Effective stack - 100BB
Hero raises 3x from LoJack
Villian calls from BB
Board - K T 6 Rainbow
villain checks

When playing this hand I thought My range should be a 1/3 pot bet due to the number of hands the BB can check raise (sets and 2 pairs and some top pair) and also the lack of “air” hands in the big blinds range (hands with less than 33% equity” .
How ever when running this sim through a solver it prefers to bet bigger 2/3 pot and some frequency of 120% over bet. I just can’t figure out why , I understand we have the advantage of nuttish hands ( 35% to 8%) how ever due to the Villiam having hardly any air in there range and an increase of nutish hands surely the solver would choose a smaller bet size at a smaller frequency .
Can anybody help me with this ?

We would probabaly need to know how your sim is setup to make sure it's not an artifact of the setup. Below are some thoughts assuming the sim setup is ok.

I find this to be a contradictory reason to prefer a small size. If villain's hands aren't air, then they should have plenty of equity to continue so could call a bigger bet. In addition you would need to apply a larger sizing to make the risk to villain's stack larger to induce folds for your bluffs.



Not sure I under stand this either. You mean specifically 2 pair? I feel like we have a much bigger range advantage on this board than a bb flat. All sets, top pair top kicker, same 2 pairs, nut straight draws etc. I am guessing some of those combination's end up in bb's other preflop ranges making most of his range medium strength hands with good showdown value that have to continue vs your larger bets.

Your assumption that we bet smaller the less air villain has is incorrect, it's actually the opposite. You want to use the sizing that puts villain in the toughest spot. When villain has plenty of air you tend to employ a smaller sizing, because villain is about indifferent towards continuing. If villain has more equity you increase your bet sizing so that villain remains closer to that indifference treshold. This is why you see plenty of tiny bets ip on paired or super dry boards, and bigger bets on dynamic boards

So even though on this board the villain has a slight increase of nutish hands than normal( 8%) we will size up due to the amount of good hands villain has in villains range ( 50-75% equity) and the lack of air hands in there range? Is that correct?


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Sorry for the awful grammar


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Using simple EV analysis, a bet size of 2/3 Pot is the minimum you should bet to do better than a fold when your equity is about 71% (35/43=81%). It is always wise to adjust a pure math-based result for such factors as opponent tendencies, future action and realized equity, stack sizes, position, etc.


I'm sure a solver does not use this approach but it might give some support to the suggested bet size.

You need to provide better info. What ranges did you use? What kind of tree did you build?

Anyway on these sorts of boards BB is lacking in two pairs cause they don't have K6o and T6o. KTo probably a pure fold too vs 3x. BB also never has top set and sometimes 3bets TT.

So as you can see the nutted portion of BB's range is very narrow. What this means is that IP can size up and be more aggressive with the top pair good kicker+ portion of it's range.

To better understand this it's useful to look at an equity graph



You can see that on KT6r BB only has about 6% hands with more than 70% equity. This sort of equity distribution mirrors the nuts vs air toy game scenario and so IP wants to polarize with big bets.

If we instead take a board like K64s we see that BB is now pushing 70%+ equity in close to 20% of it's range. This means that IP must be more careful with how much money it puts into the pot, so the small bet and checking frequencies go up.



KT6r



K64s

As a bonus here's a bit of info about the small bet with your range thing. Let's take the classic A72r board for this. Are we betting range with a small sizing on this kind of board? And if so, why? Again let's look at the equity graph.



So what we see here is that BB is actually pushing 70%+ equity quite deep into it's range. About 17% of it. This is all top pair+, however once we move out of that region BB's equity drops off a cliff. The rest of it's range has 50% or less equity. You can see that compared to the other graphs, the gap between the middle portion of the 2 lines is huge.

So what we can gather from this is that
1. We can't put in too many big bets with high frequency because BB has a lot of top pairs with great equity
2. We have a huge advantage in the middle portion of the range and we would like to leverage this somehow

These two factors together lead to:

thanks fro your reply, sorry for not explaining properly, i also got the flop wrong i mean KT7 Rainbow .
i used a tighter range for the BB :


and for the hero's range :


for the sim i used check, 1/3 pot, 2/3 pot.

after the villains checked here is what the solver suggests:


does this look right? it suggests to use bigger sized bet at a much larger frequency that i would expect.

Go big to get max value from villain's dominated Kx hands, and to make him hate life with all his gutshots, second pairs and underpairs.

Just put yourself in BB's shoes for a second. Wouldn't you hate facing an overbet on that KT7 flop when you have K8s, Q9s, QJo or JJ/99? You'd rather face a small bet so that you realize some equity cheaply.
Since the BB hates facing a big bet, that's exactly what you should make him face.

tbh im pretty sure this board is a mix strat
but ofc pending ranges

That's a great board to consider and the equity graphs are really vital to understanding the best strategy on the board. From what I can see (I'm not familiar with GTO+'s UI), the solver prefers a very small bet most of the time?

Yeah 94% of the time


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That's really interesting. With that high of a percentage, it would be reasonable to use a range bet strategy. I ask because I've seen a lot of Axx dry boards where range bets lose a sizeable amount of EV (~10%) as opposed to a mixed strategy. But maybe that deserves its own thread.