What to internalize when solver c-bets almost every combo half the time on paired boards?

You could run the sim with two different betting structures and compare the EV difference.

e.g. in the second sim you could force the solver to bet range for b33 and then see if we lose much by simplifying to that strategy. Usually this is the case in range bet type spots. I believe the amount of acceptable EV loss varies depending where you ask but anything >1 or 2% of the pot and it starts to get too damaging to simplify.

They're not supposed to fold that much to a range bet anyway. So it's hard to lose too much/any EV in this specific node. Which is basically why its torn between bet/check.

Thank you, I hadn't thought of that approach. Range-betting does lose 2% of the pot, but most of the EV loss only manifests if villain actually exploits with a 40% raise-frequency in position. Even if they "only" raise 22% of the time, range-betting then only loses 1% of the pot.

Your response also made me realize I should've run the sim at maximum precision to help it get through these tiny indecisions. At 0.1% precision some hopeless air like T6 of clubs does finally become a pure check-fold.

I've heard that studying the flop too much can be a waste of time (and I can see why), but BB's 24%-frequency raises IP and SB's flop-3bets are not entirely intuitive. Is BvB the most common situation that the IP player raises the flop (therefore necessitating a studied 3bet range from SB)?

Dunno. That's beyond my understanding currently. My guess would be pools are not wildly far off GTO frequency wise in this scenario so it'll play out quite naturally. MDA for SB v BB paired boards might tell a different story, but in general OOP in a SRP I would tend towards slightly overfolding compared to gto and playing more linearly vs action.

A lot will boil down to opponent tendencies and game dynamics too. e.g. if we're opening wider in the SB (because BB underdefends) and they catch on then they may start to take more aggressive lines, and suddenly all our 0ev Bluffcatchers become almost mandatory calls.

Your range for IP is dramatically too tight for BvB. You can bet your entire range on basically all JJX board textures SB vs BB for a small sizing without losing much/any EV.

To specifically answer your question: if you see basically all hands mixed between betting/checking, then all those hands are equivalent in EV between those two actions vs. the opponent's current strategy. If they maintained that strategy and you either checked all mixed hands or bet all mixed hands the EV would be the same.

Thank you for pointing this out, I was unknowingly using the BB range from GTO-Wizard that assumes the SB uses a limping strat some of the time. You're right, if SB tightens up to 44% and BB calls 59%, it's absolutely a range bet. Do those preflop frequencies sound more correct? I don't have paid GTO-Wizard so I don't think I can ask it to output a range where the SB doesn't limp

BB wouldn't call 59%, but in a relatively low rake environment BB would defend ~59% in aggregate vs. a linear ~44% RFI from SB of a 3.0x sizing for NLH 6-max and no antes--yes.

Sorry but I'm confused again, I figured out how to make GTO-wizard stop limping from the SB and now the BB defends 52.5% of the time but only calls 34% of combos. Can you clarify what you meant by my BB range being dramatically tight? Given this tightness, SB is back to c-betting only 50% of the time on JJ3r in SRP (which doesn't necessarily disprove that the EV of range-betting is acceptable)

Surprisingly (to me), the c-bet frequency goes down to 19% if you give BB three more suited hands of jacks than SB has (J4s-J2s) and one extra offsuit hand of J8o (all hands that could be 3bet polarized instead of flatted). Range-betting then loses 5% of the pot in EV. That seems like a huge swing in strategy relative to a realistic loosening of villain's range (I've seen regs flat J7o BvB). Does this just go to show that you shouldn't take solvers too literally?

The lesson is that when you're OOP you need to check a lot, and it's important to do it in a balanced way. You have to check a lot with good hands too so the IP player can't run you over when you check.

You're referencing 50nl ranges. I specifically caveated it with, "very low rake". Also, it will still make a big difference. Your screenshot still shows IP being quite tight in my opinion (0% A2-A5o, no k8o, q8o, 54o, 65o, 76o, 87o, all 7xo gone, no % of weaker suited hands like 62s, 73s, 84s, T5s, T4s, T3s, etc. Can you take screenshots of how you're creating your trees and the ranges for IP?

I also doubt that range betting loses 5% of the pot...

It's also important to realize that on most paired boards SB vs BB the BB is supposed to be raising small c-bets upwards of 30%+, which does not occur. They are also supposed to be folding only very close to alpha in vast majority of configurations, but population folds quite substantially more than this.

When you add in JX for IP, of course it vastly shifts the c-betting frequency. This is why low paired boards are checked very often for SB vs BB SRP node.. like think paired boards 22-88, because IP is defending hands vs. opens that SB doesn't RFI and contains these cards so IP has more of them... think like 65o, 53s, 52s, 75s, 85s, 95s, T5s, for a flop 55X... OOP isn't opening these, but IP defends them.

You can segment the SB range intelligently in order to assess the forces driving the 50/50 split strat (bet vs check):

You really need to visualize the river strats to understand this one.

• OOP
  
• Super deep
  
• These conditions let BTN maximize its advantage, basically BTN always gets "last licks", that's the primary source of BTN advantage.
  

