Originally Posted by Joe Knott
This is only true in some (very specific and not very poker-like) AKQ games. (I think you are referring to half-street, 3 cards in the deck 1PSB poker?)
Now what changes when the out-of-position player doesn't necessarily have to check? Or if instead of 3 cards in the deck it's distribution vs. distribution and the betting player is not polar?
yup, sorry, thought that's the "AKQ game" we were talking about.
The only thing I could explain with any real confidence is how to determine frequencies and sizings with PvsBC distributions. It's very easy to just start with river bet size and frequencies and work your way back in simple PvsBC scenarios.
When ranges are closer, betting is done with a merged range, there are potential slow plays mixed into the bluff catchers range, etc, I couldn't honestly tell you how to arrive at optimal frequencies and bet sizes. Sorry.
I'll tell you that sizing should get smaller as the betting range is wider and smaller when more merged/larger when polarized.
I am pretty confident that we have to use less bluffs and a smaller size if we expect the player we are betting against to have slow plays mixed into his range.
I really don't know the exact process to arrive at an equilibrium for a real poker scenario..
put into a solver?