Originally Posted by slycbnew
Only 2 K's and 2 Q's left...
I actually saw this response the other day and couldn't figure out how to respond to it without stating the obvious.
There's 2 K's and Q's.
His range pre-flop against an UTG raiser would usually be around AK/AQ, KQ, 22+ and the occasional SCer (since he's playing back at you a bit) isn't a terribly inaccurate range, and for the purposes of an example, it will do.
Before any action on the flop, that's 64 combos that you beat and 5 that beat you and 4 that you tie with.
By the time he 4bets the flop, AK/AQ will show up occasionally as bluffs, 22-JJ will individually show up almost never but combined I guess he'll bluff a little with them. The hands that you beat now make up a smaller part of his range. Like I said in the original post, I don't think hand ranges ever change it's just the frequency that hands will show up that changes so his range is still 64 hands that you beat and 5 that you don't, but the 64 is worth a lot less now.
They just wont show up as often so treating every unit of 64 the same as you would treat each unit of the 5 (which always take this line) doesn't make sense.
This is why I don't like relying on combinatorics after many actions post-flop.
More actions = more opportunities for villain to play hands different ways.
Which makes any statistical analysis way too complicated to do in real time.
I think I may be butchering the subject of "Practical use of combinatorics", but whatever.
Before any action is taken every hand has an equal chance of showing up, the more action that gets taken the further each combination is from it's initial value.
If anyone wants to add to this thread (or just explain how I've got it all wrong, if you'd like) before I over-complicate combinatorics further, please do.