1. Introduction
This is Part 9 of the article series "PLO From Scratch". The target audience is micro and low limit players with some experience from limit or no-limit Hold'em, but little or no PLO experience. My goal with this series is to teach basic PLO strategy in a systematic and structured manner.

In Part 9 we'll continue the discussion of our simple model for postflop planning based on 4 important factors:

1. The number of opponents
2. Position
3. SPR
4. Equity (given by the cards on our hand, the cards on the table and our assumptions about our opponents' ranges)

In Part 8 we talked about the factors that didn't involve the cards (1-3), and the turn has now come to factor 4, equity.

Being able to quickly and accurately estimate equity on the flop is definitely a craft, not a mysterious art. Our estimates are based on the cards that we see + assumptions about the opponent ranges we are up against. The rest follows from mathematics. We start by counting outs, then we estimate the number of "clean" outs by taking into consideration the chance of hitting an out and still losing. Finally, we convert outs to equity using the "4x" and "3x+9" rules (more about those later).

In this article we'll do a thorough walk-through of this process. Estimating equity is a very important part of the game, and it's also relatively easy to learn. Players who are sloppy when estimating equities often get away with it, especially in low SPR scenarios where there is room for error. But with high SPR, it's more important to have good control. Sloppy play in high SPR scenarios causes us to end up at the wrong end of 55-45 coinflips way more often than we should.

So even if working with outs and equity is a bit tedious and perhaps a bit boring, we have to learn how it's done. When you have learned the method, it's like riding a bicycle, and after a while you will start doing it more or less automatically. Those of you who find it difficult to count outs for the big wrap straight draws in the heat of battle will find useful stuff here, since we will define an easily memorizable notation for these draws.

When all the technical work is done, and our postflop model is ready for use, we'll start using it as of Part 10. We will begin Part 10 with a series of examples where we do postflop analysis and planning, using the framework of our model (number of opponents/position/SPR/equity). We'll pick some typical postflop scenarios and talk about how we should evaluate, plan and think when we navigate our way through them. We will also get an opportunity to repeat some important concepts from previous articles.

PLO is a game with an infinite number of variations for every possible scenario, so we will not get too hung up in details when we analyze hands. We'll first and foremost try to get the big things right, using sound PLO thought processes. If we start with a sound overall framework for PLO play, and we also know the mathematics behind pot-odds and outs, we have what we need to deal with specific postflop scenarios as they turn up.

When the discussion of general postflop planning has been concluded (at the beginning of Part 10), we'll move on to some specific postflop scenarios and apply our model as a tool for analyzing them. For example, we will end Part 10 with a thorough discussion of c-betting, and we'll see how our c-bet decisions vary as a function of the number of opponents, our position, SPR and our estimated equity.

2. Our method for estimating postflop equity
We'll now do our systematic treatment of estimating outs/equity in PLO, and we will mainly focus on situations where we are drawing and we know we have to hit an out to win. We start by defining the procedure, and then we go through various types of draws, illustrating with examples along the way.

To learn these techniques it's necessary to do a little memorization, but it's well worth it. Nothing mysterious goes on here, and it's a straightforward process. But there are some PLO specific "quirks" that makes the process a bit different from equity estimates in Hold'em, and that's why we have dedicated this article to learn it.

2.1 General procedure for estimating equities for draws
We use a 3-step process:

1. Count all our outs
2. Estimate the number of "clean" outs
3. Convert clean outs to equity

The first step is simply counting all outs we have to a winning hand. This of course depends on what we think we have to beat. For example, if you have a low pair and nothing else on the flop, you have a handful of outs against top pair, but you're drawing dead against top set.

In the second step we reduce the number of outs to take into consideration that:

1. We can hit an out and still be behind
2. We can hit an out and improve to the best hand, but on the next card our opponent makes an even better hand

For example, with a king high flush draw with nothing else to go along with it, we have 9 outs to a flush. But if someone has the nutflush draw, we're drawing close to dead. So we often can't count all outs as clean, and we have to estimate the likelihood of hitting and losing. As we shall see later in this article, whether or not we should draw to "dirty" outs is strongly correlated with SPR.

In a pot with ultra-low SPR, drawing to dirty outs is rarely a problem, since we're often getting a big overlay from the pot. But in a high SPR scenario, it's critical that we are careful with draws where many of our outs are dirty, since we now have negative implied odds and a poor risk/reward ratio. So we usually avoid playing big pots with non-nutty draws in high SPR scenarios.

Another way to hit and lose is to have winning outs on the flop, but after we hit, our opponents can draw out to a better hand on the river. For example, if you have the nutflush draw on an unpaired flop (e.g. A J 9 8 on a K 7 2 flop), and Villain has top set, you have 8 clean outs (all hearts except 2 ). But if you hit your flush on the turn, Villain has 10 board-pairing outs to a full house or quads. So effectively you have less than 8 clean outs on the flop. We shall learn to reduce outs to clean outs, using simple math + assumptions about our opponents' hands.

When we have estimated the number of clean outs, we convert them to equity. On the flop, where we have two cards to come, we use two simple numerical approximations (note that they give the same answer with x =9 outs):

- With x less than 9 outs: Equity =4x
- With x =9 outs or more: Equity =3x + 9

For example, with x =4 outs, we have 4x4 =16% equity on the flop. With x =14 outs, we have 3x14 + 9 =51% equity on the flop. These rules are numerical approximations to the exact equity, but as we can see from the exact calculations below, they work well:

Exact equity with 4 outs on the flop
We know 7 cards (4 on our hand + the 3 flop cards), so there are 52 - 7 =45 unknown cards, and 4 of them are outs for us. The chance of hitting on either the turn or river equals 1 minus the chance of missing on both the turn and river:

P =1-(41/45)(40/44) =0.17 =17%

Which is close to the estimate given by the 4x rule (16%).

Exact equity with 14 outs on the flop
We use the same logic as above, and get:

P =1-(31/45)(30/44) =0.53 =53%

Which is close to the estimate given by the 3x + 9 rule (51%).

We'll often get an error of a percentage point or two, but it's important to realize that the whole process is approximate. We will often introduce errors when estimating the number of outs, and then a couple of percentage points extra in the outs-to-equity conversion is rarely significant. For example, if we have counted 1 out too much or too little, we have already introduced a ~4% error in our equity estimate, which is bigger than the numerical error in the 4x and 3x + 9 rules.

