https://forumserver.twoplustwo.com/1...12/?highlight=

Yeah that thread was ok but I'm not bumping it. I was playing with math this morning in the beginners forum in an attempt to explain turn bluffcatching stuff. Here's the gist of what I got going through my head now:

There are two ev sources for bluffcatchers in equilibrium on the turn:

a) free showdown ev
b) draw value

"bluffcatching ev on the river" is not an ev source, because hands that can only beat a bluff are 0ev by definition in equilibrium, with the exception of hands with good blocking qualities, which are slightly +ev.

so to calculate (a) when facing a bet:

opponent's river check frequency * pot * my equity vs checking range = (free showdown ev)

to calculate (b) when facing a bet:

% hit hand * equity when hit hand * pot = (draw value)

the sum of (draw value + free showdown ev) = total ev of bluffcatching the turn in bb. If we set (pot = 1) then the value will be a fraction or a percentage of the pot.

free showdown equity vs 40% river check frequency: (40% * 8bb * 50%) = 1.6bb for 1 invested? This is a clear call with those assumptions.

different free showdown equity: (20% * 8bb * 50%) = 0.8bb showdown ev, we need some draw value to go along with it to make the call given these assumptions.

draw value with A7o: Maybe it's about 10% if we're lucky? debatable imo. I'll find the breakeven point given 0.8bb showdown ev: need to make up 0.2bb in draw value. 0.2bb = (8bb*%hit hand * equity when hit)

50% equity when hit and 5% hit hand result in 0.2bb draw value.

30% equity when hit and 8.3% hit hand result in 0.2bb draw value.

20% equity when hit and 12.5% hit hand result in 0.2bb draw value

so basically it doesn't take much to make this a call provided the 40% check frequency and 50% win frequency with A7o. I don't necessarily think those numbers are correct. I'm just looking for feedback, tweaks to the process.

I guess it's going to depend on the assumptions, but I think the process is correct.

thanks for reading.

I drew this for visual effect in the theory forum and thought it also had a place here.

They can't all be strong bluffcatchers with good draw value, unfortunately(top right), unless you play extra tight preflop.

Slightly profitable bluffcatchers with ok draw value find their way into our ranges frequently in limit holdem(top left).

Slightly unprofitable bluffcatchers with almost enough draw value and showdown ev to call also find their way into our ranges frequently(bottom left).

Tight turn bettors that never bluff create a very -ev spot on the river for bluffcatchers, which are effectively -1 big bet losses as a call on the river(bottom right). Even if we beat some value hands, calling may be -ev if we don't beat the bottom x% of their value range, where x = bet/(pot+bet+call).