.92%	24.92%	0%	75.08%	TT-99, AJs, KJs, QJs, JTs, T9s, 98s, 87s, 76s, AJo, KJo, QJo

• (2) What if the board is ?

On he will at least check/call with his flush draws. Whether he’s check/raising them is hard to tell, for now let’s assume he check/calls all of them (using the suit selection tool).

So the range he’s assigned looks like this:

Normal 0 21

{TT-99,77,22,87s,76s,KhQh,AhJh,KhJh,QhJh,AhTh,KhTh,QhTh,JhTh,Th9h,9h8h}

Once he bets on the turn you should just call because you're only flipping against his range and there is some chance he may even fold hands like TT or FD to a raise – in this case our equity decreases to less than 40%:

Equity analysis
Board
	Equity	Win	Split	Loss	Hand
Player 1	36.96%	36.96%	0%	63.04%
Player 2	63.04%	63.04%	0%	36.96%	99, 77, 22, 87s, 76s, AhJh, AhTh, Th9h, 9h8h

However, if we simply call we still play against his entire range:

Equity analysis
Board
	Equity	Win	Split	Loss	Hand
Player 1	53.45%	53.45%	0%	46.55%
Player 2	46.55%	46.55%	0%	53.45%	TT-99, 77, 22, 87s, 76s, KhQh, AhJh, KhJh, QhJh, AhTh, KhTh, QhTh, JhTh, Th9h, 9h8h

• (3) What do you do against a check/raise on the flop (i.e. what’s his range for check/raising and what’s your equity against it).

Without further reads we can assume the opponent is not check/raise-bluffing on the flop, as only very few opponents are capable of this move. So his range is likely to be quite strong.

He can certainly check/raise with sets, you cannot really be sure if he would check/raise TT and 99. If he does check/raise all of them, your equity is ok and you can call:

Equity analysis
Board
	Equity	Win	Split	Loss	Hand
Player 1	54.78%	54.78%	0%	45.22%
Player 2	45.22%	45.22%	0%	54.78%	TT-88, 66, 22

If you assume however that he does not check/raise his overpairs you have less than 9% equity and therefore should just fold on the flop.

• (4) What if you had 99 instead of QQ?

With 99 your equity against his turn range of {TT-99,T9s,98s,87s,76s} decreases significantly as you are now an underdog against TT and only splitting with 99:

Equity analysis
Board
	Equity	Win	Split	Loss	Hand
Player 1	27.90%	23.12%	4.78%	67.32%	99
Player 2	72.10%	67.32%	4.78%	23.12%	TT-99, T9s, 98s, 87s, 76s

If you had 99 on the turn it would be really close. You need to call €0.50 for a total pot of €2.02, therefore 0.5/2.02 = 0.2475 = ~24.8% equity. As you've just seen, you have 27.9% equity against his range so you can make a thin call.

• (5) Do you still want to call the turn bet with A8s?

With A8s our equity decreases even more than with 99:

Equity analysis
Board
	Equity	Win	Split	Loss	Hand
Player 1	21.31%	21.31%	0%	78.69%	A8s
Player 2	78.69%	78.69%	0%	21.31%	TT-99, T9s, 98s, 87s, 76s

So we have to fold to his turn bet.

• (6) What if he checks the turn to you, should you bet?

When he checks to you, the opponent's range looks different than if he had bet.

You can't simply exclude all the hands in his donk range because you don’t know if the opponent even has a donk range on the turn. Once he bets, you know that he has one, so the next time he checks to you, you can adjust his range by excluding some value hands. However, if you haven’t actually seen him doing it, you should assume that he isn’t donk betting.

So his checking range is exactly same as his check/calling range on the flop: {TT-99,77,AJs-ATs,T9s,98s,87s,76s,AQo-AJo}

However, if you bet he will not call with all hands. If he still has unimproved overcards, he will almost always fold to a bet. So in this hand his range for check/calling a turn bet is almost the same as the range you would assign to him if he led out, but excluding made straights, 2 pairs and sets because he will check/raise with these (which you fold to).

Equity analysis
Board
	Equity	Win	Split	Loss	Hand
Player1	78.64%	78.64%	0%	21.36%
Player 2	21.36%	21.36%	0%	78.64%	TT-99, 98s

We see that he only check/calls a few bad hands, check/raises most of the better ones and folds with air – do you want to bet here?

The answer is: yes! By betting you significantly limit his range and you can value bet any blank on the river. Also if we check and he bets you will usually end up calling, so you will still lose one bet against all better hands regardless.

Therefore we should rather bet the turn ourselves and get him to fold his equity share in the pot if he has Ax. At the same time we protect and get value from worse hands.

• (7) Imagine you call and the river is a K. Do you want to call another bet? Should you bet yourself if he checks to you?

It’s hard to tell which hands he will bet again. You have to watch out here that you don't fold because you think you're beaten by a pair of kings. There are no Kx hands in his range, so you don’t need to worry about him.