Finally, if we want to estimate equity on the turn, this is simply the probability of hitting on the last card. We compute this number by dividing the number of outs on the number of unseen cards. For example, with 4 outs, we have 4/44 =0.09 =9% equity on the turn. With 14 outs, we have 14/44 =0.32 =32 =32% equity on the turn.

Now we have defined our procedure, and we move on to counting outs for various types of draws. For each type of draw we'll also talk briefly about how the value of the draw varies according to SPR.

Note that the distinction between made hand and draw is more "fuzzy" in PLO than in Hold'em, and often it doesn't make sense to think about hands in terms of made hands and drawing hands. In this article we will loosely use the notation "draw" for hands that need to improve to win. This includes hands that also have value as made hands, but not enough to go to showdown unimproved if we meet aggression.

3. Flopped pair and outs to two pair/trips
When you have flopped a pair, for example with K Q J 9 on a K 8 4 flop, you also have a draw to two pair/trips. This is a weak draw in a high SPR scenario (e.g. limped and raised pots), but can be a strong draw in a low SPR scenario (e.g. 3-bet and 4-bet pots).

The strength of a two pair/trips draw is very dependent on the number of opponents, SPR and flop texture. You have to think about the hands you are up against, your immediate pot odds, then chance of improving and losing, and future betting (which can give you severe negative implied odds if the stacks are deep).

The classical example of playing a two pair/trips draw as our primary draw is heads-up against AAxx in a 4-bet pot. On a dry flop it's easy to estimate the number of clean outs, as shown in the example below:

Example 3.1: A two pair/trips draw against presumed AAxx in a 4-bet pot

CO ($10) raises to $0.35, you ($10) 3-bet to $1.20 with Q J T 9 on the button, the blinds fold, CO 4-bets to $3.75, you call. You're assuming CO has AAxx, so your plan is to go all-in on all flops where you have sufficient equity against AAxx.

Let's look at two different flops:

Flop 1: A 9 4 ($7.65)
CO ($6.25) pushes, what do you do?

You're getting pot odds 13.9 : 6.25 =2.22 : 1, and you need 1/(2.22 + 1) =31% equity to call profitably. You have flopped a pair, but you're assuming Villain has AAxx, so you're treating all flopped pairs as a two pair/trips draw. So you have 9 + 2 =11 outs to two pair/trips. That's fine and dandy, but if CO has AAxx, you're drawing dead against top set on this particular flop. So you are forced to fold under this assumption.

Flop 2: Q 4 2 ($7.65)
CO ($6.25) pushes, what do you do?

You need 31% equity as before, and now you have flopped a pair on a dry flop where AAxx usually haven't picked up any additional equity. So you can assume an unimproved pair of aces is the hand you have to beat. You start by counting 9 + 2 =11 outs to two pair/trips. Trips will almost always win the pot for you, so you count these 2 outs as clean.

But the outs to two pair need to be discounted a bit to account for AAxx's redraw to top set or a better two pair after we hit. When we hit one of our 9 two pair outs on the turn, CO has 8 outs (2 aces, 3 fours, 3 deuces) to top set or aces up on the river. On the turn we know 10 cards (the 4 on our hand, the 2 aces on CO's hand and the 4 cards on the board), so there are 42 unknown cards. This gives CO a 8/42 chance to draw out against our turned two pair, and we can round this to 1/5.

So we subtract 1/5 of our two pair outs and get 9(4/5) =7.2 clean two pair outs, which we round down to 7. Then we conservatively subtract 1 more out to account for the equity CO gets from his 2 unknown side cards. So our final estimate is 6 clean two pair outs.

This gives us 6 + 2 =8 clean outs to two pair/trips on this dry flop, and we convert this to 4x8 =32% equity on the flop. This is barely above the 31% threshold, and we have a marginal call. However, if we want to keep the variance down, and also adjust to the effect of the rake (can turn slightly +EV calls into break even or slightly -EV calls), it's perfectly fine to fold. But if we'd had a couple of backdoor draws to go along with our two pair/trips draw, this would have been an automatic call.

From the ProPokerTools-calculation below we see that our 32% equity estimate against AAxx on a dry flop was close:

With high SPR and/or many opponents, we rarely play a two pair/trips draw unless it works as a backup for another primary draw. The main reason is that in these scenarios a two pair/trips draw isn't a draw to a hand we necessarily can take to a showdown when we hit and then face aggression. With high SPR we have large negative implied odds if we get stubborn with marginal hands, so we have to be careful. So we want something more before we are comfortable playing a big pot with high SPR. Below is an example where you have a naked two pair/trips draw in a multiway pot with high SPR:

Example 3.2: A two pair/trips draw in a limped multiway pot

Button ($10) openlimps, small blind ($10) limps, you ($10) check K J 9 2 in the big blind.

Flop: A K 8 ($0.30)
Small blind ($9.90) bets $0.20. What do you do?

You fold. You almost never have the best hand on the flop, and this is a scenario with high SPR in a multiway pot, which means you want nutty hands/draws before you play a big pot. Your risk/reward ratio is poor, you have few outs (and even fewer clean outs), you have one player left to act, and and small blind is representing a strong hand when he bets into two opponents, so fold, fold, fold.

Before we finish our discussion of two pair/trips draws, we'll look at situations where we have flopped a pair as backup for another primary draw. If we get heads-up with a strong draw plus a pair, this is generally a good situation for us, since we can now be in a dominating draw vs draw match-up. If we clash with another draw similar to ours, but without a pair, we can be a big favorite. The reason is simply that our pair will often win when both draws miss. Below is an example:

Example 3.3: A pair + draw versus a draw without a pair

You ($10) raise to $0.35 with K Q J 9 on the button, small blind ($10) 3-bets to $1.15, you call. Small blind is a known TAG with a 3-betting range mostly made up of AAxx, good Broadway hands, and a few premium speculative hands.

Flop: T 9 4 ($2.40)
Small blind ($8.85) bets $2.40. What do you do?

You have been 3-bet by a TAG, and he bets out on a flop that has given you a strong draw. You have flopped one of the very good wrap straight draws (more about them later in this article), and you have 13 nut outs (4 eights, 3 jacks, 3 queens, 3 kings) to a straight. We count all these as clean, since we're drawing to the nuts on a dry flop, and we don't expect Villain to have 3-bet many hands that can flop a set on this flop.

