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General GTO question

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Posted by posted in Low Stakes

General GTO question

Just something i am trying to figure out in my head but can't decide on an answer, so thought i'd ask for some help.

The situation is: Hero is in position, and gets to the river HU. Villain checks to hero, and hero now has a betting range of K high and A high flushes. The actual board isn't relevant, but assume A high flush is the nuts, and K high is the 2nd nuts.

Hero bets, and gets checkraised to a size that, in order to be unexploitable, hero would need to defend 50% of his range (pot). Assuming he has equal combos of A and K high flushes, then am i right in thinking he only ever needs to call with A high flushes?

However, if hero is 100% certain that villains raising range will always contain the nut blocker (either as a bluff, or the nut flush), then hero can never have the A high flush. At this point hero's range becomes exclusively K high flushes. Does this mean that hero would have to call with some Kx in order to be unexploitable? I don't have a great knowledge of GT, but i know a lot of you guys do so this may be a really easy question for you. It seems to me that the idea of playing GTO means that it is irrelevant what cards villain holds when he makes a raise, but at the same time seems wrong to be in a spot where hero is folding 100% of his range.

Any thoughts?

18 Comments

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OMG_IM_SEXY 9 years, 6 months ago

This is a really really interesting one, it got me thinking quite a bit.
It seems like a spot that should already be "solved" by some smart poker brains, so it would be nice to get an answer from someone that knows the solution for certain, but I'm not the one. All i can do is give you my thought process and hope it helps.

I think the main question it comes down to here is: what bluffs in villains range do we want to make indifferent to bluffing?
Is it the random bluffs or is it the A blocker bluffs.
-If we make the random bluffs 0EV, his Ax shoves are going to be very very +EV (since we are folding range) while value bets are going to have the same EV as flatting the river.
-If we make his Ax bluffs 0EV, his random bluffs will be very -EV while the value of raising his nuts increases dramatically.

We have to now choose which bluffs it makes more sense to make him indifferent to bluffing, and that's where the solution should get kind of obvious: the second scenario aka the Ax blocker scenario is the relevant one.
As you said, in practice people will not raise the river without blocking the nut flush (assuming we're uncapped) in todays games with high level of play. Why would we make any bluffs other than our villains actual bluffing range indifferent? If they do decide to bluff other hands it will automatically be punished by them making a very -EV bluff.

We can also look at it from another standpoint: which of our strategies can be exploited? (An optimal strategy should be unexploitable, aka your opponent shouldn't be able to "unilaterilly increase the EV of his strategy" (definition from Ben's Toy Gaming videos here on RIO, definetly watch in case you haven't and want to improve your understanding of game theory!)):
-The first one can be exploited by our opponent always bluffing with the Ax blocker. (assuming he has enough unsuited Aces in his range getting to that spot)
-The second one can be exploited by him never bluffing without the Ax which he shouldnt be doing anyways, and always raising the nuts, which he will also do regardless to our strategy.
..... So i guess the second strategy actually can't be exploited at all.

Putting all the pieces of logic together it seems like "making his Ax bluffs indifferent" is very likely to be the correct solution to this problem. So maybe I did actually solve this spot while writing this response :)

PhisyFishy 9 years, 6 months ago

Really good answer, thank you for that.

And so in order to make villains Ax bluffs indifferent, we would need to call some K high flush combos?

PLOpleyah 9 years, 6 months ago

I think you can model your problem in tht way:

A: the nut flush
K: the king flush
Q: lower flushes or pure bluffs (A nutblocker or others)

So you assume hero is in position and only can have A,K (50% each), and villain can have
A,K,Q. When you have A there is nothing interesting, you always call. The interesting point is when you have K. I think that if you want solve the game you have to define the %s in this case of villain having A or Q then it's easy to solve.

z3vl0ve.x 9 years, 6 months ago

So if I understand your scenario correctly I think the solution for this spot is mainly dependant on the composition of Villains range, not by your minimum defense freq.
So lets say Heros range is:

50% Axx
50% Kxx

and Villains x/r range is:

50% Axx
50% Ax

so if Hero gets raised he will always have Kxx.
If the frequencies are like this Hero should always call. He only needs 33.3% equity to call a
pot sized raise and he has 50% vs Villains range.
This is an exploitative adjustment to the Villain overbluffing.

