GTO 3/4/5 betting pt.3

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GTO 3/4/5 betting pt.3

4. Optimal strategy pairs for raiser/3-bettor with a CO raiser out of position

After the thorough work with Alice raising ~15% in EP, we can now reap the rewards and quickly run through the same procedure with Alice raising a ~25% range in CO. She now opens a wider range, as a consequence, all other ranges get wider as well.
4.1 Alice's optimal raising strategy for CO

Raising from CO is a bit more situational than raising from EP. It's now easier to isolate the blinds, and with a tight player on the button, it might be correct to play very loosely to get heads-up with position on the blinds. Still, everybody has a core range of hands that they always play, regardless of whether they have written this range down or not.

We'll assume Alice is using a TAG core range of ~25% in CO. More specifically, this range:

Alice's CO range
22+
A2s+ A9o+
K9s+ KTo+
Q9s+ QTo+
J8s+ JTo
T8s+
97s+
87s
76s
65s

326 combos
25%

Alice's value range
Alice defends against 3-bets 30% of the time, and she does it by 4-betting 18% of her opening range for value and 12% as a bluff. So she needs 0.18 x 326 =59 value combos that she can 4-bet and call a 5-bet with. In EP she used [QQ+, AK} =34 combos, and in CO we simply add the next tier of hands and use {JJ+, AQ+} =56 combos (precise enough).

Then she needs 0.12 x 326 =39 bluff combos. She can pick ~39 specific combos and always 4-bet them (e.g. AJ, AT, TT =38 combos), or she can 4-bet all her non-value hands 15% of the time, as explained previously. We choose the latter approach, and write Alice's complete raise strategy for CO as:

Alice's optimal raise/4-bet/call 5-bet-strategy in CO:
{Alice's total CO range}
={22+,A2s+,K9s+,Q9s+,J8s+,T8s+,97s+,87s,76s,65s,
A9o+,KTo+,QTo+,JTo}
={value hands} + {4-bet bluff hands}
={JJ+, AQ+}
+ (15% 4-bet and 85% fold) x {the rest of the range}


Alice raises {22+,A2s+,K9s+,Q9s+,J8s+,T8s+,97s+,87s,76s,65s,
A9o+,KTo+,QTo+,JTo} =326 combos from CO. If she gets 3-bet, she 4-bets {JJ+, AQ+} for value, planning to call a 5-bet. Those times she doesn't have a value hand (e.g. 88, A9o, T9s, etc.), she 4-bets 15% of the time, and the rest of the time she folds. Using a random number generator fromrandom.org to randomize 4-bet bluffs has been illustrated in a previous example.

That's it for Alice's CO strategy. Over to Bob:
4.2 Bob's optimal 3-bet-strategy against Alice's optimal raising strategy in CO

Bob needs a value range, including an optimal number of 5-bet bluffs, and he needs a range of hands to 3-bet bluff.

Bob's pure value range
Bob knows that Alice now uses {JJ+, AQ+} as her value range, so he builds a range of pure value hands that have at least 50% equity against {JJ+, AQ+}. AA and KK obviously belong in this range. To see what else is included, we run equity calculations for the next tier of hands (QQ and AK):



QQ and AK are barely above the threshold, while all weaker hands will be big underdogs. Thus, Bob's pure value range is {QQ+, AK}, and he happily 3-bets these hands, and then 5-bets them all-in, purely for value.

We add 5-bet bluffs to Bob's value range
We now want to add enough Axs hands so that Alice weakest value hands (JJ and AQ) are break even when they call our 5-bet range (and the threshold is 36% equity, as shown previously). We start with A5s/A4s and see what we get:



Alice's weakest value hand is AQ, and it's a small loser with 34% equity against Bob's total value range {QQ+, AK, A5s, A4s}. Close enough for us, so the 5-bet bluffs in this case are the same as we used against Alice's EP range. However, if we want it to be exact, we need to add a couple more bluffs (for example, A 3 and A 3 ) to lift AQ up to 36%:



Bob's 3-bet bluffing
Bob's value range, including 5-bet bluffs, is {QQ+, AK, A5s, A4s} =42 combos. He wants an optimal 40/60 value/bluff-ratio, so he needs 60/40 =1.5 times as many bluff combos. This amounts to 1.5 x 42 =63 bluff combos.