You also have a pair and a backdoor flush draw. Hitting one of your kickers gives you a straight, so you don't gain anything extra from having outs to two pair. But you have 2 extra outs to trips, and 1 extra out to a backdoor flush. You conservatively estimate that these two weak draws give you 2 clean outs to go with your wrap. So you estimate 13 + 2 =15 clean outs on the flop.

This gives us 3x15 + 9 =54% equity on the flop against a better hand that doesn't have a redraw after we hit (for example AAxx with worthless side cards). The ProPokerTools calculation below confirms our estimate:

So we can definitely raise our pair + wrap for value against the AAxx part of Villain's range. Since he also 3-bets other hands, he can have flopped a draw as well, or he can have missed the flop completely. If he has a draw, it can't be better than our draw, unless he has the same wrap + a better pair. This rarely happens, so we can raise for value against his draws as well. And if he is c-betting air, we're of course a big favorite, so we raise (and we don't mind him folding his air hands in a big pot).

We conclude that a raise seems correct against all hand types in Villains range, so we simply shove all-in on the flop:

Flop: T 9 4 ($2.40)
Small blind ($8.85) bets $2.40, we ($8.85) raise all-in, small blind calls.

Turn: T 9 4 K ($20.10)

River: T 9 4 K 7 ($20.10)
Small blind has A K Q J for the same wrap as us, but without a pair. We were 66% favorite on the flop, as shown below:

66% edge on the flop is huge in PLO. But if we'd had the same wrap, but without a pair (e.g. K Q J 7 ), Villain would have been the favorite. He would now have the same wrap as us, and also the best hand with ace high on the flop:

So we see that the effect of having a pair in addition to a strong draw can be huge. Note that when we have a pair + wrap combination, the pair rarely gives us extra outs, since the kickers are a part of the wrap. We get a couple of extra outs to trips, but the biggest effect is that our pair is the best made hand on the flop. If Villain has a draw without a pair, we now win a significant number of pots where turn and river are blanks. A pair also works as a blocker against Villain's redraws those times he has flopped a set or two pair (there's one less card that can make him a full house on the river after we draw out on the turn).

We conclude that a pair can be a very valuable addition to a strong primary draw like a wrap or a nutflush draw. It's having these extra bits and pieces of equity that sets us up for getting on the right end of 55-45 coinflips on the flop, or they can turn marginal +EV to strong +EV.

4. Flush draws
The probability of the flop coming rainbow is:

P(rainbow flop) =(52/52)(39/51)(26/50) =0.40 =40%

So on 60% of flops there will exist the possibility of a flush draw of a flopped flush. This makes suitedness an extremely important property for a PLO starting hands. Every time you play a staring hand without suits, you are setting yourself up for tricky postflop decisions, and this is why we demand a suit before we label a starting hand "Premium". In our starting hand discussion in Part 2, we classified unsuited hands as "Marginal" at best, and this is the reason.

When you have flopped a hand of the type good-but-not-great, without much potential for improvement, you will often have to play defensively postflop when the flop comes with the possibility of a flush draw. But if you have a flush draw as a backup for your made hand, you can play much more aggressively, especially with the nutflush draw (which can turn your hand into a true monster).

Estimating outs for a flushdraw in PLO is more complicated than in Hold'em because of the much bigger difference between the nutflush draw and low flush draws (when you have a low flush draw, it's much more likely someone else has a bigger flush draw in PLO than in Hold'em). So instead of counting flush outs, we'll think more "holistically" about the hand, and assess the strength of the flush draw based on whatever else we have, the number of opponents, and SPR.

At any rate, a nutflush draw gives us 8 nut outs on the flop (there are 8 flush outs that don't pair the board), but sometimes we have to discount this a bit if we suspect there are other flushdraws out there and/or if we suspect someone has a set (=a good redraw against our nutflush). These considerations are particularly important with high SPR in a multiway pot, where the price of making a mistake in a big pot goes up.

The value of a non-nut flush draw is much less than the nutflush draw, since we always risk being up against the nut draw when we get action on the flop. The value of a non-nut flush draw is also extremely dependent of SPR and the number of opponents. Drawing to a non-nut flush and little else in a multiway pot with high SPR is suicidal. But a non-nut flush draw can be a strong equity component heads-up with low SPR, for example heads-up in a 4-bet pot with SPR around 1.

We can also have valuable extra equity with a backdoor flushdraw, for example A K J T on a Q 9 2 flop where we have a 13 out wrap plus 2 backdoor flush draws. We usually count backdoor flush draws as 1 out, but we can reduce this a bit (e.g. to 1/2 out) when we have many opponents and/or the draw is low.

Here is a warm-up example to illustrate the huge difference a nutflush draw can make for the value of a hand on the flop:

Example 4.1 A naked overpair compared to an overpair + nutflush draw

Button ($10) raises to $0.35, you ($10) 3-bet to $1.15 with A A 8 7 in the small blind, button calls. Button is a solid TAG.

Flop 1: Q J 7 ($2.40)
You have $8.85 behind. What is your plan?

It's obvious that you are toast if you c-bet and get raised on this type of flop. So if you bet, you are bet-folding. The flop is pretty "wet" with a large number of possible draws. It's also a flop we expect to have coordinated well with buttons range for open-raising and then calling a 3-bet (his range should contain a lot of suited high/medium card hands).

For example, if button has a random Broadway hand with 4 cards from A to 9, we are pretty much crushed, even if he doesn't always have a flush draw:

And against the nuts, we are completely toast:

So we have a flop that we expect to have connected well with Villain's range, and when he has connected well, our equity is very poor. So your options are checking and giving up, or betting and folding to a raise (and be lost on most turn cards if you get called). Now let's see how things change when you flop a nutflush draw:

Flop 2: Q J 7 ($2.40)
You have $8.85 behind. What is your plan?

Here it's obvious to bet and get the stack in if we get raised. With the nutflush draw, our equity shoots up, and against a random Broadway hand with 4 cards between A and 9, we are now the favorite:

We even have decent equity against the nuts:

Sitting with or without a flush draw is like two different worlds in PLO. Without a flushdraw on a two-tone flop, we're often forced to check and give up or bet-fold with our marginal hands. The higher the SPR, the more difficult it gets to profitably play hands without flush draws when someone else very well could have one. But with a flush draw, especially the nutflush draw, we can bet more, and with a low SPR our decisions often become automatic (for example, we happily get our stack in with an overpair + the nutflush draw in a 3-bet pot with 100 BB stacks).

