GTO 3/4/5 betting pt.1
Posted by vanity02
Posted by vanity02 posted in Gen. Poker
GTO 3/4/5 betting pt.1
Optimal 3-bet/4-bet/5-bet
1. Introduction
For my first NLHE article for Donkr, I have chosen a topic that I know many new players find difficult, namely correct strategies for 3-bet/4-bet/5-bet preflop wars in NLHE 6-max.
1.1 Presenting the problem
Against weak low limit opposition, we can get away with playing an almost completely value-based game. We 3-bet/4-bet/5-bet mainly for value, and it's not a big mistake to assume our opponents are doing the same. If we reraise as a bluff, we usually limit ourselves to the occasional 3-bet bluff. A value-based style with little bluffing works well at small stakes because our opponents use more or less the same strategy, and many of them execute it poorly. Of course, every now and then we run into aggressive players who are capable of reraising as a bluff, but there are plenty of fish that will pay off our straightforward game, even if we bluff much less than is game theoretically optimal.
But let's say our Hero has built a bankroll by patiently grinding the low limits, and now he wants to take a stab at $200NL. He will now experience a lot more 3-betting, especially if he's out of position.
For example:
Example 1.1.1: We get 3-bet out of position
$200NL
6-handed
Hero ($200) raises to $7 with J T from UTG, it's folded to the button ($200) who 3-bets to $24, the blinds fold, and Hero folds.
Straightforward, and although Hero expects to get bluffed some of the time, he really doesn't have any choice but to fold. It's correct that his hand can no longer be played for value, but as we shall see later, it's possible to turn it into a 4-bet bluff.
At any rate, Hero plays on. The players behind him keep 3-betting him frequently when he is out of position, and Hero keeps folding weak hands to 3-bets. After a while, this hand occurs:
Example 1.1.2: We get 3-bet out of position (again)
$200NL
6-handed
Hero ($200) raises to $7 with A J in MP, it's folded to button ($200) who 3-bets to $24, the blinds fold, and Hero folds.
This is getting frustrating. Hero has a decent hand, but it's not strong enough to defend against a 3-bet from out of position, so Hero folds. But he is starting to feel exploited. If only he could get dealt a good hand and punish these bastards!
What an inexperienced player now might do (as his frustration builds up more and more), is to make up his mind to fight back against the loose 3-bettors. But he doesn't quite know what to do, and therefore he will often use poor strategies, and the wrong types of hands!.
Let's look at two common (and sub-optimal) ways to defend against 3-betting, out of position with 100 BB stacks:
Example 1.1.3: We get 3-bet out of position (again) and we call
$200NL
6-handed
Hero ($200) raises til $7 with K Q in MP, button ($200) 3-bets to $24. Hero thinks for a bit, decides that this hand is too good to fold, but too weak to 4-bet, so he calls.
Flop: 944 ($51)
Hero ($176) checks, button ($176) bets $30, Hero folds.
Hero is frustrated, but he doesn't see what else he could have done out of position with a hand of this type. Too strong to fold (at least in Hero's mind) against a loose 3-bettor, but not strong enough to 4-bet. Or? Hmmmmm .... Hero contemplates his next move, and soon another 3-bet pot occurs:
Example 1.1.4: We get 3-bet out of position (again) and we 4-bet for value (or at least that's what we think we are doing)
$200NL
6-handed
Hero ($200) raises to $7 with A J from UTG, MP ($200) 3-bets to $24. Hero decides to fight fire with fire, and he 4-bets pot to $75. Button 5-bets all-in, Hero calls. MP has K K . Hero screams in agony.
Flop: Q T 7 ($403)
Turn: Q T 7 Q ($403)
River: Q T 7 Q 4 ($403)
Hero tears his clothing and sprinkles ashes over his head. Damn!!
What happened throughout this sequence of hands?
OK, I made up this story, but it illustrates several of the problems an ABC low limit player faces when he moves up to tougher games. He will get 3-bet left and right, so he will have to fold a lot out of position (which is correct). He realizes he has to fight back to avoid getting run over (also correct), but he's not quite sure how to do it. So his attempts to counter the aggression are often poorly executed, frustrating and tilt-inducing.
For example, Hero might start calling 3-bets out of position with hands he feels are too good to fold, but not strong enough to 4-bet for value. This leads to many miserable experiences like Example 1.3. Or he might start 4-betting medium/weak hands without a clear understanding of whether he is doing it for value (planning to call a 5-bet), or if he is bluffing (planning to fold to a 5-bet).
