Three-Bet Stack-Off Guide. Contents. Introduction Method Assumptions Hand Examples Reading Tables K987ss on KJ6r...

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2 Contents Introduction... 3 Method... 3 Assumptions... 3 Hand Examples... 4 Reading Tables... 4 K987ss on KJ6r... 6 QJ87ss on T95t (no flush draw) QJT5ds on 952r Q784ds on J96t (with flush draw) AQ85ss on AT7r T998ss on 863t (with flush draw) Three-bet stack-off Tables

3 Introduction This guide is meant to be used as a reference for when it is profitable to stack-off on the flop in three-bet pots. The conclusions reached in the hand examples should be applied in future in-game decisions, adjusting for specific opponent ranges and frequencies, as well as stack sizes. Method Having decided the fixed factors, the process of creating this guide was as follows. We chose the most common 3betting scenarios, CO vs BTN and BTN vs the blinds and included different hand strength examples on various board textures. On the flop, we analyze the EV of our shove versus relatively high c-betting frequencies on the drier or favorable boards for the three-bettor. On wet boards, we assumed that c-betting frequencies are lower and we generally have less fold equity. We used 50,000 trials for each simulation. We ran hands versus various opponent types and analyzed how different assumptions shift our EV in one direction or another. This is the real lesson from this guide and the hand examples are mainly a way of visualizing the information. Assumptions There are many important factors to consider when evaluating the EV of a stack-off decision. All of the hand examples start off with 100bbs and are for relatively wide three-betting ranges involved in resteal spots. All preflop bets are pot-sized. The factors that change between hands, other hand strength and board texture, are: Villain's 3bet % preflop, IP or OOP (see PokerJuice Preflop Ranges): Preflop-Ranges). Villain's continuation betting (c-betting) range. Villain's stack-off range. These factors highly impact the EV of shove, since they directly affect both our fold equity and pot equity on the flop. 3

4 Hand Examples As most boards are two-tone or rainbow as well as unpaired, we shove board textures in these categories. The situations we analyzed are the following: Positions Hand Flop SPR CO vs BTN K K J BTN vs BB Q J 8 7 T SB vs BB Q T J CO vs SB Q J BTN vs SB A Q 8 5 A T CO vs BTN T Reading Tables After each hand example there will be a table with a short summary of the hand's data. Here are some instructions on how to read the table: Hand K Vs 3b% C-bet% Equity vs SO Fold % $EV Flop K 6 J 15i 78% 33% 32.70% -$1.20 SPR i 100% 33% 47.48% $8.25 The first two columns with shading (left to right) will contain the Hand, Flop and SPR for the hand. Vs 3b% is our opponent's 3betting range by number and by position. 15i means 15% 3bet in position range, while 6o means 6% 3bet out of position range. C-bet% is the frequency with which our opponent is continuation betting on the flop. This number was reached by considering the hands people would c-bet in these scenarios. They tend to be high in 3bet heads-up pots, but range composition and tendencies will differ between opponents. Equity vs SO is our pot equity versus our opponent's stack-off range, ie our equity when called. 4

5 Fold % is the frequency our opponent is c-betting and then folding to a shove. This number shows the gap between our opponent's c-betting range and his stack-off range. In low SPR scenarios, there is usually not much fold equity after a big c-bet goes in. $EV is the expected value of our shove in dollars and also has gray shading. Since all our examples are for 100plo, $EV will be equal to our profit in big blinds. Results throughout the guide do not consider rake and will vary slightly depending on the number of trials. The purpose of these tables is to get a quick look at how EV changes due to each factor. Each hand example will have more relevant information like c-bet and stackoff ranges, c-bet sizing and opponent profile. 5