But it's easy for beginners to overvalue naked flush draws in PLO. So here are a few guidelines:

  • The nutflush draw has big value in combination with another draw or with a decent made hand
  • A naked nutflush draw has limited value
  • A non-nut flush draw can have decent value in combination with another good draw, or a good made hand
  • A naked non-nut flushdraw is mostly worthless (an exception is heads-up with ultra-low SPR)

We'll first look at a naked nutflush draw. It's always tempting to continue with this draw on the flop, and this can be correct. But we always have to take into consideration that:
  • When there is a lot of action on a two-tone flop, it's highly likely that several of our flush outs are in other hands.
  • It's difficult to extract a lot of value with the nut flush when we hit, especially when out of position

So a naked nutflush draw is not a hand strong enough to take to the river, and it's generally not a draw we bet on the flop (unless we expect to have good fold equity). And if you're playing a naked nutflush draw passively for implied odds, it's important to make an accurate assessment of how much we expect to make when we hit.

We have already looked at a combination of made hand + nutflush draw in Example 4.1. Below are 4 more examples of playing flush draws with different combinations of SPR and number of opponents. First 3 examples with the naked nutflush draw, then an example of playing a non-nutflush draw as a part of a strong combo draw:

Example 4.2: Naked nutflush draw in a limped, multiway pot

CO ($10) limps, button ($10) limps, SB ($10) limps, you ($10) check A 8 7 4 in the big blind.

Flop: K J 6 ($0.40)
Small blind ($9.90) bets $0.40, what is your plan?

Here you have to fold because of the following bad combination of circumstances:
  • You only have a naked flush draw with at most 9 outs (note that we don't expect an ace to be an out for us on this flop)
  • You're only getting 2 : 1 in immediate pot odds, and you need more than 4 : 1
  • You have poor implied odds (your opponents won't give you much action, since your hand is obvious when you hit and start betting for value)
  • You're not closing the action, and you risk getting raised if you call
  • The small blind often has a flush draw himself as a part of his hand/draw when he leads into 3 opponents on the flop. If this is the case, you have fewer outs than you think

So fold, plain and simple.

Example 4.3: Naked nutflush draw in a raised, multiway pot

CO ($10) limps, you ($10) raise to $0.45 with A 9 8 7 on the button, SB ($10) calls, BB ($10) calls, CO calls.

Flop: K J 6 ($1.80)
Small blind ($9.55) bets $0.50, BB ($9.55) calls, CO folds, what is your plan?

We start by noting that this is a flop where you should check behind with the naked nutflush draw in a 4-way pot if everybody checks to you. You have a handful of outs to the nutflush, but you're not strong enough to bet for value, and betting a weak draw as a semibluff is generally not a good idea with 3 opponents and a pretty coordinated flop.

As played, here you can call with your naked nutflush draw, since:
  • You're getting 2.80 : 0.50 =5.6 : 1 in immediate pot odds (and you need 4 : 1)
  • You're closing the action
  • You have position, and it will be easier for you to make money after you hit

So even if some of your outs sometimes are in the hands of the opposition, you can call profitably here. Unlike Example 4.2 you here have sufficient immediate pot odds, and you also have better implied odds because of your position.

Let's say you hit on the turn, and both opponents check. You of course bet, and they have to sit there and wonder if you're bluffing (unlike Example 4.2 where you would have had to bet into the field from out of position and reveal your strength). And whenever someone suspects bluffing, he will pay off more often. And when you're not checked to, this means someone is betting into you, and donating implied odds that way.

So call for pot odds + implied odds. Of course, you also have some chance of stealing the pot on the turn if both check to you. The small flop bet and the call in front of you seems weak, and both opponents could very well be planning to give up unimproved on the turn. It's also theoretically possible you can win a showdown with top pair when you spike an ace.

Top pair is obviously not a hand you can bet for value, but you will sometimes win a showdown with it if both opponents are passive enough to let you check the hand down. As an alternative, you can turn top pair into a bluff if they check to you, since you can now bet big and represent the nutstraight. At any rate, the possibility of stealing the pot later in the hand, or winning a showdown with top pair can be added to the showdown equity from the nutflush draw.

Note how easy it is to make this call when we're closing the action in position. We can sit laid back and ponder our alternatives with excellent control over pot odds and implied odds, and with more ways to win the pot than hitting the nuts.

Example 4.4: Naked nutflush draw in 3-bet heads-up pot

CO ($10) raises to $0.25, you ($10) 3-bet to $1.20 with A Q J T on the button, the blinds fold, CO calls. CO seems tight and straightforward.

Flop: 8 4 3 ($2.55)
CO ($8.80) checks, what is your plan?

Your 3-bet set you up for a very profitable scenario, namely heads-up in position against a straightforward player who is telling you he doesn't have AAxx (since he didn't 4-bet). You should c-bet virtually any flop in this scenario, and definitely a flop like this, since:
  • The flop texture is low and dry, and CO usually has flopped nothing
  • You can credibly represent AAxx which CO's range has poor equity against
  • You have the nutflush draw to fall back on if you get called
  • If you get called and CO checks the turn, you can bet again on various turn scare cards (e.g. overcards to the flop) and put a lot of pressure on his marginal hands

Like in Example 4.3 we have position, and therefore more options. But unlike the previous example, we're not basing our play mainly on the value of the draw, but on the value of position + initiative in a heads-up pot against a straightforward opponent. You can bet any random hand here and profit from it, since we expect CO to usually check-fold. Having the nutflush draw to fall back on simply makes a c-bet even more profitable.

So in this scenario the value of the draw is less important than some of the other factors we're considering. Note the different mindsets we use in multiway and heads-up pots. Sitting HU with position and initiative is a totally different world compared to sitting out of position in a multiway pot, even if we have the same cards.

Example 4.5: Combo draw with a non-nutflush draw in a 3-bet heads-up pot

You ($10) raise to $0.35 with Q J T 6 on the button, SB ($10) 3-bets to $1.15, BB folds, you call. SB 3-bets tight out of position, and you're assuming AAxx makes up a large portion of his range.