What our inexperienced Hero might not realize, is that his opponents' loose 3-betting doesn't necessarily mean they are willing to splash around with lots of weak hands in 4-bet and 5-bet pots. When two good and aggressive NLHE-players engage in 3-bet/4-bet/5-bet warfare preflop, this is what usually happens:
• Both players operate with wide ranges, and all ranges have a significant percentage of bluffs in them, especially at the early stage (raising and 3-betting)
• Both players are willing to fold most of their bluffs (but not all of them), when their opponent reraises them back
This results in ranges that start loose, but get more and more (but never completely) weighted towards value. And it's usually plain wrong to assume you can 4-bet a medium hand like AJs for value against a loose 3-bettor, and expect to be a favorite when he 5-bets all-in. Yes, AJs is a decent hand against the range that 3-bet you, but it's crushed by the range that 5-bets you, and it's your opponent who decides when the 5th bet goes in (and that rarely happens unless he has the goods).
Therefore, if you decide on a frustrated whim to "take a stand" against an aggressive and competent 3-bettor with a hand like AJs, you will discover that in some mysterious way he almost always manages to come up with a better hand when you get all-in preflop.
This has lead many an inexperienced NLHE player to lose his stack, since these players:
• Don't understand the roles different types of hands have in different types of ranges. First and foremost: Do I have a value hand that wants to get all-in, or do I have a bluff hand that I will fold to further aggression?
• Aren't willing to fold hands that are strong at the early stages, but turn into weak hands when Villain keeps reraising
Let's look at Example 1.4 again. Hero open-raised AJs (correctly), and he got 3-bet. He then decided that his AJs was a good hand against Villain's 3-bet range (debatable, but not a big mistake), so he 4-bet for value (wrong!), planning to call a 5-bet all-in. Playing AJs for value after a 3-bet and going all-in with it was a big mistake. The 4-bet in itself was not a big mistake, since Villain has a lot of bluffs in his 3-betting range, and he will fold most of them to a 4-bet. So it's not a problem to 4-bet AJs as a bluff against a range full of 3-bet bluffs. But when Villain comes over the top with an all-in 5-bet, our AJs crumbles to dust (if Villain knows what he is doing).
But our inexperienced Hero did not realize what had just happened when he got 5-bet, and he stuck with his plan of playing AJs for value against what he perceived to be a wide and weak range. The problem is that the range he faces after a 5-bet from a competent player isn't wide and weak, it's very narrow and very strong.
Note what the real mistake was in this hand. 4-betting AJs against a wide range was not a big mistake in isolation, and neither was calling a 5-bet getting 2: 1. But the combination of 4-betting AJs + planning to always call a 5-bet, now that was a big mistake against a competent opponent. It caused Hero to invest his remaining 96.5bb stack as a huge underdog. The problem was, as mentioned previously, that his opponent controlled when the 5th bet went in, and Villain made sure he had a hand.
Our goal for this article is to give Hero a set of tools he can use to comfortably counter preflop aggression when he is sitting as the raiser out of position. We'll base our work on Hero's opening ranges, and based on these, we can deduce defensive strategies against positional 3-bets. And we will use game theory to design these strategies in such a way that the 3-bettor can not exploit Hero in these scenarios. Our work on Hero's game theory optimal defensive strategies also gives us a set of optimal 3-betting strategies for his opponent, so we kill two birds with one stone.
We have here talked mostly about the ills of getting 3-bet when sitting out of position, and this is what I feel inexperienced players find hardest to deal with. But the mirror image of this scenario, with us being the 3-bettor in position, is also worth discussing. These are easier scenarios to play, but we will benefit a lot from understanding optimal 3-bet/4-bet/5-bet dynamics also from this perspective. We'll learn how to construct optimal 3-betting ranges, based on the raiser's opening range, and we'll learn how to play against a 4-bet.
Regardless of whether we're the raiser or the 3-bettor, we want to understand which hands we can (re)raise for value, and which hands we (re)raise as bluffs. And above all else, we want it to be 100% clear which of these two things we are doing before we engage in a 3-bet/4-bet/5-bet war preflop.