6 K987ss on KJ6r We will start off with a CO vs BTN situation. We open K987ss and get three-bet by a very active BTN with a 3b range of 15%. We call and the flop is KJ6r. Let's assume he c-bets $16.50 into $25.50 with every K+ and every gutshot or better (T9+). This range accounts for 78.03% of his pre-flop range. If we shove, he stacks-off with: J6+,K+:(T9+,dd,ss,hh),QT+:J+,QT9+. This should be read as any two pair or better, any King with a gutshot or backdoor flush draw, the QT open ended straight draw with a Jack or better, or any wrap. Given this input, PokerJuice calculates the EV of this shoving as -$1.20 without considering rake. This means that versus even versus a wide three-bet and a reasonable c-betting range, we are still losing money by check-jamming this top pair hand plus backdoor flush draw and backdoor straight draws. This is because we do not have significant fold equity after he c-bets (he folds 32.70% of the time), and our hand only has 33% equity versus his stack-off range. CO vs BTN, SPR

7 What if villain c-bets 100% of his range because he believes he has a significant range advantage on this board or he is overly aggressive? If he stacks-off with the same range as in our first example, he will now only be able to stack-off 52.52% of the time, which leads to an EV shove of $8.25. With a solid read that our opponent is c-betting at near 100% and his folding frequency has increased 15%, we can profitably check-jam in this spot. Since the simulation was run versus a wide three-betting range ($3b15i), you can be confident that on a heavy board like KJ6r, tighter three-betting ranges will hit the board stronger on average and fold less often to a raise. For example, versus a 3b8i range with our the first c-betting range (K+,T9+) and same stack-off range, the EV of our shove drops to $-6.70 since he only folds 23.55% on the flop. By the way, an 8% three-betting range will have a c-betting hand 89.5% of the time! 7

8 Versus tighter three-betting ranges (and reasonable c-betting strategies), you'll need a stronger hand to get an +EV shove on this board texture. Changing our hand to KT98ss, which gives us a non-nut gutshot provides us an equity boost when called that improves our EV shove to $4.80 versus the same 8% three-betting range. 8

9 In conclusion, a board texture like KJ6r tends to favor the three-bettor, even when facing a wide 15% three-betting range. A weak top pair hand is not going to be a profitable check-shove unless villain is mindlessly c-betting and over folding to check-raises at low SPRs. Versus the widest ranges, a top pair and weak gutshot is enough to get stacks in provided you have some fold equity. Versus stronger three-betting ranges like 8% and lower, we need slightly more than a pair and gutter to profitably jam. In most cases versus this sizing, we have enough pot equity versus his range that we can likely check-call the flop profitably. Hand K Vs 3b% C-bet% Equity vs SO Fold % $EV Flop Kh6sJd 15i 78% 33% 32.70% -$1.20 SPR i 100% 33% 47.48% $8.25 9

10 QJ87ss on T95t (no flush draw) In this hand example, we open from the BTN with QJ87ss and get three-bet by a tight player on the BB with a three-bet range of 6%. On this board texture, a lot of tighter players will not be c-bet folding very often. They will check-raise and check-call some parts of their range. In the first simulation our opponent is c-betting with ~53% of his hands, all of which are bet-calling versus a shove. BTN vs BB, SPR 3.96 With no fold equity, our wrap and backdoor flush draw is a barely profitable jam ($4.70) as we are flipping versus his range. In a scenario like this, calling makes sense since we are in position and have no actual fold equity. Versus a wider 15% 3bet range, our EV shove is the same when he c-bets and doesn't fold. The only difference is our opponent has to reduce his c-bet frequency because he less often has a bet-calling hand on this board. 10

11 Let's say we are up against an overly aggressive opponent who c-bets a lot and doesn't check-call much in this spot. That kind of opponent could decide to c-bet more often, so let's add the following hands to his range: AA,QJ+ and In his stack-off range, we will only allow him to call with a J87+ wrap or better, and only Aces with at least one backdoor flush draw or gutshot. This means he will be folding to a shove 19.29% of the time. This added fold equity almost triples the EV of our shove to around $ Again, we could potentially just flat-call being in position, but the more our opponent is capable of c-bet folding the more strongly we should consider shoving in this scenario. In case you're curious, changing our 7h for a 5h doesn t' add much to the EV of our shove in our original simulation. Changing our 7h to a 9d, so holding QJ98ss actually decreases our equity as we block less of his flush draws. One of the highest equity hands without two pair or a flopped flush draw we can have is QhQJ8 with a backdoor flush draw, with an EV shove of $9.10. Having the Q hearts blocker makes up for about $3 of that EV. 11

