Why Preflop Ranges Matter: Dry Overpair on a Lowcard Flop

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1 Why Preflop Ranges Matter: Dry Overpair on a Lowcard Flop In this analysis we will explore a 3way situation in a 3bet pot on a low card flop. We will see how the preflop ranges of the players involved make all the difference on this type of board. A loose player limps in middle position, and button decides to isolate him with a pot sized raise. I decide to 3bet my mediocre kings in the SB, figuring to be way ahead of BTN s range. This hand could be played as a call, but since the flop SPR is going to be less than 3 when called, it will be easy to enough to play in a 3bet pot. The limper decides to call our 3bet and BTN calls as well. We see a 753r board, and we are first to act.

2 We will start with the preflop ranges. For the limper I assign a 50% range, excluding a 12% opening range. For BTN I assign a 50% opening range, excluding AA. The first thing we ll look at is our equity against their ranges on the flop. It turns out that we are an underdog against their ranges, with 31% equity. BTN has 33% equity, and MP has the equity advantage with 36%. The fact that strong high-cards hands are missing from his range means that he has more hands that interact with this board. Now, for comparison, let s say that we were up against two tighter ranges, for example a 15% and a 25% range (excluding AA for both): in that case we would be a favorite against their ranges, with 40% equity! The 25% range will have 33% and the 15% range will have 27%. Before I calculate the E.V of pot/calling here, let s see how often they have a hand that can shove over our cbet. We give MP a stackoff range of 2 pair or better, the 86 oesd, and any pair+gutter combination. PJ Syntax: 35+,68+,(7,5,3):(4,6,98)

3 MP has a hand here 47% of the time, and our equity against that range is 33%. What about BTN? Button has a hand slightly less frequently, but our equity against his stackoff range remains the same. Not let s see what those numbers mean. We get a fold from both players only 28% of the time, so 72% of the time we get it in either heads-up or 3way at a serious equity disadvantage. Our 3way equity (in case of a 3-way all-in) is only 17%, and getting it in 3way is the worst scenario for us. Our low fold equity can t compensate for all the times we get it in bad, and we end up losing almost 8bb when we pot/call compared to check/fold. If either player decides to get it in lighter than this, our E.V starts plummeting even further. For example, if only one of the players decides to get it in with any pair that has 3 live side cards, our fold equity takes a dive from 28% to only 16%. Even though our equity when getting it in against this widened stackoff range has increased to 40% (up from 33%), the more frequent stackoffs and the diminished fold equity outweigh that fact, resulting in an even worse expectation.

4 We will now look at the same situation, this time assuming we are up against two 25% ranges (excluding AA). PJ Syntax: $FI25!AA We use our stackoff criteria of 2p+, oesd or pair+gutter. Since both player have the same range preflop, we only run the range distribution once this time. Each player will have a stackoff hand only 28% of the time, compared to 47% (MP limper) and 42% (BTN Isolator) for our previous assumptions. Not only that, but our equity against their stackoff range has increased by 2%. Our equity when the money goes in 3way also increased by 2%, and is now 19%. Again, let s see what those numbers mean. We get both of them to fold 52% of the time, and the expectation of pot/calling the flop is now +14.5bb!. We went from losing 8bb to winning 14.5BB just by changing the preflop ranges of our opponents. This is quite remarkable, and definitely a bigger effect than I have anticipated before doing the math. Lastly, I want to check what happens when we re up against one wide range and one tight range. Let s assume our limper limped with the same 50% range (excluding 12% opening range), but the player who isolated him was raising a

5 tight 25% range (you can assume he is a nitty reg isolating in the CO). We 3bet and get called by both. We are sitting deeper with the limper than we are with the isolater, so that s going to work against us. Can we still make a profit by potting the flop? Plugging the numbers again, we get both of them to fold 38% of the time. We get it in HU 49% of the time and 3way 13% of the time. Our E.V is +2.78BB. Pot/calling is marginal now (especially if we can realize even a little bit of our equity by checking) But it is not a losing play. Conclusions: 1. Preflop ranges make a ton of difference in 3bet pots, even at low-spr situations. 2. On rainbow, semi-connected low-card flops, you can cbet/call aces and kings happily at low-spr situations, even 3-way, as long as you are not facing wide preflop ranges. Peel & Stack Off: An Under-Utilized Strategy That Will Increase Your PLO Winrate Often times when players are facing heavy action on the flop they contemplate between playing for their stack by shoving and attempting to minimize losses by just folding. An option that is often overlooked is making a call for a large percentage of their stack and going into the turn with a very low SPR, intending to dodge the worst cards and get the remaining stack on the rest of them.