1.2 Our model and overall philosophy
In this article we'll design so-called optimal strategy pairs for the raiser and the 3-bettor in the following scenario:
- The raiser opens some range
- A player behind him 3-bets
- The raiser 4-bets or folds
- The 3-bettor 5-bets, or folds to a 4-bet
Note that the raiser is always out of position (e.g. UTG, MP, or CO), and that no other players interfere.
We'll define a model for this scenario with 100bb stacks and standard bet sizing. Then we'll analyze our model, using mathematics and principles from game theory (but we'll keep it as simple as possible). We then construct game theory optimal(ish) strategy pairs for the raiser and the 3-bettor (one strategy for the raiser, and one matching strategy for the 3-bettor) that they can employ in their 3-bet/4-bet/5-bet wars.
Both players are trying to play perfectly against the other, and both are assuming their opponent is trying to play perfectly as well. The two players now both zoom in on a perfect strategy, designed not to lose against their opponent's perfect strategy. And the result is a pair of strategies that are perfect against each other, and we have our optimal strategy pair.
When we have learned these strategies, we have defensive (e.g. unexploitable) strategies we can use both as the raiser out of position, and as the 3-bettor in position. Using these optimal strategies guarantees that better players can't exploit us. They will also win against players who play poorly, although they will not win the maximum (if we want to exploit opponent leaks maximally, we have to deviate from optimal play ourselves, and use strategies that target specific leaks in our opponent's non-optimal strategies).
Knowing optimal strategies also makes it easier to spot our opponents' mistakes (where we can define "mistake" as a deviation from optimal play). If we know what an opponent should have done if he had played optimally, we can conclude that he has a weakness in his game if he chooses to do something different. And we might be able to exploit these weaknesses and turn them into leaks for him.
1.3 Background material for the article
Before we get started, I want to give credit to Cardrunners instructor Matthew Janda. During the spring of 2010 he published a 3-part video series Optimal Preflop Play I-III at Stoxpoker, which contains most of the theory we use in this article. This video series was inspiring and eye-opening, but sadly it became unavailable after Stoxpoker shut down in May 2010.
Matt Janda is now a Cardrunners instructor, and he continues to produce game theory related videos. His old videos from Stoxpoker might get moved over to Cardrunners, and if that happens, I recommend you check them out.
Without further ado, let's get started:
2. The mathematics behind optimal 3-/4-/5-betting with the raiser out of position
I have chosen an approach where we first go through the necessary math and theory quickly, and then we apply it by constructing optimal strategy pairs for two scenarios:
- The raiser in early position (UTG or MP) with a 15% opening range
- The raiser in CO with a 25% opening range
Lumping UTG and MP together under the label "EP" makes sense, since most players use very similar ranges for these two positions. The percentages we have chosen for EP and CO are typical TAG ranges that can be used under all game conditions.
The exact ranges we use to illustrate the procedures aren't important. Our goal is that you learn to construct optimal strategy pair (one strategy for the raiser and one for the 3-bettor) based on your own opening ranges. And you will of course also be able to design optimal strategy pairs to use against specific opponents (not on the fly, but by doing a bit of analysis work between sessions).
2.1 Our model
We use the following scenario:
• Alice is sitting with a 100bb stack in EP or CO, and she raises pot to 3.5bb with some opening range
• Bob is sitting in a position behind Alice with 100bb, and it's folded to him. Bob 3-bets pot to 12bb
• Alice either 4-bets to 27bb (a bit less than pot), or she folds
• Bob's response to Alice's 4-bets is to 5-bet all-in or fold
• Alice's response to Bob's all-in 5-bets is to call or fold
Note that Alice doesn't defend against 3-bets by calling out of position. We could conceivably design a defense strategy where we fold weak hands, 4-bet strong hands, and call with medium hands, but this is not a good strategy out of position with 100bb stacks.
You have poor implied odds (due to low stack/pot ratio and being out of position) when you call for postflop value with implied odds hands. And it's difficult to steal and outplay Villain when you are out of position. And what you absolutely cannot do, is to call and then play fit-or-fold postflop. It will be much more fold than fit, and you are simply burning money by letting Villain c-bet his way to riches and early retirement on your expense.
With regard to Alice's choice of 4-bet size, it's standard to use 25-30bb (where full pot would be 37.5bb) with 100bb stacks. The logic behind this is that with 100bb stacks, we are putting Villain in a shove-or-fold scenario, also when we 4-bet a bit less than pot. His 3-bet bluffs will still fold, and his strong hands will still shove. So we win the same when he folds, but lose less on our bluffs when he doesn't fold. In other words: We risk less for the same reward when we're bluffing, and we don't lose anything when we're 4-betting for value. We simply choose 27bb as a representative value for a less-than-pot 4-bet, and the math won't change much if you use any number between 25bb and 30b instead.
