I've played with continuation bets a lot and have tried anywhere from 1/2 pot sized to full pot. Thinking about the "optimum bluffing frequency" chapter from the Theory of Poker, I thought perhaps its possible to find an optimum sized continuation bet.

You raise with AKo and have one caller. Assume that your unimproved AK cannot be best (for instance their range of calling hands is 22-QQ). You have decided that every time you raise AKo you will bet the flop if checked to heads up, and your opponent has decided to check to you every time. How much should you bet?

You want to bet an amount that makes it such that they can't win. If they call every time? They lose. If they fold every time? They lose.

You have a 32.5% chance of having flopped the best hand (did I mention that your opponent can't flop sets ).

If you bet the full pot (which I used to do) every time, they can make money by simply calling every time.

I have just come across the fact that a) there is no such thing as a mathematically correct continuation bet size or b) I can't figure it out

I merely stumbled upon what % of flops to bluff at given a specific post flop bet size. ::sigh:: What a failure I am.

Its a question with no answer. They wont call every time. If the flop is Q73 and they have 55, do you think theyre calling every time?

Yea, even with all the hypotheticals there isn't, because no matter how big you bet its always +EV for them to call if you bet every time (given my earlier parameters).

Right. But it's not surprising that there is no winning strategy here, considering that your opponent apparently knows precisely what cards you have! If you can dream up a strategy that wins money from an opponent even after I flip over my cards, please send it to me ASAP.