6 Have a look at this hand that I played: We open our BTN with a marginal hand and face a 3bet from the small blind who s a pretty aggressive and somewhat spewy fish. This is not a great hand to open against an aggressive 3bettor in the blinds, but being in position 230BB deep against SB I felt pretty comfortable opening this hand and calling a 3bet if necessary. On the flop, I decided to raise for value and protection. Even though our hand doesn t fare very well against a stackoff range at such a high SPR (14), I figured it s strong enough to raise against a wide 3bettor who I expected to cbet a lot and peel too too loose against a raise. Once we get 3bet on the flop, villain s range gets narrowed considerably. We know that he has a hand he likes enough to go with in a deep pot, and even for an aggressive player this represents a pretty strong range. We need

7 42.6% equity against villain s range to stackoff on the flop. Here s the snapshot of the situation: Now it s time for some assumptions. Preflop, I give villain a 3betting range of 20%. As for villain s flop range for re-raising us, I built a range that includes very few light stackoff hands and a lot of nutted made hands and draws. This range includes any made hand J7 or better, Any nut flushdraw with a pair or a wrap, some 2nd nut FD with wraps and J4 with spades. PJ Syntax J7+,(J,7,4,QQ+):Ass,(356+,T89):Kss+,J4:ss This range comprises 11% of villain s preflop range, which means it s a fairly narrow range. Let s use the range distribution model of PokerJuice to see how often villain has a hand from each category.

8 Those are the different categories I have used: A: Better made hands (44+) B: Same hand as us (J7) C: Overpair or better with NFD D: Flopped pair with NFD E: Wrap with 2nd nut or nut FD F: J4 with spades As you can see, villain has a better made hand ~16% of the time and we are crushed against that range with only 9% equity. J7 is 18% of his range and we re a 60/40 underdog against that part of his range due to freerolling. 56% of his range is consisted of pairs with a nut flush draw. This number looks huge, but given that we block all three cards on the flop and that we have no spades in our hand, we can see why villain s range is very flushdraw-heavy

9 even if he sticks to nut flushdraws. It s also important to remember that the 7 and the 4 don t really hit a 3betting range very hard. Categories E and F are insignificant in their size, and will not have a large impact on our results. Now, one might say that getting it in with 7x and a nut flushdraw is somewhat spewy at this SPR, but consider two things: 1. 7x hands that 3bet preflop will usually have a gutter to go along with the pair and the nut flushdraw. In cases where they don t, they will usually have two overcards to the Jack. So overall those hands have a lot of equity against flopped top two. 2. Our reads on villain is that he s somewhat spewy, so this weaker part of his shoving range can definitely be considered as a representation of that read. Now, how much equity do we have against villain s re-raising range? Care to guess? The answer is 44.6%. Given that we need 42.6% to stackoff, we know that shoving is slightly profitable. And indeed, shoving nets us 7.81$. But what if we don t shove? When we flat, the SPR on the turn will be 0.9 and we will need 32% equity to stackoff. Let s have a look at our turn equity distribution. The grayed columns represent turns where we don t have enough equity to stackoff. The number at the top of each column represents our equity against villain s range. Have a good look at this chart, and try to figure out what we can learn from it.

10 There are a few important things to notice here: 1. Hero stacks off on the majority of turn cards (73.3%). 2. on 14 turn cards, hero s equity goes up by 9% or more compared to his flop equity. 3. On the 12 cards that hero dodges, his average equity is 15.3%, way less than the equity he needs to stack off (32.2%). All of those three points are indicative of a good spot for a Peel & Stack Off line. Let s discuss them briefly. Point 1 tells us that we don t have to fold on many turns. No need to explain why this is a good thing. Point 2 implies that we stand a decent chance of improving significantly on the turn. This is also good for obvious reasons. Point 3 is sometimes overlooked but it s possibly the most important: The fact that we have such a low equity on the turns that we dodge means that we don t fold out a lot of equity in the pot when those turns hit. This is a crucial thing:

11 When villain s flop equity is largely attributed to having turn outs that crush hero s range, denying villain from getting the rest of Hero s stack on those turns will result in a big EV gain for Hero. Now, remember that when calculating the EV of a Peel & Stack Off line we assume that villain is committed and will get the rest of his money in on all turns that we choose to. This will not be true in every situation but in the case of this hand it is very much true. If you look at all the turns we stack off on and think about Villain s range, he will either have a made hand or strong draw. Since Hero doesn t represent sets after peeling the flop, we should not expect villain to check/fold on pairing turns with a hand like AA+NFD given a SPR of 0.9. Now, you waited long enough. What s the result of peeling and stacking off on our selected turn cards? We run the PokerJuice Peel & Stack Off module and we get our result:

12 Hero gets his money in on three quarters of the turns with 55% average equity and nets 30.43$ compared to the 7.81$ he would have made by shoving. This result really surprised me. Not because I didn t expect P&SO to do better than shoving, but because I did not anticipate such a huge different. Of course there s always room to play around with the assumptions. If we change villain s flop range to be even narrower and more made-hand heavy, the EV gain from peeling would be smaller. But this result speaks very clearly in my opinion. Assumptions aside, I believe that anything but peeling his raise should be considered sub-optimal. I hope you ve enjoyed this article and that you understand better how to use this strategy to increase your winrate. Flushing Turns in 3bet Pots Part 1 Flushing turns are unique. Like pairing turns, they can turn a dynamic texture into a static one. However, while pairing turns usually favor the range of the flop aggressor, a flushing turn will often have an opposite effect aiding the range of the flop caller. Today I m sharing with you the first article in a 2-part series that will attempt to offer some insight on flushing turns in 3bet pots. I have learned a lot from writing this and it s exactly the type of content I want to share only with my subscribers. Our example hand is a 3bet pot between the button and the small blind. BTN opens for 2.5x big blinds, SB decides to 3bet and BTN calls. The flop comes A86cc and SB fires a cbet for 75% of the pot:

13 As always, we start by making a few assumptions about each player s range. We assign BTN with a wide 90% opening range and assume that SB 3bets a decent 12% range OOP. BTN will continue against the 3bet with his entire range, excluding a 4% 4bet range. The first number we have is the range vs range equity on the flop. SB is of course a big favorite on this flop with 61% equity against BTN s range. We proceed by building a wide cbetting range for SB consisting of any top pair or better, any FD and any gutter. PJ Syntax A+, 54+, cc. This results in a cbetting frequency of 82% which seems reasonable for this situation. Some players will cbet 100% of their range on this board, but I went with a slightly more conservative assumption. We will touch on the implications of a 100% cbetting range later in this article. Now we build a flatting range for BTN against a cbet. We start by deciding what hands he raises the flop with: any set, A6/A8 with additional equity and

14 any nut oesd or wrap with a FD. We exclude all those hands from his flatting range. PJ Syntax: 66+, A6+:(54+,cc),79+:cc We assume BTN calls the cbet with the following hands: any FD with a pair or a gutter, any naked 2nd nut or nut FD, any wrap and any top pair or better. We include some lighter floats in the form of any OESD with either a pair or a nut flushdraw blocker. PJ Syntax: cc:(54+,6+), Qcc+, 574+, 57+:(6,8,A,Kc), A+ Overall BTN continues against the cbet 52% of the time flatting 45% and raising 7%. We can already see that SB should be cbetting a wide range here. SB s cbet only needs to work 43% of the time to break-even and BTN is folding 48% of the time. Since BTN s preflop range is so weak, SB can profit on a cbet with any four cards. In our example hand BTN decided to flat the cbet and the turn brought the deuce of clubs. Since each flushing turn is slightly different, I want to start by comparing two different club turns the highest club and the lowest club and figure out the difference between them. We start with the lowest flushing turn the deuce of clubs:

15 First of all, we see that the range vs range equity has shifted from a 61/39 in SB s favor to a 50/50 tie. We can already tell that this is a good card for BTN s range. Comparing the likelihood of holding a flush for each player, SB completes a flush on this turn 31.6% of the time while BTN completes a flush 34.6% of the time. While the players have equal range vs range equity, BTN holds a bit more flushes which gives him a slight advantage. He also has position in a spot where two more bets can go into the pot. All things considered, he is definitely in a better spot than SB now. But what about the highest flushing turn? Let s look at the Kc turn: We can see that SB retains some of his equity advantage, mostly because he makes a lot of two pair combos on this turn that have a lot of equity against the non-flush hands in BTN s range. However, this turn is not necessarily better for SB than the 2c turn, since he now suffers from a bigger polarity disadvantage: He makes a flush on this turn only 27% of the time compared with 33% for SB. This is definitely significant, especially OOP. We see that when a strong preflop range cbets the flop against a weak preflop range, a flushing turn can be very good for the weaker range. This is something I already touched on in my article range distribution on a flushing

16 turn, but here we get to see that the same applies even in a battle between a 3betting range and an ultra-wide opening range. If you wonder why SB makes less flushes on the Kc turn, there s a simple explanation to that: since SB s range is much more high card heavy, a bigger percentage of his flush draws are high flush draws. As a result, a high flushing turn blocks more flush combos for his range than it does for BTN s range. Now, we said earlier that some players in SB s spot will always cbet this flop. What will be the implications of such flop strategy on our flushing turns? You can probably guess yourself that SB s equity and flush frequency will go down, but let s look at some numbers to get a better feel for this effect. Assuming a 100% cbet range for SB now, we take a second look at the 2c turn. I have made a small table for comparison: Flop Cbet Frequency Turn Equity VS BTN Flush Frequency BTN s Flush Freq. 82% 50% 31.6% 34.6% 100% 43% 26% 34.6% A pretty significant difference. Now, let s do the same comparison for the Kc turn:

17 Flop Cbet Frequency Turn Equity VS BTN Flush Frequency BTN s Flush Freq. 82% 53% 27% 33% 100% 49% 22% 33% We can see that a cbetting frequency of 100% puts SB in a real problem on flushing turns. On the 2c turn, his range vs range equity drops to 43% and he has considerably less flushes than BTN, both are big problems especially OOP. On the Kc turn, his equity disadvantage is insignificant. However, this turn presents a significant polarity problem for him: He only holds a flush one out of 4.5 times while BTN holds a flush one third of the time. Since flushes have extremely high equity against non-flush hands on the turn, this is a very significant difference. Now, this doesn t imply that a cbetting frequency of 100% of the flop was a bad strategy. We already saw that SB had a lot of immediate fold equity against BTN s range. But we did learn that one of the downsides of this strategy is an increased vulnerability to flushing turns. This is something to keep in mind when you are in BTN s spot on the turn. Ask yourself: Is my opponent cbetting this flop 100% of the time or close to it? If the answer is yes, you should consider putting pressure on them when the turn brings a flush. In summary, we have learned that flushing turns help to close the gap between tight and wide ranges and in some cases even turn the situation upside-down putting the flop underdog in the driver s seat. We also learned

18 about two important things to pay attention to the rank of the flushing turn and the flop cbet frequency of the aggressor. Higher flushing turns, while helping the 3bettor make stronger non-flush hands, result in a bigger disparity in flush frequency which translates to a polarity disadvantage. In addition, higher flop cbet frequencies for the aggressor can magnify this disadvantage. We saw examples of how those two parameters can make a big difference. On a 2c turn, assuming a 82% cbet for SB, we saw a rather small advantage in flush frequency for BTN. On a Kc turn, assuming a 100% cbet for SB, we saw a very big difference. We see again that seemingly small details can make a big difference when added together. I highly suggest reviewing the numbers in the tables at least one more time. Paying attention to more details than your opponents can give you a significant edge over them. In part two, we will look into BTN s strategy facing a check from SB on a flushing turn. Should he bet the turn with any flush? If called, what s the weakest flush he can shove for value on the river? Those are just some of the questions I will tackle in part two. Flushing Turns in 3bet Pots Part 2 In part 1 of this series we talked about how a flushing turn in a 3bet pot can take the lead away from the preflop raiser on an ace high board. If you haven t read part one, I really recommend that you read it now since it s the foundation for this second part. Even if you already read it, it might be a good idea to give it a second look before jumping into part two.

