The situation is we are in a 3BP as IP PFR. I have a bluff combo and I'm trying to decide if I should use the BBB line or BXB line to get my opponent off his hand.

I know the universal folding %'s of population folding to turn barrels and folding to river barrels. I also know the folding %'s of my opponent calling the flop and folding the river in XC-X-XF line.

Do I need to get river probe %'s as well?

Basically what I'm asking is, is it possible to calculate the highest EV line in a vacuum if you have all these percentages and then use the EV equation of EV = (%W*$W)-(%L*$L)?

I know board textures will highly influence folding %'s but I'm just looking at overall numbers and wondering if this calculation is possible.

I saw your other post earlier and was thinking about this from the perspective of being on the turn and deciding whether to bet or check.

Assume the hero bet flop with a 0-equity bluff, got called and plans to bluff one way or another, ignoring runouts. I think the EVs starting from the turn would look like this.

EV of bluff in barreling turn and river, B-B, line, assuming no villain river donk =

-TurnBarrelSize + VillianFoldToTurnBarrel%(InitialPot+TurnBarrelSize ) +
VillianCallTurnBarrel%(– RiverBarrelSize + VillianFoldToRiverBarrel%(InitialPot+2*TurnBarrelS ize +RiverBarrelSize)).

EV of bluff in the checked turn, X-B or X-R, line. We bluff when checked to or bluff raise a bet on the river =

VillianXRiver%(- RiverBetSize + VillianFoldRiverToBet%(InitialPot +RiverBetSize)) +
VillianProbeRiver%(-RiverRaiseSize + FoldvsRaise%(RiverRaiseSize + VillianRiverProbeSize +InitialPot))*HeroBluffRaise%.

You need river probe and turn XR %.

Okay let me just rattle off some #'s here that I know to be true.

Turn barrel size is going to be 66% on average because of the geometric 33/66/66 sizing.

Villain fold to turn barrel is 48% (XC-XF line)
Villain fold to triple barrel is 54% (XC-XC-XF line)
Villain fold to BXB line (XC-X-XF line) is 56%
Villain fold to River raise line (XC-X-BF) is 66%

I have good samples on all those lines.

I'm looking at river probe %s in the XC-X-B line as 3BP PFC OOP. I don't see that stat in my DriveHUD I'll ask FreakDaddy how to make that one.

I have GTO % for river probe in 3BP at 42% so maybe we can just use this number for now?

I have raise turn cbet % in 3BP at 11% but it's not specific to OOP.

What else do we need?

Can someone better at math than me calculate this I can get all the numbers you need.

Just two things

I) What is the villain river probe size that happens 42% in GTO? (XC-X-B line)

II) What do you want to assume our river raise size is facing that bet? All in? Could also leave it free so you can vary it.

Once you give me those I'll work out the EVs using the formulas I gave.

I'll use VillianCallTurnBarrel% = 1 - VillianFoldToTurnBarrel% - VillianRaiseTurnBarrel% = 1 - 0.54 - 0.11 = 0.35, or 35%. Using the 11% raise turn cbet you mentioned.

Thx taggsy.

1) I actually don't know this but just from playing around with a solver, the sizing's range from 1/3 to OB based on the runouts. So can we just make it 66% for river probe to meet in the middle?

2) If we use 66% probe sizing for the river then the raise size will almost always just be a jam. So that's like 16.5bb pf/5.5bb OTF/27.5bb OTT but it goes X/X. River probe is 66% so ~18BB sizing. We have to call before we raise so 27.5 + 36BB = 63.5BB and IP will have 69BB left from a standard 100bb stack so a little over 100% PSB raise size?

I realize it's not 100% rigorous but let me know if you need any other numbers

For B-B-B assuming pot of 35bb and stack sizes of 85bb with turn bet of 20bb and river jam for 65bb into pot of 75bb

EV(b-b-b)=0.48*35-0.11*20+0.41*(0.54*55-0.46*75)=12.36

For X-B

EV(x-b)=0.58*(35*0.56-0.44*20)=6.26
This is assuming we just fold vs probe. If we also bluff raise is gets closer but cbet is still good

Of course when you play bigger factor would be in which line your hand retains equity and then you pick that one.

Okay so let's say we never fold to the river probe and always jam. How much better does the BXB line become?

By my calculations, the BBB line wins 36.2% of the pot, the bxb line wins 15.6% of the pot (with bet sizes of 66% of pot ott and Otr). Based on those numbers, both lines are extremely profitable.

The bxr line wins 27% of the pot Vs the 66% sizing. But the BBB line will win 31.7% of the pot if we jam the river, rather than bet 66%. Might be wrong, but it seems similar to other results.

If he bets 20bb and we jam 85
EV=0.66*55-0.34*85=7.4

So you add 7.4*0.42=3.1bb to bx line.

If you're playing in an anon pool, you'll be printing with any of those lines.

So BBB is higher EV than B-X-Jam over river probe?

Yeah I know they are both profitable I was just wondering which one was more profitable.

yes. With 0 equity hands and these exact sizes.

Cool thanks for that.

Did not expect that conclusion.

Made a mistake here should be 1-0.48-0.11=0.41, 41%.

I’m late to the party, but betting turn being more profitable than the checking lines also holds for geometric turn-river barrel sizing in this scenario too.

Assuming
Turn effective stacks = 87
InitialPot =27.5 (pot size on the turn)
TurnBarrel = 23.5
RiverBarrel = 63.5

For B-B turn and river, we get
EV = -23.5 +0.48(27.5+23.5)+
0.41(-63.5+0.54(27.5+2(23.5)+ 63.5)) = 5.4982 which is 19.99% of initial pot.

And for the EV of checking and going B-X-B or B-X-Jam over the probe assume
VillianRiverProbe = 18 (also our bet size facing check)
RiverRaiseSize = 87 (our jamsize)

Then

EV = 0.58(- 18 + 0.56(27.5 +18))+
0.42(-87 + 0.66(87 + 18 +27.5)) = 4.5274 which is 16.46% of initial pot

Thanks taggsy!

So you come to the same conclusion that BBB is higher EV in a vacuum than BXB or BXJam?

I wasn't expecting this conclusion, this is why data>intuition I guess.

Yeah, same conclusion as the others.