12 Hand Q J 8 7 Vs 3b% C-bet% Equity vs SO Fold % $EV Flop T 9 5 6o 53% 47% 0% $4.70 SPR o 65.45% 48% 19.29% $

13 QJT5ds on 952r In this hand, we raise the SB with QJT5ds and call a three-bet versus the BB with a three-bet range of 12% that includes almost every combination of Aces and decent KKx hands. The flop is 952r and we have two backdoor flush draws. This flop texture is so dry and light, it's hard for either opponent to have hit the flop very hard. That said, a lot of players in BB's spot will attempt to win the pot by making a medium sized c-bet. Since we are rarely up versus a set, we tend to have decent equity when holding a pair and overcards type of hand. It's a spot where our fold equity is very dependent on how wide an opponent betfolds versus a raise. Due to the board texture and how wide our stack-off range could be, many players tend to bet-call many of their Aces, Kings and most of their 9x hands. Our first simulation will be run versus a loose and aggressive opponent who will c- bet 100% of his preflop range and stacks off relatively light. SB vs BB, SPR

14 As we said, villain c-bets 100% of his range for slightly over half pot. We define his stack-off range as: 9+:A3+,52+,674+,9$np,KK+:(ss,dd,hh), which means any 9 or better (including TT-AA) with at least one gutshot, any two pair or better, any wrap, any 9x without a pair in it (like AJT9ss), and any Kings or better with at least one backdoor flush draw. This means that given his three-betting range, he will have a stack-off frequency of 52.20%, versus which we will have 38% equity with our hand. Shoving has an expected value of $5.90. We could also opt for a smaller check-raise sizing due to the board texture and the amount of backdoor draws we can barrel. Players that c-bet fold more often with one pair hands should be targeted for this sort of light check-raise. You should also take into account the sizing of our opponent in these simulations. If they c-bet bigger and folded to a shove with the same frequency, then our risk/reward scenario would improve, and EV of our shove would increase. As a warning though, people generally don't fold after betting near pot on this board texture. By the way, the point where the EV of shove turns negative versus the smaller sizing is if we are playing versus a tighter opponent with only a 6% three-bet range. With the same stack-off range, this opponent stacks-off 70.35% of the time and our EV shove is -$

15 Hand Q T J 5 Vs 3b% C-bet% Equity vs SO Fold % $EV Flop i 100% 38% 47.8% $5.90 SPR i 100% 38% $

16 Q784ds on J96t (with flush draw) In this hand we make a loose open with a poorly connected double-suited hand from the CO. The SB is a TAG and has a three-bet SB vs CO of 8%. We flat-call in position and flop a Queen-high flush draw on J 9 6 with a weak open ended straight draw. CO vs SB, SPR 3.69 This is a spot where villain tendencies are very important. Some will c-bet too wide and fold to a raise, and others will develop a check-calling range and mostly c-bet when they are planning on calling a shove. In the simulation above, villain is c-betting with: 69+,J+:(7T+),9+:78+,ss:(9+,57+),KK+,Ks+!ss. That is 80.40% of his preflop range. Let's say he prefers to c-bet his KK and AA hands, as well as Ks and As blocker hands that can turn equity. He likes to check-call with many of his wraps and some weak combo draws. Given his range and being OOP, when c-betting he bets 80% of the pot. Versus a shove, he is only folding his Ks and As blocker c-bets that otherwise don't have good 16