We use the previously defined candidate list for 3-bet bluff hands:

Candidate list for 3-bet bluffing:
- Ace high: A9s-A6s ATo-A8o (52 combos)
- King high: K9s-K6s, KJo-K9o (52 combos)
- Queen high: Q9s-Q6s, QJo-Q9o (52 combos)

We bluff these hands some fixed percentage x, and for this to effectively correspond to 63 bluff combos, we need x =63/152 =41%. We can round this to x =40% to make it easy to remember.

We remember that we used a 20% bluff candidate frequency against Alice's ~15% EP range. So when Alice moves from a ~15% EP range to a ~25% CO range, our 3-bet bluff candidate frequency doubles. We only need to memorize the candidate list, and these two numbers (20% vs EP and 40% vs CO), and then we know all we need to know about 3-bet bluffing optimally against Alice's EP/CO ranges.

At any rate, against Alice's optimal CO raising strategy, Bob gets:

Bob's optimal 3-bet strategy against Alice's optimal raising strategy in CO
{Bob's total 3-bet range}
={value hands and 5-bet bluff hands} + {3-bet bluff hands}
={QQ+, AK, A5s, A4s}
+ 40% x {A9s-A6s,ATo-A8o,K9s-K6s,KJo-K9o,Q9s-Q6s,QJo-Q9o}


Using a randomizer from random.org to randomize 3-bet bluffing has been illustrated in a previous example.

Bob's total 3-bet% for this scenario is:

- Value part: 42 combos (3.2% of all hands)
- Bluff part: Effectively 40% of 152 =61 combos (4.6% of all hands)

This results in a total 3-bet range of 3.2 + 4.6 =7.8% against Alice's ~25% CO range. The value/bluff ratio, using our numerical rounding, is 42/61, which is very close to the optimal 40/60.

When Alice moves from EP to CO and her opening range changes from ~15% to ~25%, Bob responds by loosening up his 3-betting range dramatically. This is an interesting observation. Those of you who use a more or less static 3-betting range (for example, the generic {JJ+, AQ} without any 3-bet bluffing that is recommended on many low limit forums) now have game theoretical "proof" that we can get away with a lot of 3-bet bluffing on the button against a CO raiser.

Even against a TAG CO raiser with a solid ~25% opening range, you can 3-bet almost 8% on the button and there isn't anything he can do to exploit your loose 3-bets. And if he defends poorly, for example by not 4-bet-bluffing enough, or not being willing to use JJ/AQ as value hands, you can deviate from optimal play and attack him even harder. The first adjustment against a weak/passive CO raiser who folds a lot to 3-bets is to increase your fixed 3-bet bluff percentage for the candidate list. You might increase the bluff candidate 3-betting frequency from 40% to 60%. If Villain (and the blinds) doesn't adjust to your exploitative, loose 3-betting, you'll be printing money.


5. Summary

We have gone through the theory for game theory optimal(ish) raising/3-betting/4-betting/5-betting with the raiser out of position, and then we demonstrated how the theory can be implemented and used at the table.

We constructed optimal strategy pairs (one strategy for the raiser, and one for the 3-bettor) for two scenarios. First with the raiser in EP (UTG or MP) with a ~15% range, and then with the raiser in CO with a ~25% range. In both scenarios we gave the raiser a standard TAG opening range. We then deduced optimal strategies for both players as a function of the raisers opening range. We observed that the strategies for the CO scenario involved considerably looser ranges than the strategies for the EP scenario.

