Stopping Bluffs

[Garbonzo]

[ QUOTE ]
Without the math and estimating a pot of 10 BB I thought around 10%. Then I did the math and learned a valuable lesson.

-rory

[/ QUOTE ]

Please share.

[rory]

I'm sure Sklansky will close this thread with the math.

-rory

[David Sklansky]

nm

[DiceyPlay]

Raise one in three times and lay it down all other times. Do this until something changes. He should start bluffing less very quickly. When you notice this start raising less frequently and and folding to his non-bluff bet more frequently. Just a guess.

[droidboy]

I read rory's origianl post (before he deleted it, I have a copy if you really want to see it), and his math was all wong.

I'm fairly certain that you would flub the math too.

- Andrew

www.pokerstove.com

[felson]

About 5%.

[rory]

Yeah my math was all cocked up. Let me try again:

Using the always call strategy your EV is:

P(bluff)*Pot - (1 - P(bluff)) * 1 = EV

If our opponent is always bluffing (best case for us) our EV can be +Pot and if he is never bluffing (worst case for us) our EV -1 BB per hand.

Using the always fold strategy our EV is:

(1 - P(bluff)) * 1 - P(bluff) * Pot = EV

If our opponent is always bluffing (worst case for us) we can lose up to -Pot and if our opponent is never bluffing (best case for us) we can win (save) up to +1 BB per hand.

So in the 10 BB pot situation where our opponent is bluffing 1 out of 3 times, plugging in the numbers in the always call equation gives an EV of 2.66 BB per hand. So the conclusion is that we can never get our opponent to not bluff enough where it becomes more profitable than is 1 out of 3 bluffs, because the most we can win (save) by always folding is 1 BB.

So the lesson is this:

P(bluff)*Pot - (1 - P(bluff)) * 1 = EV is the always call equation.

Let EV = 1 since that is the best we can do if we always fold and our opponent never bluffs. So solving for P(bluff) we find that if our opponent is bluffing at more than:

P(bluff) = 2 / (pot + 1) we should let him keep bluffing because we cannot do better than if we make it so that he never bluffs and we never call.

So in the 10 BB example if he is bluffing at more than 18% of the time we should let him keep doing it because we cannot possibly do better than if he never bluffed.

Is this still not right? It seems not but getting it fixed will help my thinking. [img]/images/graemlins/smile.gif[/img]

[droidboy]

[ QUOTE ]
So solving for P(bluff) we find that if our opponent is bluffing at more than:
P(bluff) = 2 / (pot + 1) we should let him keep bluffing because we cannot do better than if we make it so that he never bluffs and we never call.

[/ QUOTE ]

That looks like what I get. I got it a bit differently though, and I'm not sure about some of your details. The EV for folding is always 0, but you seem to have smoothed out that wrinkle somehow. Anyways, the difference in EV between calling and folding is the absolulte value of the EV for calling. If we write p(bluff) as k*p(optimal) we get:

delta EV = |[k*p(optimal)]*(pot+1) - 1|

where p(optimal) is the optimal bluffing frequency. But the optimal bluffing frequency is simply 1/(pot+1), so we have:

delta EV = |k-1|

Where k is the fraction of optimal bluffing that the opponent is performing. So if he never bluffs (k=0) we can improve our EV by 1 bet by chosing the folding strategy.

Assuming he bluffs too much, k>1, we see that if k>2 then delta EV > 1, which is better than we could ever do if he bluffed too little.

Essentially we agree:

If your opponent is bluffing twice as much as he should -- 2/(pot+1) -- or more, then you cannot profit more by getting your opponent to bluff less.

It's a pity you didn't let Sklansky flounder around with this a bit more.

- Andrew

www.pokerstove.com

[David Sklansky]

"Essentially we agree:

If your opponent is bluffing twice as much as he should -- 2/(pot+1) -- or more, then you cannot profit more by getting your opponent to bluff less."

- Andrew

Is he right?

[tolbiny]

Alright, for once i havent read any of the replies so i may be reiterating a redundantly repeated point, or i may be way off.

I would think that it would be in relation to the pot and the bet size. say the pot is 10BBs with his bet, then he needs to be bluffing more than 10% of the time to make your call correct.
i cant think of anything else that comes into play in the you win if hes bluffing you lose if hes not scenario.
I wouldnt know how to go about figureing it if you will also win when he thinks hes value betting but you have a slightly better hand, and other such situations.