17 equity, and his Kings and Aces that don't have a backdoor flush draw or at least a gutshot draw. Under these assumptions, the EV of our shove is almost $5.50 before rake. This is surprisingly low for a hand like ours, however our hand is so easily dominated on this board by an 8% three-bet range that is not c-betting at 100% frequency. Again, being in position and having a lot of pot equity, we should consider the option of just flatting unless our opponent is c-bet folding at higher frequencies. Since we are often going to be stacking off versus combo made hands and draws, any additional equity we hold helps the EV of our shove. Making our straight outs less vulnerable or more nutty or adding showdown value to our hand with a pair would considerably improve our EV shove result. The best thing would be to have more fold equity, particularly when we hold Queen high. Let's say our opponent is three-betting a 15% range and c-betting all his J+, flush draws, and pair+oesd. He is stacking off with the same range as the first example, except he now calls with any flush draw: 17

18 Our opponent is still c-betting 80.1% of his prelfop range, but since his c-betting range includes more bet-folds (23.42%), the EV of our shove increased to $ We still have 43% equity versus his stack-off range, but now he is folding almost 1/3 of the time. There are still some players like this at the tables but solid opponents have mostly learned not to c-bet as wide on this board texture without a specific read. Hand Q Vs 3b% C-bet% Equity vs SO Fold % $EV Flop J 6 9 8o 80.4% 43% 15.74% $5.50 SPR o 80.1% 44% 23.42% $

19 AQ85ss on AT7r In this hand we attempt a BTN steal with AQ85ss and get three-bet by a good opponent with an SB three-bet resteal of 12%. We call and the flop is A T 7. He c- bets for 2/3 pot. On this board texture, he will have a hand to stack-off with more than half the time. A quick look at his range distribution reveals he has an Ace with a gutshot or better, two pair, or a wrap 54.64% of the time. BTN vs SB, SPR 3.69 That said, we still have 49% equity versus his range (green circle). Assuming he c-bets 100% of his pre-flop range, what is the EV shove for our hand if he only stacks off with A+:(QJ+),T7+,QJ8+? 19

20 The EV of our shove is around $8.50. We don't have great pot equity versus his calling range, but he folds almost half the time after c-betting! Again, we should consider flatting since we are in position, and have such an equity advantage versus his betfolding range. Let's now assume our opponent checks some of the time on the flop. He c-bets any Ace or better, any gutshot, and any wrap. With the same stack-off range, he now only folds 34.70% of the time and the EV of our shove is only $2.50, while our pot equity versus his c-betting range drops to 43%. 20

21 Even though it's +EV to shove, there are better hands to shove with. There are many hands that retain more pot equity when called. This example below shows how having only 5% more pot equity versus his stack-off range, even though he folds less often will increase our EV slightly. Also, we have less pot equity versus his bet-folding hands so getting him to fold those works out well for us. 21

22 Hand A Q 8 5 Vs 3b% C-bet% Equity vs SO Fold % $EV Flop A T 7 12o 100% 35% 45.4% $8.50 SPR o 83.7% 35% 34.7% $

23 T998ss on 863t (with flush draw) In this hand we open T998ss from the CO and get 3bet by the BTN. Both blinds fold and we call. The flop is 8 6 3, which is an above average flop for our holding. Our opponents c- betting strategies will differ, but reasonable players check back some portion of their air range and hands with equity that wouldn't like to get check-raised. CO vs BTN, SPR 3.45 This opponent is c-betting all his QQ+ (this range is mostly AA as there are only premium Queens in his three-betting range), two pairs+, top pair+ with a nut gutter+, a flush draw with an 8+ or a gutshot+, any King high flush draw+, and any time he has the King or Ace of diamonds blocker. That accounts for 66.8% of his preflop range. Out of his c-betting range he is folding the King and Ace blockers, and Queens+ that don't have additional equity like a gutshot or backdoor flush draw. This means our opponent is folding 32.41% of the time. Versus his stack-off range, we still have 39% pot equity, so we have an EV shove of $