Our optimal strategy pairs confirmed that it's correct to 3-bet a wide range on the button against a CO raiser, even if he starts with a solid opening range, and defends optimally against a 3-bet. And if he doesn't defend optimally, we can loosen up even more. When you see a good and aggressive NL player dominate the table by 3-betting loosely in position, this is what happens. Loose, positional 3-betting is game theoretically correct, even against strong players. And against weak players, it's even more correct.

As a result of our work, we ended up with specific and concrete implementations of the theory, both as the raiser and as the 3-bettor. You can implement these strategies immediately in your own game by following the procedures outlined in this article. The strategy pairs depend on the raiser's opening range, but the ~15% and ~25% EP and CO ranges are relatively standard, and you will meet many opponents who play close to these ranges. If you need to apply the theory to other ranges, just plug them into the method, and construct the strategy pairs yourself.

We didn't look at small blind vs big blind in this article, even if it falls under the same category with the raiser out of position. I elected to leave this situation out, since blind vs blind dynamics is very dependent on the players involved, and the history between them. So it's difficult (and probably not very useful) to try and generalize and assign SB a standard opening range. But if you want to do this, you can use the method and construct the optimal strategy pair yourself.

Those of you who enjoy experimenting with ranges and numbers can now start to apply the optimal strategies in your own game, using your own ranges. Plug your own opening ranges for EP and CO into the theoretical "machinery" outlined in this article, and produce optimal strategy pairs, based on the ranges you use at the table. Remember that everything follows from the opening ranges, and remember that you will get both an optimal strategy for the raiser (you), and the positional 3-bettors optimal strategy against you.

Learn both parts of every optimal strategy pair. When you are the raiser OOP against an unknown 3-bettor, you can simply play optimally and assume that he is playing optimally too. You now have 100% knowledge about the raiser's range (since this is your range), and you know the optimal strategy pair for this situation exactly. Since the 3-bettor doesn't know these things precisely, he will make mistakes, and you won't.

When you have position on the raiser, things are slightly less straightforward, since he is the one who chooses the opening range. But against an unknown raiser, you can start by assuming he uses opening ranges that are close to your default ranges. Then you simply respond with the corresponding optimal 3-betting strategy. If he uses ranges that are only slightly different from yours, the optimal strategy pairs will be similar.

And if you should need optimal strategy pairs for opening ranges that are very different from your own (for example, if you meet a CO raiser who opens 45% of his hands), you can quickly construct the corresponding optimal strategy pair for him and yourself. Remember that you don't need to know his opening range in detail, you only need to know the number of hands that he opens. This number is relatively easy to estimate from a HUD, even if the sample isn't big.

To be prepared for any opening range you might encounter as a 3-bettor, you can sit down and do the work for 10%, 35% and 45% opening ranges on your own. Then you'll have have a set of optimal strategy pairs that cover almost all cases of EP and CO open-raising you are likely to encounter in practice.

Again, when you are the raiser, everything follows from your ranges, and you can do this work once and for all (assuming you have a well-defined set of default core opening ranges) and memorize it. Then you can play optimally from out of position, and sniff around for opponent leaks. If you don't find any, keep playing optimally. If you find some exploitable leaks, think about how you can adjust to increase your EV. But you don't have to adjust until you are sure. Remember, if you are playing optimally and your opponent isn't, you gain from his mistakes (although you might gain more by switching to an exploitative strategy).

A classic opponent mistake at the low limits is not 3-bet bluffing enough (or at all) in position. Love these guys, because it's easy to exploit them. For starters, they are "exploiting themselves" by allowing you to run over them by not 3-betting you nearly as often as they should. And when they do 3-bet, you know that they are strong. So you simply drop all your 4-bet bluffs from your range and continue with a 4-betting range of only value hands, planning to call a 5-bet. Easy decisions and easy game.