Here are a few assumptions/statements we will use:
• Bob knows Alice's opening range. Not necessarily all the hands in the range, but he knows the percentage of hands Alice opens
• Both Alice and Bob are trying to play perfectly, under the assumption that their opponent is also trying to play perfectly
• The worst hands in a bluffing range or calling range should be break even
The last statement needs an explanation: When we're 3-betting/4-betting/5-betting as a bluff, we should not lose money on our bluffing hands, and the worst of them should be no worse than break even. The same goes for when we're calling for pot odds. This makes sense if you think about it. When we're making a play that loses money, we should stop doing it to increase our EV.
Note that we're not concerned about the effects of deception when we work with game theory. We're only concerned with immediate EV. Also, if we're making money on all our bluffs or our calls, we can make even more money by bluffing more and calling more. So we keep adding bluffs and calling hands until our weakest hands are at the break even point, and then we stop. Conversely, if we're losing money on some of our bluffing or calling hands, we remove them from our ranges. Again, this results in our weakest bluffing/calling hands being no worse than break even.
Under these assumptions, we'll find an optimal strategy pair with a raising strategy (including defense against a 3-bet and against a 5-bet) for Alice, and a 3-betting strategy (including defense against a 4-bet) for Bob. We'll find a unique strategy pair for each of Alice's positions (e.g. for each of her opening ranges). We'll soon see how these strategy pairs follow from Alice's opening range, but first, let's talk a bit about optimal strategy pairs:
What is an optimal strategy pair?
When our two players Alice and Bob are playing optimally against each other, Alice's strategy and Bob's strategy make up an optimal strategy pair. When both are playing optimally, neither of them can gain from changing to a different strategy. If one of them can gain from switching to another strategy, then the original strategy wasn't optimal.
It's important to realize that a game theory optimal strategy doesn't try to maximize +EV against a random opponent. It's trying to maximize EV against an opponent who is also playing perfectly. Sometimes, this means the best result for both players is to break even. A game theory optimal strategy is first and foremost a defensive strategy, designed not to lose. However, an optimal strategy will win against players who are using non-optimal strategies. But If we see an opponent making big mistakes, we will win more by switching to an exploitative strategy, designed to exploit this opponent's specific leaks maximally.
But by changing our strategy from optimal to exploitative, we are moving away from optimal play. By doing so, we are creating weaknesses in our strategy, and other players might be able to exploit those weaknesses (although they might not see them). But if the weak player we are trying to exploit has big leaks, this trade off will usually be worth it. The art of playing against fish and regs at the same time is to exploit the fish, while we're defending ourselves against the regs. Against very poor opponents, we use very exploitative strategies. Against players who are as good as us, or better, we can fall back on optimal strategies so that they can't exploit us.
To balance these two goals well, we need to have an understanding of what optimal play is. Playing optimally (or, more likely, close to optimally) defends us against the good players, and understanding optimal play also makes it easier to spot mistakes in weak players (where "mistake" can be defined as deviating from optimal play).
With these concepts at the back of our mind, we move on to the mathematics behind optimal strategies for raising, 3-betting, 4-betting, and 5-betting with 100bb stacks:
2.2 How opening ranges, 3-betting ranges, 4-betting ranges, and 5-betting ranges are connected mathematically
We work our way through the raise/3-bet/4-bet/5-bet war, one step at a time, and construct all the mathematical tools we need. We jump back and forth between Alice and Bob, and we'll see how they influence each others' strategies when they both are trying to play perfectly against each other, assuming the other player is also trying to play perfectly.
What is Alice's optimal 4-bet%
The process starts with Alice raising some opening range known both to her and to Bob. When Bob 3-bets, Alice's most pressing concern is the following:
Alice can't fold so much that she gives Bob an opportunity to make a profit by 3-bet bluffing any two cards
So how often does Alice have to 4-bet? This follows from the pot odds Bob is getting on his 3-bet bluffs. There's 1.5 + 3.5 =5bb in the pot from the blinds and Alice's raise, and Bob 3-bets to 12bb to win this. Bob is then risking 12bb to win 5bb, and he's getting effective pot odds 5 : 12 on a 3-bet bluff.