It's best to fold to a bet here because most opponents don’t think properly about your range and will put some kings in there. That's why he's afraid to bet any hand that doesn’t beat Kx. So if he checks you  should definitely value bet. As mentioned, he'll bet top pair or better. So once he checks he cannot have those anymore and you're more or less guaranteed to have the best hand.

• (8) If he check/calls the turn and the river is a 2, should you value bet?

In (6) you saw that his check/calling range for the turn looks like this: {TT-99,98s}. So with a 2 river you're still ahead of all hands in his range, therefore you should definitely put in a value bet.

Use your predefined range for the BU vs BB scenario again here. To do this we open the range selection window and simply select the "BU vs BB reg flatcall" range under "user-defined ranges".

A cbet for value is possible on the flop. A check behind is an option against aggressive opponents as well, because you're  not in a great position against their check raising ranges and there aren’t many worse hands they will check/call – basically only some pocket pairs.

You check behind on the flop, therefore the opponents range on the turn is exactly the same as his calling range preflop (assuming he never leads out on the flop).

On the turn he bets out small. It’s hard to say whether he wants to induce a call (or even a raise) or just has a weak hand and wants to take the pot down cheaply. It's reasonable to assume he will bet the entire range, because he will sometimes slow play made hands and sometimes give up with air. So overall his betting range is still balanced in roughly the same way as his total range.

You can also exlude some air hands from the range to be on the safe side.

The next question is whether to raise or call. To figure out what the best move is, analyse the opponent's entire range and how it performs on river cards. You need to look at his raising rangeas well and ask yourself how much value you can get from it immediately.

Calling the turn bet

If you call the turn bet you’ll have 57% equity against his range:

Equity analysis
Board
	Equity	Win	Split	Loss	Hand
Player 1	57.10%	57.10%	0%	42.90%
Player 2	42.90%	42.90%	0%	57.10%	TT-22, AJs-ATs, KTs+, QTs+, JTs, T9s, 98s, 87s, 76s, AQo-AJo, KJo+, QJo

The question is how much playability do you have on different river cards? The Scenario Analyser can help you find an answer:

see image 10: the Scenario Analyser with data from sample hand 2

You can see that you do well against his range on most river cards. In fact only if you only hit a diamond you're equity will fall well below 50%.

Raising for a free showdown

The second option you have on the turn is to put in a small raise for thin value and a free showdown.

If you raise, your opponent will fold some hands. You estimate his calling range to be something like: {Ats,KTs+,QTs+,JTs,T9s,AQo,KJo+,QJo,AdJd,9d8d,8d7d,7d6d}

You only have 42% equity against this range:

Equity analysis
Board
	Equity	Win	Split	Loss	Hand
Player 1	42.22%	42.22%	0%	57.78%
Player 2	57.78%	57.78%	0%	42.22%	ATs, KTs+, QTs+, JTs, T9s, AQo, KJo+, QJo, AdJd, 9d8d, 8d7d, 7d6d

So you're actually an underdog against his calling range. Of course he folds some hands with equity, but most of the hands he’s giving up only have a few outs. So you’re better off flat calling his turn bet.

• (1) What’s you equity against a 6%, a 10% and a 15% preflop range? Do you want to call a 3-bet against all three of those ranges?

A 6% range looks something like this: {88+,ATs+,KQs,AQo+}. You only have 34.69% equity against this range with AJo, therefore you should just fold against an opponent who 3-bets so tightly.

It’s a lot closer against a 10% range, for example {77+,A9s+,KTs+,QTs+,AJo+,KQo}. Here you have 34.47% equity. As you're in position and can out play the opponent, you should call the re-raise in most cases.

You have 51.62% equity against a range with the best 15% of his hands: {77+,A7s+,K9s+,QTs+,JTs,ATo+,KTo+,QJo}. So you should definitely call the 3-bet.

•  
• (2) What’s your equity against either of the ranges above on the flop? what should you do if the opponent bets - should we fold, call or raise?
  Hint 1: what part of his range will Villain fold to a raise? What does that mean in terms of your fold equity?
  Hint 2: to evaluate the call, you can simulate different turn carsds with the Scenario Analyser.

You only have 21.80% on the flop against a 6% range, even assuming that the opponent continuation bets 100% of his range (never checking cards such as KQ).

Equity analysis
Board
	Equity	Win	Split	Loss	Hand
Player 1	21.80%	17.14%	4.66%	73.54%	AJo
Player 2	78.20%	73.54%	4.66%	17.14%	88+, ATs+, KQs, AQo+

So you have to fold to any bet unless it'st extremely small – and even then you should only fold because you probably have reverse implied odds.

Although this is one of the best boards you can possibly hit, but you can still only fold to a cbet. This emphasises even more that you should fold preflop against a 3-bet.

We do a bit better against a 10% range:

Equity analysis
Board
	Equity	Win	Split	Loss	Hand
Player 1	35.02%	28.43%	6.59%	58.39%	AJo
Player 2	64.98%	58.39%	6.59%	28.43%	77+, A9s+, KTs+, QTs+, AJo+, KQo

You should usually call the flop bet against this range, especially as a lot of opponents don’t follow through on the turn but simply check/fold better hands like AQ and AK, even some pocket pairs like 77-99.