Flop: 9 8 4 ($2.40)
SB ($8.85) bets $2.40, what is your plan?

Automatic shove all-in. You have a strong 13 out nut wrap plus a 3rd nutflush draw, and it's difficult for Villain to have you crushed. If he has a random AAxx, you are a big favorite:

However, if he has AA + nutflush draw, we're struggling a bit:

But this is only a small portion of his AAxx hands, and we can confirm this with ProPokerTools' "count" function. There are 5085 combinations of AAxx, given the known cards in our hand and on the flop:

But only 921 of them has a higher flushdraw (we also count the AAxx hands with a K high flush draw for the sake of completeness):

So the chance Villain has a better flushdraw to go with his AAxx hands is only 921/5085 =18%, and we still have about 36% equity in this case, so it's not a disaster for us.

Villain might also have various other combinations of premium high card hands, but we're doing OK against these hands on average, since Villain needs a better flush draw to have good equity against us. So given our read on small blind and the estimate of our flop equity, it's a straightforward shove in a 3-bet pot.

In situations with multiple opponents and high SPR, we have to be a bit more cautious with strong combo draws that have a non-nut flush-component. For example, the value of the draw in the example above would have been drastically reduced in a singly raised 3-way pot if there had been a bet + raise in front of us on the flop. Now we would have a significant chance of clashing with a better flush draw and/or a wrap similar to our own. We would also have a worse risk/reward ratio (because of higher SPR), and going with the hand on the flop would no longer be automatic.

This type of flexible thinking on the flop, where we assess our hand strength as a function of the number of opponents, position, SPR and equity estimates, is precisely what our model for postflop planning is all about. When our discussion of equity is done, we will put all the pieces together in Part 10 with a series of thorough examples where we focus on the whole.

We now move on to the last type of draw we'll consider here, namely the straight draws with focus on the strong wrap straight draws:

5. Straight draws
When big PLO pots get built postflop, the equity match-ups frequently revolve around straight draws. This means that when 2 or more players are willing to build a big pot postflop, this usually involves at least one big straight draw. To see why this is the case, look at the two flops below, and assume the pot starts out small:

Flop 1: K 7 2
Flop 2: A 8 3

For a big pot to get build on Flop 1, we need two players to have a set, and this rarely happens. And even when it happens, the player with the lowest set will (or should) understand that the other player also has a set when he gives a lot of action on this extremely dry flop, and this will (or should) slow down the action.

On flop 2 the nutflush will get some action from lower flushes, but a competent player with a low flush will slow down when he sees he is up against another flush. And he will not always be willing to take his low flush to showdown if the nutflush bets big on all streets.

Now consider the flop texture below:

Flop 3: J T 6

This is an action flop with a large number of possible straight draws, and many of them are strong draws:

- 97xx/87xx =4 out gutshots
- KQxx/Q9xx/98xx =8 out open-enders
- AKQx/987x =13 out wraps
- AKQ9 =16 outs wrap (with only nut outs)
- KQ9x/Q98x =17 out wraps
- KQ98 =20 out wrap

We can make 3 important observations:

1. Flop 3 is an action flop with lots of straight draws
2. Some of these draws are nutty, and some aren't
3. Flop 3 therefore gives bad players plenty of opportunities to make big mistakes!

Action flops with straight draws invites aggressive play with draws. And when two draws clash, a good player has an opportunity to outplay a bad player by using his superior understanding of starting hand strength/playability preflop and equity postflop. A good players edge becomes even greater on flops where a flush draw is possible (more opportunities for the bad player to make mistakes) and when the SPR is high (deep stacks magnifies the effect of mistakes).

The significance of straight draws in PLO is clearly reflected in our categorization of starting hand strength (Part 3). For example:

A T 9 8

are all premium/near premium starting hands, while

K K 8 3
A J 6 2

are both marginal hands that are unsuitable for playing big preflop pots (we prefer to keep the pot small preflop and wait to hit the flop hard before we build a big pot). The first three hands all have excellent straight potential in addition to various other strength components (a high pair, a suited ace, and high card strength, respectively). The last two hands only have one single (but nutty) strength component, and non-existent or minimal straight potential.

We'll split the discussion of straight draws into two parts:

- Weak straight draws (gutshots, open-enders)
- Wraps (defined as straight draws with more than 8 outs)

I feel it's important to treat the weak straight draws (e.g. the standard straight draws we also have in Hold'em) separately, since overvaluing them is a common error among PLO beginners. We'll see why these draws are much weaker in PLO than in Hold'em, also when we're getting seemingly very good pot odds. But we'll also see that they can be valuable equity components when the conditions are right, for example when they work as backup for another primary hand/draw in a medium/low SPR scenario.

Then we'll move on to the fun part, namely the big wrap straight draws. We'll learn to quickly count outs for them, and we'll learn to distinguish between nut outs and non- nut outs. This distinction is important when we build big pots in high SPR scenarios, and bad players make many big mistakes in this area.

5.1 Weak straight draws
For many new PLO players it's tempting to simply write the following, and then be done with it:

- 4 outs
- Example: K Q 9 8 on a 7 5 2 flop

- 8 outs
- Example: A J J T on a 9 8 3 flop

But this would be highly misleading. The reasoning is similar to our discussion of non-nut flush draws. The value of the draw is highly dependent on the specifics of the situation (number of opponents, position, SPR), and we can't simply count 4 outs or 8 outs and be done with it. We have to think through which hands we're facing, whether or not we're getting freerolled by a dominating straight draw, the chance of hitting and losing, and the negative implied odds we have when that happens.

In other words: A 4 out or 8 out straight draw rarely has 4 or 8 clean outs, even if we have 4 or 8 immediately clean outs on the flop. Remember that a clean out is an out that always wins the whole pot for us, and we rarely have many clean outs with a weak straight draw when we get lots of action on the flop.

Below are two examples to illustrate how the strength of a weak straight draw varies with the situation, and in which scenarios they perform well:

Example 5.1.1: An open-ender in a limped, multiway pot

UTG ($10) limps, CO ($10) limps, you ($10) limp A T 9 4 on the button, SB ($10) limps, BB ($10) checks.

Flop: K 8 7 ($0.50)
SB ($9.90) bets $0.50, UTG ($9.90) calls, CO ($9.90) calls, what is your plan?

