Hello guys,

I am having trouble with a game theoretical issue.



For an easier discussion I will number my questions.



Assumptions:

Villain bets the river potsize and is all in.  We do not know anything about his range
composition.

We get to the river with a total of 100 combos.

Lets assume this:

20 combos nuts (assumption: these nuts beat all of Villains vbets)

70 combos bluffcatchers (assumption: these beat all of Villains Bluffs)

10 combos total air (assumption: these beat nothing and loose to all bluffs of
Villain)

1.1.) Since Villain bets Potsize, our
minimum defence frequency is 50%, right?

I am having
two approaches to this, and I am a bit confused, please help me out here.



OPTION 1:

We call our 20 combos nuts, and 30 combos of our bluffcatchers.

We fold 40 combos bluffcatchers and our 10 combos air.

-> We call 50% of the time and achieve therefore the desired minimum defence
frequency of 50%.



OPTION 2:

We call 20 combos nuts and 35 combos of our bluffcatchers.

We fold 35 combos bluffcatchers and 10 combos air.

-> We call 55% of the time and do not achieve the minimum defence frequency
with our whole range, BUT:



2.) Isn´t the idea behind the min. defence frequency with bluffcatchers, to
make them 0EV? (a.k.a: indifferent to calling/folding?)



My point here is: if we choose option 1, we treat our nuts as bluffcatchers,
although they beat all of villains betting hands.

3.) Therefore we are making our whole range indifferent to calling/folding?

4.) Wouldn´t that mean, that we intentionally make our bluffcatchers –EV?
(Since our nuts are +EV anyways)

5.) Shouldn´t we therefore use option two and call 50% of our bluffcatchers,
making our 70 combos of bluffcatchers indifferent to calling/folding?



I hope you guys can follow me, and understand why I am a bit confused here.



Thanks for any advice on this.

J