His formulas are not wrong he just have weird normalization. When he shows 0.09 for EV of a call, that is 9% of pot+bet, not 9% of initial pot.
This is bad imho because 0.09 for 3x ob is smaller 0.09 vs 4x ob, but it looks the same when you look at the it.

You can use these formulas
If player overfolds by C, EV of bluff scales as C*(1+x) where x is size of the bet in pot units
If player overbluffs by C, EV of calling scales as C*(1+2x) where x is size of the bet in initial pot units

https://www.desmos.com/calculator/d9fyhntpht
a-overfolding
b-overbluffing

For raising is the same. If he over folds value bets, EV of your raise scales up with your raise size. As side note if you dont have trash/non SDV hand and your opponent is overbluffing, raising should be +ev, UNLESS he defends more than GTO or you have really bad blockers.

Those formulas are super helpful, thanks Haizemberg.

So in the case of the opponent overfolding by 5% vs 2x pot bet and opponent overfolding by 10% vs 1/3 pot bet.

Is this how you calculate it?

10%(1+1/3) = .1333
5% (1+2) = .15

So the opponent overfolding by 5% vs 2x pot bet is higher EV since .15>.1333?

Yes.

It's not normalized weirdly, my formula gives the actual expected value in big blinds. It's mathematically identical to yours!

Edge (Risk + Reward) is just what the math reduces to. It's easier to remember one formula rather than making a new one for each situation.

Bluffing (initial bet):


Calling a bluff-catcher:


Bluff-Raising:


It's also easier to remember breakeven poker formulas (1-MDF / Pot Odds / Required Equity% / Breakeven Fold% / etc) when you realize that it can all be written using the same formula:
Breakeven% = Risk / (Risk+Reward)

Ahh nvm, just realized you were referring to Patrick Howard's equations not mine lol

A call would be way higher EV in that case. Think about it this way. If you call, you make 10%(pot+bet). If you raise, you breakeven and make 0 because they defend MDF.

Now imagine you only fold out bluffs and get called by value. If you raise, your risk (the raise) increases substantially relative to calling, but your reward (their bet+pot) stays the same. Your success rate (probability of folding out or calling a bluff) is the same in this scenario. Therefore calling is always the better option if your opponent is perfectly polar.

The size of the bet and raise certainly matter. Imagine overbluffing by 10% while putting in a 1% pot-sized bet. Now imagine overbluffing 10% while putting in a 300% pot-sized bet. One of them is gonna be far more exploitable. Similarly the size of the raise matters a lot. MDF and Bluff% don't scale linearly, so the edge does not scale linearly either.

Thanks Tombos, still going to think about this some more. At least I got my little calculation right

Is it too much to ask for Tombos to do a GTOW Video on this concept? I think it would be awesome haha.

Hmm maybe. It seems a bit too short to make a video about. Could do an article though.

What would you want to see covered?

I was thinking a video with multiple examples because I don't think it is very intuitive (maybe it is to you) but I'll take anything I can get.

The most relevant spots would be 3BP's because there is a lot of jamming going on vs bets. Also 3BP's are less studied than SRP's so I think it would be more beneficial to the audience.

If I am getting greedy then I would like you to compare it to MDA and show why one play is better than the other when GTO disagrees but that is probably not going to happen, I've just basically heard no one talk about this and I think it's important.

Another idea for a video/article would be showdown bias and it's effects. That seems very complex but would make for a great topic.

As an aside, I am in Metagame CFP and I asked a bunch of 500nl/1k nl players about the original HH and NONE of them could do the math so I don't know what's going on there. I really appreciate you taking the time to educate us less mathematically inclined players.

Thx again Tom

I threw in a reference to the math behind this post in my latest video:

(Timestamp 21:43)



Covering into Mass Data Analysis is tricky right now. There are some things out of my control that prevent me from making content about MDA. However, when we add GTO Reports, I suspect this will become a central focus!

All the best and thanks for the interesting thread, DDP.

Thank you Tombos I will have to watch that video and I have another question wrt to this exact topic in another spot and wanted to get your take on it.

Here is the hand in question.



This is a 0 EV spot in a solver

But it just outlines what I've been thinking about recently. So I know X-B70-B70 is overbluffed by 3% in this formation (30 weak is GTO) on flush complete rivers. But I also know SB vs a 4x raise will fold 68% of the time.

So if we layout the problem like this:

$12 pot OTF XX. B$7 OTT Call $7.

River B$18 ($26 pot) Raise $72

$44/$116 = 1-.38 = 62% MDF. So there is a 6% discrepancy without accounting for showdown bias (not sure how to calculate this yet)

So I already know Raising>Calling>Folding in this 0 EV theoretical spot right?

The next part is where I stumble a bit and need your help, I want to take your formulas and plug in the numbers.

Calling a bluff catcher: EV = Edge(Call + Bet + Pot)

So 3%($18 +$18+$26) = 3%($62) = $1.86 or .93BB is that correct?

But Bluff Raising = Edge(Raise + Bet + Pot)

So 6%($72 +$18+$26) = 6%($116) = $6.96 or 3.48BB right?

I just wanted to confirm this math as I have been having fun finding the MDF discrepancies in MDA OTR.

We basically go from a 0 EV spot in a solver to calling (.93bb win) to raising (3.48bb win).

Can you confirm I did that correctly or tell me where I went wrong? Thanks Tombos!

Yep, looks spot on DDP!

Sweet!

Thanks for confirming that

Okay here is my theory on how we can account for showdown bias, you tell me what you think.

We look at a solver and look at the action we want to do. We see that raising OTR is a negative EV play, anywhere from -1.19BB to -2.05BB with this exact combo of J6.



But we know raising is actually positive 3.48BB and calling is a.93bb win.

So can we subtract this range of -1.19bb to -2.05bb (showdown bias tax) from the 3.48bb win and still get a net win of 1.43bb-2.29bb range.

And since that is greater than the calling of .93bb, raising will still be higher EV than calling even with showdown bias included.

Let me know what your thought's are on this topic! It's very interesting to me and I'm still waiting for someone to deep dive it.

J6s is -ev in solver because it has bad blockers for calling and raising. I don't think it has anything to do with SD bias.

Just to point out, not every flush river will be over bluffed and over folded by same amount. Blokers are also important esp for raise, SB b/c range ends up being 50-100 combos, so blocking few combos can make or break this play.

J6s is 0 EV for calling not negative EV, I won't speak on SD bias because I don't know enough about it.

I think you are too caught up on the 6% discrepancy though, we can easily manipulate that number. What happens if I instead raise 3.5x instead of 4x?

Now MDF is 44/107 = 1-.41 = 59%. Now there is a 9% discrepancy. This raise will be better than both calling and folding by a wide margin and the combos of the hand aren't going to make it less EV than either of the other options.

If you min raise it's even better!!!