If Villains range would be:

66.7% Axx
33.3% Ax

Hero would have a break even call and be indifferent between calling and folding.

If Villain bluffs less than 33.3% Hero should fold his entire range in this spot.
This again would be an exploitative adjustment to the Villain underbluffing.

Sauce123 9 years, 6 months ago

Phishy, this question has two answers depending on the ratio of NF:NFB in villain's range. If villain has less than 2:1 NF:NFB, then you can never call a pot sized raise, so your strategy is to bet and then call with exactly the NF. If his range is less than 2:1 NF:NFB, then you must deny him a +EV bluff with his NFB and you'll be forced to call with approximately alpha of your 2NF.

z3vl0ve.x 9 years, 6 months ago

Hey Ben,
do you mind checking if my reasoning in the comment above is sound?
If I understand your answer correctly I arrived at the same conclusion but I'm not totally certain about my train of thought.

Sauce123 9 years, 6 months ago

z,

We're saying the same thing yea. I just referenced what the equilibrium is supposing villain has >33% NFB:NF which you didn't explicitly do.

Steve Paul 9 years, 6 months ago

This is a bit nitpicky but one issue with the setup of your question is that hero should not bet the K-high flush. So I'm going to alter the question and say we're potting equal parts A-high flush, K-high flush and bluffs (so 2:1 value to bluff) and villain raises pot, risking 4 to win 2. So we need to call 1/3 of the time to stop him from being able to profitably bluffraise.

Vs no blocker hands this is just the nuts, which we have 1/3 of the time.

Vs K blocker hands, we have the nuts 1/2 the time, so these are just terrible bluffs.

Vs A-blocker hands, we have 1/2 bluffs, 1/2 K-high flush. So if he has enough of these such that we need to make them indifferent to bluffing (see Ben's post) then we call 2/3 of our K-high flushes.

Sauce123 9 years, 6 months ago

Yea Steve, I considered making this point as well for completeness but didn't because we happen to be calling alpha against his bluffs by accident supposing we pot balanced and add bluffs.

singdean 9 years, 6 months ago

"Assuming he has equal combos of A and K high flushes, then am i right in thinking he only ever needs to call with A high flushes?""However, if hero is 100% certain that villains raising range will always contain the nut blocker (either as a bluff, or the nut flush)"

When Hero has an A-high flush, he will never get raised by villain. Since the ace card is in Hero's hand, villain will never have the nut-blocker (you mentioned that villain raising range always contained the nut blocker). Hence there will be no scenario where Hero will be pondering a call with a calling range consisting of 50% nut flush and 50% 2nd nut flush.

When villain raised, hero will always have 100% K-high flush in his calling range. Hence if Hero's goal is to be unexploitable (i.e. make villain indifferent to bluffing), the calling range should just simply be the GTO ratio 1 minus alpha - 50%.

The villain's range should not come into consideration at all when pondering a call with a 100% K-high calling range.

Steve Paul 9 years, 6 months ago

"The villain's range should not come into consideration at all when pondering a call with a 100% K-high calling range."

small caveat that villain's starting range does matter if it does not have enough potential bluffs. e.g if he has 10 Asxs for every 1 Asx, then you should never call a raise (of any size) with Ksxs

singdean 9 years, 6 months ago

Yeah, except when Villain has so many nuts vs nut-blocker hands that villain can just simply claim the pot.

But back to the question, just wanted to point out that hero will never be in that difficult situation which Phishyfishy described where hero will only be calling with only nuts and folding all 2nd nuts when raised by villain, as long as villain only bluffs with the netblocker.

cos when hero has the ace, hero actually blocks the nut-blocker, so villain will never be raising him.

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