24 Since we are out of position and a flop check-call will lead to an awkward 1.3 SPR turn scenario, check-shoving seems like a decent option. This would be especially true when having more fold equity, like versus an opponent that c-bets more often or stacks-off less frequently. Versus an opponent with a 15% three-bet range that will c-bet any 8+, flush draw or back-door flush draw (83.2% of his preflop range), he would likely fold to a check-shove around 42.2% of the time. Our equity versus his wider stack-off range would be 41%, increasing the EV of our shove to $14.00! Versus this kind of opponent check-shoving is a no brainer, especially because we will likely have to forfeit some of our equity when check-calling OOP and are likely to face a turn shove. Hand T Vs 3b% C-bet% Equity vs SO Fold % $EV Flop i 66.8% 39% 45.4% $7.10 SPR i 83.2% 41% 42.2% $

25 Three-bet stack-off Tables Here are the tables from the six previous hand examples, so you can take a quick last view and compare the data between different ranges, hand values, and board textures. Hand K Vs 3b% C-bet% Equity vs SO Fold % $EV Flop K 6 J 15i 78% 33% 32.70% -$1.20 SPR i 100% 33% 47.48% $8.25 Hand Q J 8 7h Vs 3b% C-bet% Equity vs SO Fold % $EV Flop T 9 5 6o 53% 47% 0% $4.70 SPR o 65.45% 48% 19.29% $13.90 Hand Q T J 5 Vs 3b% C-bet% Equity vs SO Fold % $EV Flop i 100% 38% 47.8% $5.90 SPR i 100% 38% $1.80 Hand Q Vs 3b% C-bet% Equity vs SO Fold % $EV Flop J 6 9 8o 80.4% 43% 15.74% $5.50 SPR o 80.1% 44% 23.42% $10.30 Hand A Q 8 5 Vs 3b% C-bet% Equity vs SO Fold % $EV Flop A T 7 12o 100% 35% 45.4% $8.50 SPR o 83.7% 35% 34.7% $2.30 Hand T Vs 3b% C-bet% Equity vs SO Fold % $EV Flop i 66.8% 39% 45.4% $7.10 SPR i 83.2% 41% 42.2% $

26 Final Thoughts Hopefully by reading through the material you've understood how to make a PJ Shove vs Stack-off Range simulation. You can use the Game Builder to create any scenario and flop, choose your hand and play around with his preflop, c-bet and stack-off ranges to represent various kinds of opponents and scenarios. The important thing is to be realistic about people's ranges, otherwise you will be learning incorrect or useless data. Pay attention to assumptions. Specific three-b ranges, c-bet sizing, and more importantly, specific c-bet and stack-off ranges. Note all these hands are borderline decisions. The lesson to learn is how a better situation should be increasingly +EV, and if you are in a slightly worse scenario then it should be clearly -EV to shove. A better situation is one where: We are up against a wider, weaker preflop range. Our opponent continuation bets too often. Our opponent stacks-off too infrequently (increased fold equity). Our hand has more pot equity or will retain most of its equity versus our opponent's stack-off range. In the hand examples, we usually have a decent amount of pot equity with our hand versus preflop range. After we narrow their c-betting ranges, shoving isn't massively +EV. This is because opponents will usually be c-betting less than 100% and since they three-bet preflop, we tend to be up against relatively strong ranges. Also, we purposely chose hands that are too strong to fold but that we are not eager to put all the money in. Particularly in the hands we are in position, we would usually do better by flat-calling the c-bet and playing the turn versus his whole c-betting range and with more information. One last thing to consider is villain's actual range composition for their three-bet, c- bet, and stack-off ranges. Most of the frequencies we used were representative of a somewhat linear c-betting range. Some players will tend to c-bet more polarized or merged than others or use different sizing. Likewise, stack-off ranges will vary depending on opponent tendencies. Some people bet-fold a surprising amount while other's stack-off threshold is really low. It's your job to gather information on your opponents and use it to make the most accurate decision possible at the time of the hand. Until next time, run good and have some nice hands! 26