If the opponent checks to you, you should bet every turn.

You even have 41.69% on the flop against a 15% range. This means you can call a bet and re-evaluate on the turn.

Equity analysis
Board
	Equity	Win	Split	Loss	Hand
Player 1	41.69%	36.62%	5.07%	53.24%	AJo
Player 2	58.31%	53.24%	5.07%	36.62%	77+, A7s+, K9s+, QTs+, JTs, ATo+, KTo+, QJo

You can consider putting in a small bluff raise on the flop against an aggressive opponent with a range wider than 10%. If you opponent is capable of 2nd barreling as a bluff, you will end up folding a lot on the turn. In other words, you call the flop to fold to further action on the turn (for example with a week hand such as AJo), making the 2nd barrel even more profitable for him, because you're throwing dead money into the pot.

Of course if he overdoes it with the 2nd barreling, at some point you can start calling the flop bet with the intention of bluff shoving on the turn. However, this play requires strong reads and isn't recommended it until you have a good idea about his ranges and what you’re doing.

The EV of a bluff raise

To calculate the EV of a bluff raise on the flop, we need to have a look at our fold equity.

Assuming he open raises a 15% range and cbets 100% of the time, his range looks like this (including card removal):

{JJ+, 99-77, AJs+, A9s-A7s, KJs+, K9s, QJs, AJo+, KJo+, QJo, AdTh, AdTs, AhTd, AhTs, AsTd, AsTh, AcTd, AcTh, AcTs, KdTh, KdTs, KhTd, KhTs, KsTd, KsTh, KcTd, KcTh, KcTs, AdTd, AhTh, AsTs, KdTd, KhTh, KsTs, QdTd, QhTh, QsTs, JdTd, JhTh, JsTs, TdTh, TdTs, ThTs}

There are 187 combinations of hands, or 14.1% of all hands.

If you raise, he will probably fold the following hands:

{99-77, AJs+, A9s-A7s, KJs+, K9s, QJs, AJo+, KJo+, Qjo}

That's 130 combinations, or 9.8% of all hands.

So your fold equity is 9.8%/14.1% = 0.695 = 69.5% assuming you bet €3.20, you risk €3.20 to win a total pot of €2.45+€1.20+€3.20 = €6.85. So you need €3.20/€6.85 = 0.467 = 46.7% fold equity. As you have 69.5%, it is definitely +EV to raise.

The EV of a bluff raise is 0.695*€6.85-€3.20 = €1.56.

If your opponent calls your raise with the rest of the range, you even have some pot equity. However, for the sake of simplicity we’ll assume that the opponent either folds or shoves (in which case you fold and therefore have 0% pot equity).

Remember that a thinking opponent will realise that you don’t represent many hands by raising on the flop. Here, it's generally better just to call the cbet because he might play on and shove hands like AQ and AK. This means your fold equity decreases and therefore from a certain point there’s no more +EV in raising on the flop.

• (3) If Villain 3-bets 10% preflop and cbets 100% on the flop, how would you do with 99 instead of AJo?

Against a 10% range that cbets 100% of the time you have roughly 55% equity:

Equity analysis
Board
	Equity	Win	Split	Loss	Hand
Player 1	55.79%	55.16%	0.62%	43.59%	99
Player 2	44.21%	43.59%	0.62%	55.16%	77+, A9s+, KTs+, QTs+, AJo+, KQo

You've got an easy call here.

Raising is not a particularly good idea because Villain will just fold hands like overcards and even 88 and 77, so you would isolate yourself against a very strong range that crushes your equity.

• (4) What if you have 99 and the flop is , or (again against a 10% range that cbets on the flop 100% of the time)?

With 99 on you have roughly 42%:

Equity analysis
Board
	Equity	Win	Split	Loss	Hand
Player 1	42.92%	42.29%	0.63%	56.45%	99
Player 2	57.08%	56.45%	0.63%	42.29%	77+, A9s+, KTs+, QTs+, AJo+, KQo

You can still call the continuation bet because most opponents will not follow through as a bluff. You can check the hand and win at the showdown.

On our equity is roughly the same as with :

Equity analysis
Board
	Equity	Win	Split	Loss	Hand
Player 1	42.95%	42.29%	0.66%	56.40%	99
Player 2	57.05%	56.40%	0.66%	42.29%	77+, A9s+, KTs+, QTs+, AJo+, KQo

So you can call one bet on this flop as well.

On however, your equity decreases:

Equity analysis
Board
	Equity	Win	Split	Loss	Hand
Player 1	35.67%	34.99%	0.68%	63.65%	99
Player 2	64.33%	63.65%	0.68%	34.99%	77+, A9s+, KTs+, QTs+, AJo+, KQo

It's usually better to fold here.  The situation is very close and most players will be inclined to bluff 3-bet with Axs hands. If your opponent had 3-bet bluffs in his preflop range, he now has the best hand significantly more often than you might expect.

LINKS
Links: Pokerstrategy.com Equilab Videos: PokerStrategy.com Equilab introduction Coaching Podcast - Equilab Live with Bierbaer