So broadly there's these segments that drive the whole thing:

• [*]55-TT, 22-33:
  [*]Ace-high
  [*]King-High
  [*]Q-high (to some extent)
  
• All vulnerable to different degrees, especially as the game unfurls more through the tree and some combination of betting narrowing ranges plus overs+draws peeling. All these suck away showdown value from underpairs A-high, K-high
  
• BTN can always act last and usually with tons of chips relative to the pot. Even on clean runouts you'll be able to value small pairs, there are even certainly runouts where you can value A-high--but BTN can likely always find at equilibrium in all river nodes a raising range that can force you into indifference as part of an unexploitable strategy
  
• How can any of these always bet if they can't even always get to showdown?
  
• But why should any of these always check if they can potentially get 2+ streets or fork into bluffs?
  

• [*]T-high and worse
  
• now you're starting to have problems even finding worse in IP's range. Clearly can't always bet--but shouldn't be too hard to see that on JJ4 even something like 65o can turn/river something making it a value bet. Say a 6--a clear combo that can delay a river. It can also stab as air. So why always check?
  

Basically just leaves QQ-AA, Jx, 44. These want to bet a ton--but AA, JJ ,44 need little to no protection. So why always bet? All the pressure from the mixing forces on A-high, 33, KQ etc means lots of stabs means lots of incentive to trap. The arrows point pretty neatly in the same direction for this segment as the others--clear reasons to play a betting an checking strategy.

Roughly 50/50 mix is because ranges are quantitatively "wide":

• So there's really no true air yet
  
• most of your range then needs more cards to peel to really crystalize its categorization on later streets.
  
• I'm talking the 65, T7, Q2 etc--all of these can be bluffs of value bets depending on runout.
  
• I'm talking TT-55, 22-33 all of these can be value bets or x-c or x-f or b-c or b-mix depending on runout.
  

Wow, THANK YOU for this response! It really strikes at the fundamental question I didn't even know I was asking, and I can feel new neurons forming around ideas like "there's really no true air yet."

A bit of a tangent, but I've gradually stopped semi-bluffing players I perceive as passive/fishy. Especially in position, the thought process goes "If I perceive overcalling/checking, why bet with king-high when I could checkback and potentially be betting a king-high flush next street?"

So I ask: would you significantly curb this "no true air yet" mentality against a passive player, or would they need to be "unrealistically" passive (even the most passive players fold junk and raise the nuts) for these bets to stop being +EV?

Welp, you caught me again. Looks like the rake of the game I play is actually closer to the 500NL model and I need to adjust my preflop ranges AGAIN! Obviously very grateful to have this pointed out, I appreciate your patience.

Correcting the rake and simplifying the tree a little makes it so that we cbet 31% even when BB has the contrived 24-extra combos of jack-containing hands, and range-betting now only loses 2% of the pot.

Please let me know if this tree is overly simplified for the purposes of becoming familiar with how ranges interact: SB goes 33 -> 50 -> 50, BB goes 33 -> 75 -> 75. I'm considering adding overbet to turn/river and just making the solve less accurate to compensate for the extra complication

Few quick thoughts:

1. This range just looks like you didn't solve it down to a low enough nash distance. Improve the accuracy and you'll see less mixing.

2. Here's the

https://app.gtowizard.com/solutions?soltab=strategy&solution_type=gwiz&gmfs_solution_tab=ai_sols&gametype=Cash6mSimple_6mNL500R2&depth=100&gmfft_sort_key=0&gmfft_sort_order=desc&history_spot=5&gmff_favorite=false&preflop_actions=F-F-F-F-R3-R9&gmff_rake=NL500&gmff_depth=100&gmff_type=simple

GTO Wizard

GTO Wizard

3. Your tree is too simple. Your sim will take advantage of the limitations of it. As an example, you can 3-bet a ton if you know you will never have to face a 4-bet.

4.

There's a reason for that. Consider what might be the incentives for this.

My GTO+ program seems to autogenerate further raises even if I don't fill out the "3Bet" field. If it's all blank, it 3bets to 3.25x the size of the 2bet and then creates a 2.6x 4bet (and then 5bet shoves).

After solving to 0.1% accuracy and reading Eggs' comment, my assumption is that the solver is making sure that it can credibly make a pair with any turn/river cards while also completing any possible backdoor straights or flushes in both its checking and betting lines. It therefore only designates a "pure" checking range to hands that can't accomplish any backdoor draws. This is why it will check-fold 96s without a BDFD to 33%, but check-call with 75s or 87s lacking a BDFD

Regarding making pairs: it's unintuitive to bet weak offsuit ace-highs, but if you always check them then you won't connect to ace turns often enough.

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Also thank you for the GTO Wizard solve, but I noticed it's calling 437 combos in the BB because your sim has "Preflop Only" selected. With "Postflop included," BB calls 547 combos. I can't find any threads or documentation about what this setting actually changes about preflop ranges, could you enlighten me?