He then needs to win more than 12/(5 + 12) =70% to have a profitable bluff. So if Alice folds more than 70%, Bob will have an automatic profit by 3-bet bluffing any two. Alice needs to prevent this, so she has to 4-bet enough to make Bob's bluffs break even.
Alice's optimal 4-betting strategy is therefore to 4-bet 30% of her opening range, and she will 4-bet a mix of value hands (planning to call a 5-bet) and bluffs (planing to fold to a 5-bet). We'll compute Alice's optimal value/bluff ratio in a moment, but first we have to find Bob's optimal ranges for 3-betting and 5-betting. These ranges follow from Alice's opening range:
What is Bob's optimal value/bluff ratio in his 3-bet range?
When Alice 4-bets to 27bb, she is risking 23.5bb (27bb minus he 3.5bb raise) more to win a 17bb pot (1.5bb from the blinds + Alice's 3.5bb raise + Bob's 12bb 3-bet). The effective pot odds for Alice's 4-bet bluffs are 17 : 23.5, and she can make a profit by 4-bet bluffing any two (of the hands she open-raised) if Bob folds his 3-betting hands more than 23.5/(23.5 + 17) =58%.
Bob can't allow Alice to 4-bet bluff any two cards profitably, so he defends optimally by folding exactly 58% of the time, and 5-betting all-in (including some 5-bet bluffs as we shall soon see) 42% of the time. Therefore, 42% of Bob's 3-bets need to be value hands that he plans to 5-bet all-in (including some 5-bet bluffs). We now define a 3-bet for value as a 3-bet where we plan to 5-bet all-in after a 4-bet. If this is not our plan, we are making a 3-bet bluff that we will fold to a 4-bet.
To make these percentages easy to remember, we round Bob's optimal 3-bet value/bluff ratio to 40/60. So now we know that 60% of Bob's 3-bets should be bluffs, and 40% should be for value (including some 5-bet bluffs). But we still don't know how many hands Bob should 3-bet overall. To find this number, we first have to find which hands Bob can 5-bet for value.
What should Bob's 5-betting range look like?
Bob first chooses the type of hands to 5-bet bluff with. He wants hands that have decent equity when called, and we can use Axs hands A5s-A2s for this purpose. Axs hands work as blockers against Alice's AA/AK (an ace in Bob's hand makes it less likely Alice has AA/AK), and they always have at least an overcard when Alice has another high pair. They also have straight and flush potential.
Axs has minimum ~30% equity when we 5-bet and get called, even against a strong range, as shown below:
So Bob will 5-bet a mix of true value hands and some Axs bluff hands, and he expects to have about 30% equity when his bluffs get called. So when he 5-bet bluffs and gets called, he will have ~30% equity in a 201.5bb pot where he invested 88bb with the 5-bet. Bob first 3-bet to 12, so the 5-bet is 88bb more. On average, Bob gets 0.30 x 201.5 =60bb back from the pot, so his net loss after 5-betting and getting called is 88 - 60 =28bb.
The pot size before Bob's 5-bet is 40.5bb (1.5 from the blinds, + 27 from Alice's 4-bet + 12 from Bob's 3-bet). So Bob is effectively risking 28bb to win 40.5bb when he is 5-bet bluffing. The effective pot odds are 40.5 : 28, and Bob needs to win at least 28/(28 + 40.5) =40% to profit from 5-bet bluffing any two (or more precisely, any Axs hand, since we base our calculations on having ~30% equity when called).
For Alice, this means she has to call a 5-bet 60% of the time to prevent Bob from making a profit by 5-betting any two. So Alice's 4-betting range has to contain 60% value hands and 40% bluff hands. Now we know everything we need to know about Alice's 4-betting range. She 4-bets 30% of her opening range, and she uses a 60/40 value/bluff ratio. We'll summarize Alice's total optimal strategy below, but first we'll find out how often Bob should 3-bet.
We know which type of hands Bob should 5-bet bluff (Axs), and we know he should use a 40/60 value/bluff ratio (which, coincidentally is the opposite of the ratio for Alice's 4-bet range). The last piece of information we need is Bob's total 3-bet percentage in an optimal 3-betting strategy. We find the answer by observing that Bob should 5-bet bluff enough to make Alice's weakest value hands break even. He he bluffs more, Alice can gain by calling with more hands, and then Bob's strategy can't be optimal. And if he bluffs less, Alice can gain by folding more hands, and Bob's strategy can't be optimal in this case either.