19 This series of posts is going deeper than anything I ve written so far. If you make the effort to study this content, I promise you it will be worth your time. This second article will discuss situation that BTN faces when he completes a flush on the turn and the SB checks to him. Here are some of the topics we ll talk about in this article: How thin can he bet with flushes on the turn while still pushing an equity edge against SB s continuing range? How does things change when SB is capable of slowplaying the nut flush? How thin can BTN shove for value on the river? To start, let s assume that BTN (from this point called Hero) has completed a pretty weak nine high flush. SB has decided to check and Hero needs to decide if he wants to bet or check back. There are many different factors that can go into hero s decision here, but I think the most fundamental thing to be considered is whether or not hero

20 pushes an equity edge against SB s calling range. If the answer to this question is no, then this bet doesn t make much sense as a value bet. As you can see in the picture, our equity against SB s overall turn range is 72%, but that number will obviously go down significantly when he continues against a bet. We will analyze two different assumptions: 1. SB checks his entire range. Since he is aware of being in a range disadvantage (as covered in part one), he decides to play defensively and check his entire range, including the very top of it. 2. SB would continue barreling with a polarized range of nut flushes and nut flush blockers, checking the rest of his range. We already know that if villain is using startegy 1, his range will be stronger. This will result in us not being able to value bet or bluff as much and it s probably the biggest benefit of using this strategy from his point of view. Let s see how this plays out in practice. I used the PokerJuice RD module to split villain s range into 5 categories: 1. Better Flushes 2. Weaker Flushes 3. Sets 4. Aces Up (A2+) 5. Everything Else

21 Let s start with looking at the range distribution for the villain who plays strategy 1: If villain check/calls with A2+, he ll be check/calling 54% of his turn range. Even though better flushes comprise only 23% of his overall turn range, they account for 43% (!) of his turn continuing range. Remember, better flushes are hands that we have zero equity against. Given this data, it s easy to guess that the nine high flush is behind SB s continuing range in terms of equity. Asking PokerJuice for the accurate number we get 48.1%. What about the villain who plays strategy 2? Just to remind you, this villain barrels off with the nut flush and the nut flush blocker, checking the rest of his range. Again with use the PokerJuice RD module using the same sets of ranges:

22 As expected, we see a decent drop (about 30%) in the size of range A. Given that this range has us drawing dead, it s obvious that this drop has a significant positive impact on the value of our nine high flush. And indeed, our equity against a continuing range of A2+ goes up to 57.5%. Betting the nine high flush for value doesn t seem ambitious at all anymore. I have repeated this entire process for the ten high flush. For the sake of not dragging the article too long, I ll just drop the equity figures from PokerJuice against each strategy: Vs Strategy 1: 54% (up from 48% for the nine high flush) Vs Strategy 2: 64% (up from 57% for the nine high flush) We can see that moving one rank higher has a pretty big impact, even though our T high flush is still only the 4th nuts. While the nine high flush seemed like a prudent check against an opponent capable of slowplaying, the ten high flush seems to be a comfortable bet even if the nuts is still in our opponent s range. Now, let s move on to the river. We assume that villain check/called the turn with A2+ and the river came an offsuit jack.

23 Building a river calling range for villain is more tricky, since different players have different hero-calling tendencies and a lot will depend on the hero s image and the dynamic between Hero and Villain. Having said that, we can make some general assumptions to get the overall feel for the situation. I think it s fair to assume that flushes will be reluctant to fold the river, and that some of the non-flush made hands will decide to give up, especially if they don t hold a club blocker. Again, we use the PokerJuice RD module to split villain s range, this time into 4 categories: 1. Better Flushes 2. Worse Flushes 3. A2+ with a club blocker 4. Everything else

24 we assume villain calls the river with ranges A, B & C and that he folds hands from range D. We start with the uncapped range, that still contains the nut flush. We can see that range A (better hands that call) is much bigger than ranges B & C together (worse hands that call). Even though villain only check/folds 37.4% of his range, our nine high flush is still not close to being a value bet, with only 32% equity against Villain s river calling range. In fact, villain has to check/call with 85% of his range before we break-even on a shove here. We know that things will change for the better if we were facing a capped range. But will it be enough to make this a value shove? running the numbers against strategy 2 we get the following result:

25 Again, range A is significantly bigger than B & C put together. Our equity against villain s calling range has gone up to 41%, but we need more than 50% equity to make this a value shove. I ran the same numbers for the Ten high flush, and just like before I m gonna give you the short version. The numbers represent our equity against villain s calling range. Vs Strategy 1: 41% (up from 32% for the nine high flush) Vs Strategy 2: 53% (up from 41% for the nine high flush) We can see that shoving the T high flush for value on the river is quite marginal and depends heavily on our opponent s range being capped. Before we wrap up, let s look at the numbers for the Jack High Flush Vs Strategy 1: 54% (up from 41% for the ten high flush) Vs Strategy 2: 73% (up from 53% for the nine high flush)

26 Once we get to the Jack high flush, we have a close shove against the uncapped range and a clear shove against the capped range. I d be happy to shove this hand for value against all but the tightest players, even if they still hold the nuts in their range. Calls from worse flushes and hero calls with weaker bluffcatcers seem to make up for the chance of running into a better flush. Flushing Turn in 3Bet Pots Part 3 In part 2 of this series, we began analyzing the situation where we complete the flush on the turn and the SB checks to us. We talked about what flushes we can comfortably value-bet on the turn and river and we saw how villain s strategy with the nut flush affects our ability to value bet. Let s say that based on villain s tendencies and on our findings from part 2, we decide to to bet the turn and shove the river with the ten high flush or better. What hands should we be bluffing with? And how frequently?

27 At this third and final part we ll attempt to build a solid betting range for hero, with a good balance of value hands and bluffs. Our primary goal it to put most of the SB s range in a very tough spot. We want to avoid betting too wide or too narrow, which would be easy for him to exploit. Size Matters Before we decide what hands we ll be betting, we need to choose our bet sizing. Since we re betting a very polar range, we re going to pick our bet sizing based on the principle of geometrical growth of the pot. To learn more about this concept (and many other useful concepts) I recommend Will Tipton s excellent book Expert Heads-Up No Limit Holdem: Part 2. This book, as well as it s predecessor, explains a wide range of poker theory topics in the clearest, most interesting way possible. In short, betting for geometrical growth of the pot requires that we bet the same percentage of the pot on each street, with the final bet being an all-in bet. In our example, this requires we bet 55% of the pot on the turn and 55% of the pot on the river. Many players bet the turn small in this spot, aiming to go for a pot sized shove on the river, as they feel this puts more pressure on villain. I feel like this is mostly a result of not wanting to end up with a small river shove on a bluff. However, Theoretical models show us that this strategy actually allows us to bluff more, not less. So, now that we picked our bet sizing, how do we build a balanced betting range for the turn and river?

28 Starting From the River and Going Backwards How many hands we can shove on the river, while still making villain indifferent between calling and folding with a bluffcatcher? When we bet 55% of the pot on the river, we re giving him odds of 2.79 to 1 and he needs 26.3% equity to call. That means we can have up to 26.3% of our river range be bluffs. If we have more bluffs than that, he should always call with his bluffcatchers. The ten high flush or better comprises 26.6% of our total turn range. If we add in 9.5% of our hands to be used as bluff, we will strike the right balance. We re giving villain 2.7 to 1 on a call, and we have 1 bluff for every 2.7 value hands in our range. Overall, 36.1% of our turn range can shove the river. Now, if we were to the bet the turn with this frequency, villain would always fold his bluffcatchers, since we ll be jamming the river 100% of the time. When we jam a balanced range on the river, villain s EV with a bluffcatcher is going to be zero. And if we always bet the river and put him with in a zero-ev spot, how can he call a turn bet? Adding Turn-Only Bluffs We need to add some bluff combos to our turn betting range that we intend to give up with on the river. How do we figure out how many? We start by treating all of our river shoving hands as value hands on the turn. This is a bit tricky for some people to understand.

