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Old 11-14-2017, 03:20 PM   #1
poker-hero
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2nd nuts vs River Check raise : need maths plz

cashgame nl500 6max :

UTG & MP fold
CO raise KcQd
BTN & SB fold
BB call

Flop : Qc9c5s (pot = 1)
BB check
CO bet 0.5
BB call 0.5

Turn : 7c (pot = 2)
BB check
CO bet 1
BB call 1

River : 2c (pot = 4)
BB check
CO bet 2
BB raise 4x2=8
CO?

So the pot size is 14 and I have to call 6. I hold 2nd nuts.

Is there a mathematical way to solve that?

I am not looking for an exploitative logic based on reads, Villain's profile, etc. Let's say we face a balanced strategy : I'd like to know if there's a mathematical solution.
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Old 11-14-2017, 04:51 PM   #2
ZKesic
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Re: 2nd nuts vs River Check raise : need maths plz

If you're holding the second nuts here at 500NL, call xD

on a serious note:

6/(14+6)= 30% is the amount that we should be winning when we call, for our call to be 0 EV. Therefore that's how much villain should be bluffing (when he's counting in the effect of our bluffcatcher's blockers).

If we include the 5% rake for example, it would be 6/(20*0.95)= 31,6%.

If we include the fact that we beat/block some of his value range here, our call becomes +EV. The exact math depends on how often he has Kc/Qd in his value range, or Qd in his bluffing range, but this should be one of our best bluff catchers.
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Old 11-14-2017, 04:58 PM   #3
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Re: 2nd nuts vs River Check raise : need maths plz

We should be bluffing river here 2/8 = 25% of the time.
When we're check raised by the GTO strategy, we should be folding 8/14 = 57% of the time to be balanced.
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Old 11-14-2017, 05:39 PM   #4
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Re: 2nd nuts vs River Check raise : need maths plz

ty ZKesic for your answers

Quote:
Originally Posted by ZKesic View Post
We should be bluffing river here 2/8 = 25% of the time.
where do you get this from? I don't understand the idea here. You are talking about Villain, right? or Hero?

Quote:
Originally Posted by ZKesic View Post
When we're check raised by the GTO strategy, we should be folding 8/14 = 57% of the time to be balanced.
I don't get this one either sorry.
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Old 11-14-2017, 05:43 PM   #5
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Re: 2nd nuts vs River Check raise : need maths plz

Quote:
Originally Posted by ZKesic View Post
6/(14+6)= 30% is the amount that we should be winning when we call, for our call to be 0 EV. Therefore that's how much villain should be bluffing (when he's counting in the effect of our bluffcatcher's blockers).

If we include the 5% rake for example, it would be 6/(20*0.95)= 31,6%.
OK, so Villain should do this move with a range including 30% (or 31.6%) of bluffs, right?
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Old 11-14-2017, 06:06 PM   #6
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Re: 2nd nuts vs River Check raise : need maths plz

Quote:
Originally Posted by poker-hero View Post
OK, so Villain should do this move with a range including 30% (or 31.6%) of bluffs, right?
yes

Quote:
Originally Posted by poker-hero View Post
ty ZKesic for your answers

where do you get this from? I don't understand the idea here. You are talking about Villain, right? or Hero?
When we bet 2 into a pot of 4 on the river, opponent has to call 2 to get 6 right? So our bluff:value ratio should be 2:6. Therefore, we should be bluffing 2/(6+2) = 25%, for opponent's blufcatchers to be breakeven.

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Originally Posted by poker-hero View Post
I don't get this one either sorry.
When opponent check raises river to 8, he's risking 8 to get a pot of 6.
Meaning, his bluff has to work 8/(8+6)= 57% of the time.
That's why we're folding 57%. If we folded more, his bluffs would be +EV, if we folded less, he shouldn't ever be bluffing.
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