Fold. You have a naked open-ender in a 4-way pot, and you have to assume you're often dominated by better straight draws (e.g. wraps). A weak player might think he's getting almost the immediate pot odds he needs (getting 4 : 1, and needing 5 : 1) and a dash of implied odds, but in reality he is donating significant negative implied odds to his opponents.

To see this, let's play out the hand like an optimistic fish might play our cards:

Flop: K 8 7 ($0.50)
SB ($9.90) bets $0.50, UTG ($9.90) calls, CO ($9.90) calls, Mr. Optimist ($9.90) calls.

Turn: K 8 7 6 ($2.50)
SB ($9.40) bets $2.50, UTG ($9.40) folds, CO ($9.40) folds, Mr. Optimist ($9.40) raises all-in, SB calls.

River: K 8 7 6 9 ($21.30)
SB wins with Q J T 9 , Mr. Optimist, who now has a counterfeited A T 9 4 thinks ("bad beat!").

Really? Not really. Let's look at his equity against SB on the flop and turn:

His equity on the flop was seemingly OK (54%). The mathematical reason for this is that we have the best hand with ace high, which means we will win lots of pots when the turn and river blanks, or when we improve to top pair. However, this equity edge is an illusion, since it will be impossible for us to get to showdown with ace high or top pair if SB keeps semibluffing his big draw (which, of course, is precisely the reason why semibluffing big draws works so well).

So in reality we only have our straight outs. But now our problem is that the best these outs can do for us is split the pot. Therefore, SB is freerolling us (he can't lose the pot, only split or scoop). If we look more closely at the calculation for the turn equity, we see that SB has 11 outs to a winning hand (all clubs and nines), and he splits the pot with us on the remaining 29 cards.

Using these numbers, we can calculate the EV for raising all-in on the turn with our naked nutstraight against SB's nutstraight + redraw. 11 times we lose $9.40, and 29 times we get back our $9.40 plus half the initial turn pot (0.5 x $2.50 =$1.25) for a net gain of +$1.25.

EV (raise turn)
=(11/40)(-$9.40) + (29/40)(+$1.25)

So this was a situation where we had the nuts on the turn, but still we couldn't make a dime by raising all-in, even if the initial turn pot had a lot of dead money in it. What went wrong?

The biggest mistake in this hand was calling with a naked open-ender on the flop in a multiway pot after SB elected to bet into a field of 3 opponents. His flop bet signals a strong made hand and/or a strong draw, and when both UTG and CO call behind him, we have to assume we're often up against a dominating straight draw. Thus, calling on the flop sets us up for lots of scenarios where we're getting freerolled, which means the best that can happen is we split the pot.

This isn't necessarily all that bad in a heads-up pot with low SPR, but it can be a disaster in a high SPR/multiway pot scenario. So we have to be picky about the quality of our draw in these spots and get out early if we see the threat of a negative freeroll looming in the horizon. When we're up against many opponents and the stacks are deep, it's not enough to have a handful of outs to the nuts. What we really want is outs to the nuts with redraws to better nuts. And this was precisely what SB had here.

SB started with a 13 out nut wrap + backdoor flushdraw, and he elected to semibluff into the field. This strategy will force out lots of better hands either on the flop or by betting again on the turn (it will be increasingly difficult to keep calling with marginal hands when the pot grows bigger). And if he doesn't succeed in stealing the pot, he has a draw that will give him a nut straight approximately 3 x 13 + 9 =48% of the time, and also a backdoor flush (about 1 out =4% additional flop equity).

SB then hit the nut straight on the turn, and he got a flop caller tagging along who did precisely what SB hoped for, namely raising all-in with the naked nuts. Note that getting raised all-in is better for SB than winning the pot on the turn. Folding the naked nuts is EV =0, while raising all-in gave us EV =-$1.68.

The observant reader will see that there are two solutions to Hero's dilemma when he suspects he is up against the same nut draw + redraw:

- Fold on the flop
- Don't raise all-in on the turn

The first solution is obvious. But when we have stumbled into this particular turn predicament, it's possible to save chips by only calling SB's turn bet, planning to get the rest of the chips in on a blank river. This will be a good plan against an SB player of the weak-tight kind (he will bet the river with the nuts, but check his non-nut hands).

Against this type of opponent we can conclude we're behind if he bets all-in on a river scare card, and we save a large bet. And if he checks a river scare card (e.g. a board-pairing card), we'll have an opportunity to win the whole pot by turning our straight into a bluff and hoping SB folds the same straight.

But even if we have options on the turn in this nuts vs nuts+redraws scenario, particularly against a weak opponent, it's generally better to avoid these scenarios to begin with. Sometimes it's unavoidable (for example, if we stumble into a straight with a hand where the weak straight draws worked as a backup for another hand/draw), but usually we can control this nicely on the flop.

So remember:

With a high SPR and many opponents we want straight draws that are to the nuts, and that also have redraws to better nuts. In other words, we want strong and nutty wraps.

We conclude this section with an example of playing a weak straight draw as a backup draw in a heads-up pot with low SPR:

Example 5.1.2: A gutshot in a 3-bet heads-up pot

Button ($10) raises to $0.35, you ($10) 3-bet to $1.15 with A A 9 8 , button calls.

Flop: J 6 5 ($2.40)
You have $8.85 behind. What is you plan?

This is an obvious bet-and-get-it-in spot. The flop is very dry, so unless button has many mysterious JJxx/55xx/44xx/J5xx/J4xx/54xx combinations in his range (unlikely), you are almost always ahead. And if you should be behind, you have 6 nut outs to a gutshot or top set, and also a backdoor nutflush draw (1 out).

So you are in a situation where you expect to pick up the pot with a c-bet most of the time. And when you don't, you have ~7 nut outs, so you are never in very poor shape here. Your plan is therefore to bet out and call a raise.

5.2 Wrap straight draws
We define wrap straight draws as any straight draw with more outs than the standard open-ender. In other words, any straight draw with 9 or more outs. We can divide wraps into two classes:

- Medium strong wraps (up to 13 outs)
- Monster wraps (16, 17 and 20 outs)

Keep in mind that we need ~14 clean outs to be a favorite heads-up on the flop (for 3 x 14 + 9 =51% equity). So the 13 out wraps are near the threshold for monster draws that can be bet and raised for value on the flop, regardless of the number of opponents. Therefore, conceptually it makes sense to treat the wraps with 13 outs or less as medium strong, while the bigger wraps are monster wraps.

