optimal bluffing frequency

"Mathematically, the optimal bluffing strategy is to bluff in such a way that the chances against your bluffing are identical to the pot odds your opponent is getting."

Although Sklanksy says "mathematically", he doesn't explain how it is mathematical. Also, what does he mean by "the chances against your bluffing"?

From here.

From what I understand, he means that if you bluff too much people will start challenging your bluffs so they're not as profitable. And if you bluff too little, they'll see that you usually bet for value and won't pay you off as much when you have a legitimate hand.

So ideally, you want to bluff that unknown percentage of the time that matches their pot odds. Hence they can only make mistakes, either calling too much or folding too much. But as I stated, that percentage can only be guessed at because there are too many unknowns.

i kind of get it better, but what does it mean to "match their pot odds"? what are you supposed to match it to (is it the percentage of times you bluff?)

Yeah its to do with game theory. You want to bluff at a frequency which makes your opponent indifferennt to either calling or folding. If you bluff too much you will always get called. If you dont blufff enough your opponent will fold to you too often meaning you couyld have made more successfull bluffs and also when you get a hand you get little action.

The idea of bluffing to the pot odds is to estimate how often your bluff would be succesfull i.e 1:5 1:6 etc and then bluff pots with those pot odds thus if you have a 1:5 chance in succeeding and do it on a 5:1 pot you will break even.

(I cant offer much advice on how to estimate this.. sorry I know the theory but havnt the experience to put it into practice!!)

You need to take into consideration the odds that the pot gives though as the higher the pot odds the harder it would be to bluff as people will be getting good odds to call.

A good book to read about game theory and poker is "the mathmatics of poker by Bill Chen and Jerrod Ankenman".

It expalains things like optimal bluffing frequency but I will warn you that if you have no experience of maths beond high school level then it may be a bit too advanced as it is presented in a very mathmatical way.

I havnt touched on maths for years and I have to say I did struggle a lot with it.. but the book is very well written!! So if it dosnt overwealm you then read it bit by bit and you willl get though it.

actually i'll be studying math in college so that sounds interesting. thanks.

The odds of your bluff working depend on the other players (calling stations, fish, tight players, etc) and your table image (loose aggressive, tight, etc), so there's little way to work it out mathematically - you can only really estimate those odds based on your analysis of the other players and your own experience. It's also varied by how respectable a hand the other player thinks they have, and whether there was a scary card for them.
That said, if you use something like Poker Tracker (with PokerAceHUD to display the stats) or PokerOffice, then you can see stats on other players like how often they fold on the turn or river, which helps to estimate the likelihood of this.