Aaaand one more GTO question :-)
Posted by ActionFalko
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ActionFalko
posted in
Gen. Poker
Aaaand one more GTO question :-)
I saw in a video that a Villain donked 1.5x the pot OTR after xc Flop and xc Turn.
GTO said we should call with 40% with all our hands that we have at this point THAT BEAT A BLUFF.
I understand the 40%. But not why we shouldnt call with 40% of our entire river range. Why only 40% of all those hands that beat a bluff.
This makes our calling range very small, doesn' it?
Thanks again so much
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This one would really interest me. Anyone? Please.... :-)
Our goal is to prevent Villain from gaining money with his bluffs. If he bluffs with a hand that still beats our air, he isn´t winning when we´re folding. That way, it´s not necessary to defend our range with hands that we would have lost anyways.
Like, take the following scenario (ignore the "sense" of my range-assumptions, it´s just for the sake of the example):
We are on the river, the board is T92sKA, we have QJs, AXs and 87s in our range. Villain donks 1.5x pot and we can´t reraise, we can only call or fold. Now, if Villain is bluffing with Q8s, it´s "okay" to fold 87s, as he has the better hand anyways, so we don´t have to defend an equity that we never had. We have to defend with our showdown hands though (the ones that beat a bluff), because now, Villain is essentially stealing our share of the pot, if we let him doing so.
It makes no sense calling with a hand that does not beat a bluff. Right?
Do we really have to defend exactly 40% or 1,5/(2*1,5+1)=37,5% ?
you are making a confusion between 2 different frequencies :
40% is the Optimal Calling Frequency (MOP p113 : "1-alpha") when facing a polarized bet : to prevent the bettor to make a profit on his bluffs.
37.5 % is the bettor's (with a polarized range) Optimal Bluffing Frequency and is always equal to the pot odds offered to the caller (with a bluff catching range).
Check this link :
GTO simplified (OTR)
> I understand the 40%. But not why we shouldnt call with 40% of our
entire river range. Why only 40% of all those hands that beat a bluff.
40 % of our whole river range, not 40 % of the % of our range that beat a bluff
:-)
"40 % of our whole river range, not 40 % of the % of our range that beat a bluff"
No, that´s not correct!
Assume, we have the following ranges:
Hero: QQ (6), 77 (6), 98 (16)
Villain: AA, KK (12), 22 (6)
Hero checks, Villain bets pot with KK+ and "balances" his 12 valuecombos with 50% bluffs, so he adds his six 22-combos for a total of 18 combos.
We are getting 2:1 and have 28 combos. If we wanted to defend with (1-alpha) based on our entire river-range, we had to defend with 50% (as Villain lays himself odds of 1:1) of our range, namely half of our 28 combos, so we had to start calling with two of our entirely worthless 98-combos. Obviously that would be nonsens. Now, one could argue that we made a mistake on previous streets, but it´s different: when Villain had checked behind with his 22, he had won the pot in 16 of 28 times, netting him a profit of 16/28 x pot. That´s the baseline. So, we have to call with our QQ/77 often enough that villain can´t relentlessly bet his deuces and make more profit than his fair share of 16/28 pot. Hence we defend only 50% of your QQ/77-combos, which means we call with all QQ (21.5% of our range) and fold the rest.
OK?
ofc, nonsense to call with 98.
> Now, one could argue that we made a mistake on previous streets
was about to post that; it does seem like there's a problem if we can't find enough BC in our range.
Might be also that I miss completely the point :-)
BigFiszh,
I can't relate your made up example with the theory.
Could you please point me to some theory content (written or video) where your assertion (not your example ofc) is explained/demonstrated ?
If your assertion is right, it looks like the polarized range will be incentivized to bluff more than equilibrium.The fact that the bluff catchers (the calling range) need to beat a bluff is just a property, but doesn't imply your assertion which is :
to make the polarized range indifferent to bluffing and checking, we need to call X % of our bluff catching range (so X % of X %)
instead of :
to make the polarized range indifferent to bluffing and checking, we need to call X % of our whole river range.
If we arrive at the river with such a big portion (bigger than "alpha") of hands that can't beat a bluff , that's another problem.
Just skimming quickly through MOP, I find (p113) the indifference solution described for the caller as :
"X calls with 1 - alpha of his hands total",but maybe I miss some other explanation.
moved
Not an expert on this so just trying to clarify my own thinking on this as much as anything. Two points:
Given that most of TMoP games are single/half street games - it seems to me that our river range is not the range we had left after the turn. Another card has changed the texture of the board. Depending on what that card is some of our "leaving the turn range" needs to just be discarded. If it's a huge portion, that's a problem - which is why we fold the weakest draws on the Turn or Flop on draw heavy boards - to ensure we have a balanced range.
iirc There are situations where we can never bluff catch even the smallest bet (ie regardless of alpha) because we are at such a disadvantage. (Don't know if this applies here.)
Ok so we only call with 40% of our combos that beat a bluff.
Example: We bet the Turn with 100 combos. 75 for value and 25 bluff combos. River bricks.
Now Villain donks 1.5x the pot OTR. So we have to call 40% of those 75 value combos vs a completely polarized range.
But that would make the bluff super profitable for Villain, right?
Cos he needs 60 combos to fold.
but we fold the 25 combos(bluffs) anyways plus the 60% of our value combos (45) = we fold 70 combos.
Where is my logic mistake.
I'm essentially rephrasing your post, lol.
In your example, Villain needs us to fold at least 60 %, so we need to call 40 % to make him indifferent to bluffing or checking.
Imo, you don't make a mistake in applying BigFiszh's reasoning:
40 % OCF applies to the bluff catchers, not the zero % equity hands, you get to fold 25 turn bluff combos (0% equity) + 60 % = 45 combos of your 75 bluff catchers
You fold a total of 70 % of your river range instead of the required 60 % maximum.
This must be wrong, as it allows Villain to make a profit on his bluffs.
Why whould you not call with 10 more BC combos to make up for the 40 % OCF ? That's the only way to make Villain truly indifferent to bluffing or checking his bluffs.
Problem happens when we get to the river with so many zero % equity hands that we can't find enough BC in our range.
Anyways, I'm still looking for an analysis of this situation in MoP, Will Tipton's books, anywhere, in fact :)
If the river bricks off (as if it were never dealt and we were playing a 4 street game) then this is effectively check -> bet -> raise.
So we have 100 hands, 75 of which beat a bluff (they were value hands and nothing has changed - in real life, at least one of these is still nuts and not in our bluff-catching range, but this is complicated enough already.) and we need 40, so we pick the best 40 - we have another 35 we could have used if he bet less. The reason we don't call all 75 is to stop him profiting when he has nuts and not a bluff.
Bit of a Bump, but this was linked in the Sauce Toy Gaming comments and is very useful! Thanks to those that contributed!
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