This idea comes from trying to answer a question in Exitonly's post
Exitonly is a call station
Question
We have taken a line such that we believe that we are ahead on the turn. The problem is, we are out of position and the pot is getting large. We have checked, our opponent bets, should we take the pot with a push (we know we can), or should we let him see a free river with the chance he will bluff off the rest of his chips. Lets make things easier and assume that their are no big draws on board.
**This general set up can be used to think about a lot of hands. Once we decide we arent going to fold. The range of hands where the villan will make the same decision, regardless of what you do, can be safely ignored. We only care about his potential hands where our line matters. This is why I assume a push would work, b/c without huge draws on board, hands that call our push would likely have gotten all-in regardless.
**We will also assume that the only reasonable bet for the villan on the river is a push. Given the shallow stacks of most online MTTs, I think that is very reasonable.
What do we want to know?
How often will the villan have to bluff the river to make giving him a free card a good idea?
What do we need to know?
How many outs the Villan has against you
Yep...thats it.
[0-5 outs]
% of time he must bluff = (outs x 2%) * {1+ (Pot when you call / His remaining chips)}
[5+ outs]
% of time he must bluff = (outs x
2.5%) * {1+ (Pot when you call / His remaining chips)}
Look at his remaining stack, and fill in the blank
The pot is ______ times as large as his stack
-add 1
-multiply that number by (outs x 2~2.5)
I know most of us rely on our 'gut' to decide this play, but it is always nice to know the kind of assumptions our gut is making. Just looking at the equation should confirm your poker intuition. As the pot gets large compared to our stacks, the rate at which he must bluff the river goes up. The more outs he has, same effect.