But the strength of a wrap is not given only by the number of outs. We have to distinguish between nut outs and non-nut outs, especially when we begin the postflop play with many opponents and high SPR. Therefore it's critical that you're able to quickly count nut outs when you have flopped a big wrap in a multiway pot.

Let's first get the simplest and weakest wrap out of the way. This is the 9 out inside wrap. This wrap is created by having 3 cards inside a 3-gapper, as shown below:

A 8 7 6 on a 9 5 2 flop.

All the 9 outs to the inside wrap above (3 eights, 3 sevens, 3 sixes) are to the nuts, so even if it's not a strong wrap, it's nutty. In a heads-up ultra-low SPR scenario an inside wrap can be all we need. If it also comes with a pair or some other extra pieces of equity, it can be enough to go profitably all-in on the flop with medium SPR (for example in a heads-up 3-bet pot).

We now move on to the wraps with 13+ outs. We'll systematically count total number of outs and number of nut outs for 3 classes of wraps:

1. Wrap around a connector on the flop
2. Wrap around a 1-gapper on the flop
3. Wrap around a 2-gapper on the flop

These scenarios are created when there is a connector (e.g. 9 8 2 ), or a 1-gapper (e.g. J 9 4 ), or a 2-gapper (e.g. A 9 6 ) on the board, and we have some rundown hand that wraps itself around the board cards in some way (hence the name "wrap").

We now list these wrap straight draws using a generalized notation. We let "x" denote a card on our hand, while "y" is a board card. For each draw type we write the type of draw we have, followed by a number that tells us how many of the cards in our hand are over or below the board cards. Then we write down the total number of outs, followed by the number of nut outs in parenthesis, and then an example.

Here is an example of this notation to make things crystal clear:

3-0 wrap around connector
General form: xxxyy
Outs: 13(13)

Example: Q J T 2 on a 9 8 5 flop.

There is a 98-connector on the board, and we have a wrap around this connector with 3 cards over it and 0 cards below it. The result is a 13 out wrap (all queens, jacks, tens and sevens) and all 13 outs are to the nuts.

Now we grit out teeth and do the same for all wraps around connectors, 1-gappers, and 2 gappers, in this order. We start with the biggest wraps for each category and move down towards the weakest ones.

Wrap around connector
2-2 wrap around connector
General form: xxyyxx
Outs: 20 (14)

Example: K Q 9 8 on a J T 4 flop.

2-1 wrap around connector
General form: xxyyx
Outs: 17 (11)

Example: 8 7 4 2 on a J 6 5 flop.

1-2 wrap around connector
General form: xyyxx
Outs: 17 (7)

Example: J 8 7 5 on a A T 9 flop.

3-1 wrap around connector
General form: xxxyyx
Outs: 16 (16)

Example: K Q J 8 on a T 9 2 flop.

3-0 wrap around connector
General form: xxxyy
Outs: 13 (13)

Example: A K Q on a J T 7 flop.

0-3 wrap around connector
General form: yyxxx
Outs: 13 (3)

Example: 7 6 5 4 on a A 9 8 flop.

Wrap around 1-gapper
For these wraps one of our cards always fills the gap, while the remaining cards are distributed around it.

1-1 wrap around 1-gapper
General form: xyxyx
Outs: 17 (11)

Example: J 9 7 5 on a K 8 6 flop.

2-1 wrap around 1-gapper
General form: xxyxyx
Outs: 16 (16)

Example: J T 8 6 on a A 9 7 flop.

2-0 wrap around 1-gapper
General form: xxyxy
Outs: 13 (13)

Example: A 8 7 5 on a K 6 4 flop.

0-2 wrap around 1-gapper
General form: yxyxx
Outs: 13 (3)

Example: A J 9 8 on a Q T 5 flop.

Wrap around 2-gapper
For these wraps 2 of our cards always fill the gap, while the 2 remaining cards are distributed around it. There is obviously only two ways to do this:

1-0 wrap around 2-gapper
General form: xyxxy
Outs: 13 (13)

Example: J 9 8 2 on a T 7 4 flop.

0-1 wrap around 2-gapper
General form: yxxyx
Outs: 13 (7)

Example: A 7 6 4 on a K 8 5 flop.

Summary of wraps around connectors, 1-gappers and 2-gappers
First, below is a more compact version of the information outlined above. The draws are sorted by structure, with outs and nut-outs listed to the right:

Wrap around connector:
2-2 x x y y x x 20 (14)
2-1 x x y y x 17 (11)
1-2 x y y x x 17 (7)
3-1 x x x y y x 16 (16)
3-0 x x x y y 13 (13)
0-3 y y x x x 13 (3)

Wrap around 1-gapper:
1-1 x y x y x 17 (11)
2-1 x x y x y x 16 (16)
2-0 x x y x y 13 (13)
0-2 y x y x x 13 (3)

Wrap around 2-gapper:
1-0 x y x x y 13 (13)
0-1 y x x y x 13 (7)

This information can be easily memorized, and as such it is "low hanging fruit". Know these draws in and out so that the out counting process becomes automatic. For example, if you have 9 8 7 6 on a A 5 4 flop, your thought process should go "Ding! I have a 3-0 wrap around a connector with 13 outs and 13 to the nuts". I can guarantee you that the majority of low limit PLO players don't know these things as well as they should. This is of course why they so often overplay non-nutty draws, only to get their asses handed to them in big pots.

If you want to print out this overview, or have it available on-screen while playing, you can download this text document: wraps.txt (right-click the link and choose "save as").

It's worth noting the big differences in quality for these wraps. The larges possible wrap is a 20 out 2-2 wrap around a connector, but this draw only has 14 nut outs. In practice, if a big pot is brewing in a high SPR scenario, we would rather have a 16 out wrap composed solely of nut outs, in other words a 3-1 wrap around a connector or a 2-1 wrap around a 1-gapper.

On the other side of the wrap spectrum we have the non-nutty 13 out draws (0-3 wrap around a connector, 0-2 wrap around 1-gapper and 0-1 wrap around 2-gapper). The latter (7 nut outs) performs a little better than the first two (3 nut outs), but in general these draws are garbage wraps that we don't want to play a big pot with against many opponents and/or with high SPR. But they can of course perform well with low SPR, or as backup to another hand/draw.