How many Axs hands we need to make Alice's weakest 5-bet calling hands break even varies with Alice's value range (60% of 30% of her opening range), which follows from her opening range. So we have to compute this result on a per-case basis, for every one of Alice's opening ranges. We'll give a quick example in the summary below, and the procedure will be thoroughly discussed later in the article.
2.3 Summary of Alice's optimal raising strategy
We summarize everything we have learned about Alice's optimal strategy for raising, 4-betting and calling 5-bets:
- She needs to 4-bet 30% of her opening range
- Her 4-betting range should have a 60/40 value/bluff ratio
So Alice's optimal strategy is:
• Alice open-raises some opening range
• When she gets 3-bet, she 4-bets 30% of her opening range with a 60/40 ratio between value 4-bets and bluff 4-bets
• Alice therefore 4-bets 0.60 x 30 =18% of her opening range for value and 0.40 x 30 =12% of her opening range as a bluff
• If Bob 5-bets all-in, Alice calls with all her value hands, and folds all her 4-bet bluffs
So Alice's value hands are the top 18% of her opening range. For example, if she opens 15% from UTG, this corresponds to a value range of 0.18 x 0.15 =2.7% of all hands. This makes up 0.027 x 1326 =36 combos, e.g approximately the range {QQ+, AK} =34 combos. We'll use this value range example when we summarize Bob's optimal strategy below. And then we'll illustrate each strategy step thoroughly when we apply the theory to Alice's EP and CO openraises.
2.4 Summary of Bob's optimal 3-betting strategy
We summarize everything we have learned about Bob's optimal strategy for 3-betting and 5-betting:
• Bob starts by finding which hands he can 3-bet for value, planning to 5-bet all-in against Alice's 4-bet value range. For this purpose, he needs hands that have at least 50% equity against Alice's value range
• Bob then adds enough Axs hands as 5-bet bluffs to make Alice's weakest value hands break even when calling Bob's total 5-bet range
• Bob's value hands and 5-bet bluffs are joined to a total value range (where value range =the range he 3-bets and 5-bets all-in)
• Finally, Bob chooses a 3-bet bluff range so that the ratio of his value hands (including 5-bet bluffs) to his bluff hands is 40/60
• When Alice raises, Bob 3-bets his value range and his bluff range
• If Alice 4-bets, Bob 5-bets his value range all-in and folds his bluff range
For example, if Alice raises 15% from the UTG, her optimal value range is {QQ+, AK} as shown previously. Bob chooses value hands that are at least 50% against this range, and his pure value range becomes {KK+}. Then he adds Axs hands as 5-bet bluffs until Alice's weakest value hands (QQ and AK) are break even against his total 5-bet range.
Alice then calls her remaining 73 BB to win a 189.5 bb pot (1.5 from the blinds, 100 from Bob, 27 from Alice's 4-bet), so her pot odds are 128.5 : 73. She needs minimum 73(/128.5 + 73) =36% equity to profit from calling, so Bob makes sure her weakest value hands have against his 5-bet-range. Later in the article we'll show that Bob ends up with a total 5-bet range of {KK+, A5s, A4s} when Alice's value range is {QQ+, AK}
This gives Bob {KK+, A5s, A4s} =20 value combos that he 3-bets, planning to 5-bet all-in. Then he picks hands to 3-bet bluff until he has a 40/60 ratio between value combos and bluff combos. Bob needs 60/40 =1.5 bluff combos for every value combo, so he will choose 1.5 x 20 =30 bluff combos against Alice's {QQ+, AK} value range.
You should memorize both Alice's strategy and Bob's strategy until you know them cold. It's not really complicated at all. Just remember that Bob uses a 40/60 value/bluff ratio for his 3-bets, and Alice uses a 60/40 ratio for her 4-bets, and then you know the most of it. Value hands are per definition hands we plan to raise and reraise until we are all-in. Bluff hands are hands we plan to fold if our opponent reraises us back.
We now begin the job of constructing optimal strategy pairs for Alice and Bob. First when Alice raises a 15% range from EP, and then when she raises a 25% range from CO. We'll do this thoroughly and methodically, so that you can learn the procedures inside out. I hope you'll see that these strategies aren't really complicated to construct and then apply at the table.
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