When someone has raised in front of you, you ideally want to use an optimal strategy for each opponent, and for each of his positions (since optimal 3-bet strategy is a function of the raiser's range). This might sound like a lot of work, but in practice it all follows from estimates about the ranges you meet. And small deviations don't change things dramatically. For example, when you know the strategy pair corresponding to a 15% opening range, you can apply the same strategies against a 12% raiser and an 18% raiser without losing much accuracy. You won't play optimally in these cases, but near-optimally is close enough. Besides, pin-pointing opponent opening ranges to within +/-1% or less is difficult, so using near-optimal strategies is the best we can hope for in practice.

The nest step of the process is the most interesting one. When you have trained optimal play, you will discover that it's now much easier to spot opponent mistakes. For example, when you come across an opponent who doesn't 4-bet bluff (and these are common at the low limits), you immediately know that this is a leak, and you know how to exploit it. Tight and straightforward players who refuse to 4-bet bluff can be exploited by 3-betting a lot, and not 5-bet bluffing at all. You can 3-bet a metric fuckton of bluff hands, and when they finally pick up a hand good enough to 4-bet, you fold all your bluffs and ship a tight value range (sometimes as tight as {KK+}). Just keep an eye on the other players to see if they are trying to exploit your loose 3-betting (tighten up a bit if they do), and you'll do very well in this spot.

Another leak you'll see is spazzy 4-betting from players with insufficient understanding of the theory behind optimal 3-bet/4-bet/5-bet wars. This might happen when you have driven someone crazy with your loose 3-betting, and he starts to tilt. Or when someone tries to fight back in a controlled manner, but he doesn't quite know how to do it (so he starts 4-bet bluffing way too much).

The first thing you have to realize when you are playing optimally, and then spotting a leak, is this: It's not necessary to deviate from optimal play to benefit from his mistakes. If you keep playing optimally, and your opponent doesn't, you will win from him in the long run, period. The question is now whether you should deviate from optimal play yourself, in order to win more. If you have a clear idea about how to exploit your opponent maximally, by all means go ahead and make the adjustment.

But be cautious when you adjust to spazzy and unpredictable opponents. Remember that your optimal 3bet/4-bet/5-bet strategies are designed to protect you, and there is nothing a maniac can do to exploit you in these scenarios, even if he raises and reraises at every opportunity. If you see concrete adjustments you can make to win more, go for it, but be careful if you tilt easily (preflop raising wars have a tendency to trigger tilt). Then you might be better off sticking to optimal play against hyper-aggressive opponents, let the ranges do the work for you. You can use your focus to terrorize the passive and easily exploitable players instead.

Finally, if you meet tough regs who don't give up preflop edge in these scenarios (at least any edge you can see), these optimal strategies will protect you from getting exploited. They can't take advantage of you in preflop 3-bet/4-bet/5-bet wars, so don't worry about it if they try. Follow the optimal strategies, and the mathematics of the situation will protect you. But don't forget to sniff for leaks against regs. Everybody has leaks, and your knowledge about optimal 3-/4-/5-betting will make it easier for you to find them. And pay close attention if you see a reg starting to tilt! Now he might blow up completely in preflop raising wars, and you can adjust accordingly.

I hope this article will be useful for those of you who find it difficult to play well in preflop 3-/4-/5-bet wars, and that you have learned to implement the optimal strategies in your own game. And for those who already knew these things, I hope that this systematic discussion of the topic has given you things to think about.

I chose to name this article "Optimal 3-bet/4-bet/5-bet strategies in NLHE 6-max - Part 1", even if a Part 2 hasn't been planned yet. But I do have some more ideas about the topic, and I might write more. For example, we could do one article about optimal strategy pairs with the raiser in position (e.g. after a 3-bet from the blinds). Then we could dedicate one article to discussion about optimal versus exploitative play, and talk about how to apply one or the other against different opponent types.

Good luck!
Bugs
 
found on en.donkr.com by bugs

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