29 Since villain is not making money against our river shoving range (assuming we shove a balanced range), he can only make money vs our river check back range. The same way we created a balance between value hands and bluffing hands on the river, we create a balance between double-barrel hands and single-barrel hands on the turn. And since we re using the same bet sizing (and giving him the same odds), we use the exact same ratio. We want to have 2.79 double barrel hands for every single-barrel hand. Since we bet 36.1% of our range on the river, we can add an additional 13.34% single-barrel bluffs, resulting in a turn betting frequency of 49.5%. With deeper stacks, we would have been able to bet higher frequencies on the turn and the river. For example, with two pot sized left bet on the turn, we could have potted the turn with 59.2% of our turn range. This is why getting the EV of holding a bluff-catcher goes down with deeper stacks you get to showdown much less frequently against a tough opponent. So, how do we build a 49.5% betting range on the turn? We already know what hands we re betting for value, so our goal is to fill up the remaining combos from bluffs. Every weak holding in our range is a bluffing candidate, but some hands are better than others. We re mainly looking for 3 things: 1. Low showdown value 2. Blocker value 3. Some equity vs villain s calling range I have defined showdown value as any hand better than one pair that s not in the value range. A weak two pair hand like QT86 had 34% equity against

30 villain s overall turn range, which means that attempting to show it down should result in a pretty good EV. We re not folding many better hand when we bet 86 here, and as we ll see we don t lack weak hands to bluff with. A Closer Look at Our Range I ve split our range into 6 categories, and we ll quickly go over them. Category A is our value bets the T high flush or better. Category B is the hands we check back for showdown value all made hands 2pair or better, including weak flushes. Here are a few examples: Now, categories C, D and E will be hands that we use as bluffs. They ll have low SDV (weaker than 2pair) and at least one of two favorable features a draw or a club blocker. Category C: Hands with a draw and a club blocker. This includes any hand with at least a gutshot straight draw and one club of any rank. Category D: High club blockers without a draw. I ve defined those as the T high blocker or higher.

31 Category E: Decent draws without a club blocker. Those include all open ended straight draws and wraps. Again, here are a few examples (all three categories are represented): Category F includes all the other hands left in our range. Those are mostly hands without much showdown, but we won t use them as bluffs since we ve filled up all the bluffing spots in our betting range. Those hands still stand a chance to win at showdown sometimes, as they often have top pair. For example: Now, let s look at how often we have hands from each category:

32 If we sum up all the categories of hands we ll be betting the turn with (A,C,D,E), we ll achieve our desired betting frequency on the turn: This, of course, didn t happen by chance. I added and removed hands from the bluffing categories (C,D and E) until I got to my target betting frequency. There are different ways to go about this. You can add more club blockers and take out a few straight draws. You can do the opposite as well. Unlike NLH, We can t really solve spots like this in PLO down the specific combos, but as long we build our betting ranges in spots like this based on solid principles we ll be putting our opponents in difficult spots and minimize the EV of their bluff catchers. Giving Up On the River Let s assume that villain calls our turn bet and we get a blank river like the jack of spades.

33 as we established earlier in this article, we need go give up with some of our bluffs. But how do we know which bluffs to give up on? Unlike the turn, where we listed three attributes of a good bluffing hand, only two things matter on the river: showdown value and blockers. Since we were betting the turn with a polarized range and the river didn t improve any of our semi bluffs, all of our turn bluffs still have low showdown value on the river. If the river was a ten, for a example, we would have an easy give up with our 97 combos. A rivered straight can win pretty often at showdown against the two pairs and sets in villain s range, making it a very standard check-back. Since all of our turn bluffs didn t catch any showdown value, we ll choose our river bluffs only on the merit of blocker value. When we look at our river distribution on an offsuit jack after betting the turn, our value hands comprise 52.8% of our river starting distribution. The other 48.2% are our turn bluffs. Given the pot odds we re laying for villain (2.79 to

34 1), we can bluff with 19.5% of our range, for a total betting frequency of 72.3%. Betting the river at a high frequency is a result of our turn range construction. Had we bet the turn with a wider range (without expanding our value range), we would have been forced to give up too often on the river, allowing villain to call the turn profitably. On the river, if hero bets the 8 of clubs or higher, he s bluffing with 18.4% of his range, a little bit short of the 19.5% he needs to balanced. If he adds the 7 of clubs to his betting range, he s now bluffing 24.25% of the time, which means he is over-bluffing. A good river strategy in this spot would involve always betting with the 8 of clubs or higher and betting with the 7 of clubs only occasionally. This, of course, is not a conclusion we ll be able to draw in-game. But we dive into numbers to build better intuition, understand how ranges look and get an idea of proper betting frequencies for different spots. This is how we get better.