We end Part 9 with two examples of counting outs for wraps and playing them on the flop. In both examples we assess the value of our hand based not only on outs, but also on the other situational factors (number of opponents, position and SPR), and we'll make a habit out of doing this kind of quick, initial postflop analysis every time we see a flop and have to make postflop decisions.

Example 5.2.1: Wrap in a raised, multiway pot

You ($10) raise to $0.35 with 9 8 7 6 in MP, CO ($10) calls, button ($10) calls, SB ($10) calls, BB ($10) calls.

Flop: J T 5 ($1.75)
SB ($9.65) checks, BB ($9.65) bets $1.75, what is your plan?

We raised a double-suited rundown from MP and ended up in a 5-way pot with a wrap and 2 backdoor flush draws. The postflop scenario is:
  • 4 opponents
  • Out of position
  • SPR =5.5 (low/medium)
  • A 0-3 wrap around a connector with 13 (3) outs + 2 outs to backdoor flush draws

When BB bets the flop our position becomes a little worse, since we're now forced to make a decision with two unknown quantities (CO's and button's hands) behind us.

So we have 3 nut outs, 10 outs to a non-nut straight, and 2 outs to non-nut flushes. Is this enough to get involved in this pot? The answer is definitely no after BB bets into the field with 3 players (including the preflop raiser) behind him. If BB knows what he's doing, he needs a very strong hand, and on this type of flop texture his range will be weighted towards quality wraps (that have our non-nutty wrap dominated). And even if BB should be splashing around, this flop will often have hit CO or button, and sometimes SB will also have a strong hand, looking to checkraise.

This scenario is pretty poor for us, and if we continue, we will mostly get a lot of chips in with insufficient equity. We note that having memorized the wrap outs gives us strong control over the situation. We immediately know both the number of outs and the number of nut outs, and it's the lack of nut potential that forces us to fold in a multiway pot. We have too many opponents, too little information about their hands, and too high SPR to be splashing around with a non-nutty draw.

Example 5.2.1: Pair + inside wrap + flush draw in raised, multiway pot

CO ($10) limps, button ($10) limps, SB ($10) limps, you ($10) raise to $0.50 with A K Q J in the big blind, CO calls, button calls, SB calls.

Flop: A T 7 ($2)
SB ($9.50) checks, what is your plan?

This looks much better than the previous example. The postflop scenario is:
  • 3 opponents
  • Out of position
  • SPR =4.8 (low/medium)
  • Top pair/top kicker + nutflush draw + inside wrap

In other words, pretty similar to the previous example, with the exception of our equity, which is much better. Here we have a true monster. Our top pair of course has limited value in a multiway pot, but we're backing it up with two strong draws. The nutflush draw gives us 8 nut outs (the T pairs the board), and we have 8 additional non-spade inside wrap outs. This gives us a total of 16 nut outs on the flop.

So let's do a worst case equity estimate and see how we do against the current nuts (top set):

We then have 16 outs on the flop to a nut straight or the nut flush. But if we hit on the turn, Villain's top set has 9 outs to a full house (note that he doesn't have 1 out to quads, since we have an ace on our hand). This means he draws out on us 9 out of 43 times (there are 43 unknown cards in the deck, since we know our cards, the cards on the board, and Villains two aces). We round this to 1/5.

So we subtract 1/5 of our outs and reduce 16 outs to 16(4/5) =12.8 clean outs on the flop. We conservatively round this to 12 clean outs to account for the unknown equity Villain has from his side cards. This gives us 3 x 12 + 9 =45% equity against the flopped nuts.

If we get all-in heads-up against the nuts on the flop, we get all-in with 45% equity in a $2 + 2 x $9.5 =$21 pot where our investment on the flop is $9.50. The EV for going all-in is then:

EV 0.45($21) - $9.50 =-0.05

In other words: We are break even in the worst case all-in scenario, even if we get it in against the nuts. A ProPokerTools simulation confirms our equity estimate:

Of course it's overkill to calculate our equity against the nuts here, since it's obvious that we have monster draw strong enough to get all-in against anything. But it's good practice to do these equity calculations from time to time, even if they are obvious. This trains our ability to quickly and accurately estimate equity on the flop against various hands we might meet.

At any rate, on this flop we can get it in heads-up against any hand, even top set. This is good news, but not the best news. The best news is that the flop is an action flop where we expect to get action from a wide range of made hands and draws that we crush!

When we bet out on this flop, we can expect to get action from many Broadway hands (two pair, top pair + straight draw, top pair + flush draw, etc.), and all of these are dominated by our extremely nutty top pair + draw combination. We might also pick up action from hands that have some non-nutty pair + draw combination involving the T7-combination on the board.

Betting out and getting called or raised in a multiway pot would be a wonderful result for us, so we c-bet pot and hope we get plenty of action. This is the type of nutty hand/draw we dream about having when we get involved in a very multiway pot, and they don't give us many tricky decisions.

6. Summary
In Part 9 we have done a systematic discussion of equity for various draws. We have learned to estimate outs, and we have seen that the value of a draw can be very dependent on the other situational factors.

The best way to assess the quality of a draw is not to count outs in a vacuum, but to look at the whole picture. We estimate outs, and then we look at the other factors and think about the type of hand we need to be comfortable playing a big pot.

This concludes our work with the simple model for postflop planning, where we systematically look at the factors:

- Number of opponents
- Position
- Equity

From here on we'll think through these factors every time we see a flop, just like we did in the last two examples. If you make a habit out of it, this kind of structured thinking will eventually become automatic. Of course you'll still be faced with tricky postflop decisions, but this structured model for postflop planning will stop you from doing lots of obvious and boneheaded mistakes. In other words: It provides lots of low hanging fruit.

We'll begin Part 10 with a series of examples of postflop planning where we use our model. All examples will be "real life" and taken from hands I have played myself, or particularly interesting hands I have found in training videos or on forums. This will provide valuable training in adjusting to different types of opponents, various stack sizes (=multiple SPR values on the flop), and all kinds of other information that we have to process and adjust to.

The rest of Part 10 will be about c-betting on the flop. After Part 10 there will be at least 1, possibly 2 more articles about postflop play. And after that there will be a concluding article where we summarize our work and discuss the practical bankroll building project ($5PLO to $200 PLO).

Good luck!