I have both GTO+ and Pio and was comparing results for a hypothetical river spot where OOP jams 1 PSB with a balanced range and the two solvers give different call frequencies for their bluff catchers. I know that if OOP jams a balanced range, IP's bluff catchers are indifferent to calling or folding so in practice their call % shouldn't matter, but why do the two solvers give different answers?

Board: 9s 9h 9d 2h 3d
Pot 100
Rake set to 0 for both
OOP jams 100
OOP value range: JJ-AA (24 combos)
OOP bluff range: JTs, QJs, QTs (12 combos)
IP range: 22-88

GTO+ calls 1/2 of the time, which is what I would expect if IP is indiff, but Pio calls 1/3 of the time. Again I know it doesn't matter but I'm just trying to understand how the systems work.

https://imgur.com/a/tZYqVjG

I think it's because GTO+ can converge to 0% exploitability while Pio will be stuck at something like 0.01%

Post both game trees. So we can double check them.

I set both to 0.002 since that's what pio caps at for me.

You mean this? https://imgur.com/a/i4U12VL

If that is the game tree you used for pio, it is two different game trees.
The pio tree, with those settings. (Just an all-in) is not the same as the gto+ tree.
(I don't think it is) , that game tree does not even work.

To see the pio game tree, click build tree, then go to the browser, then follow the game tree, and make sure the one you use is exactly the same as the one you use for gto+.

Double check the ranges used too.

Side note: your betting a pot size bet on river with 24 value combos and 12 bluff combos.
Is that balanced?
I seriously don't know. I am not very good at the balance stuff.

Must be with however they are solving, I'm sure if you add more potential bluffs to OOP range then IP will defend 50% to make sure OOP can't just jam all bluffs.

edit: could be wrong I guess. Just think that solver pry doesn't give af what it does IP if OOP has a fixed freq of bluffs.... all ip calls are 0ev regardless.

Add 4 more bluff combos and your Golden

Yeh so I just ran the sim in pio and i get the same results as OP, but if you add in .01 extra combos of any potential bluff the ip defends 50%

I figured betting 100 to win 100. So, call is 100 to win 200, for the call to be indifferent you want 33% bluff combos.
This is wrong huh?

he has 33% bluff combos

Hahahababa
It was 12 geez.
24 value and 12 bluff.
Am I tripping
Edit: Yeah, that's 33%
Edit: no that is half
**** ****
Edit: no that is 33%

I figured it out. It does not matter if its 30% or 50% , your indifferent to calling or folding.

As a test you can lock the pio tree to bet 100% and the exploitable will go to 0%. Then you can lock call to be whatever you want and OOP EV will always be the same.

When you add .01 combos call does go to 50% but OOP checks some bluffs at a small % cause your not balanced any more.

The 50 percent threshold is usually in trees where oop can check the nuts, so bets have to be defended at MDF. The 33 percent calls are usually in trees where oop jams the nuts, and calling is purely vs the entire range.

In both solvers OOP bets 100 into 100 at a 100% frequency: https://imgur.com/a/5AiSah8

But IP responds differently: https://imgur.com/a/tZYqVjG

The trees are the same in both solvers

Look at the pio tree. It is not %100. You can not see this in the pic but you can see it off to the side. Its %99.9 or something. This is because of the check. Either remove the check lines in both trees or lock the pio tree to solve at a true %100 bet.

And the point is, either way, the call/fold frequency is trivial. The caller is indifferent. When you solve the tree to a true %100. It will not matter the call/fold frequency. That is the point of this exercise.

Try again but node lock the pio tree to a true %100

yeah you're right. I got it now thanks. Looks like GTO+ got these quirks worked out better then since it's not checking the 0.01%

Its not quirks. Its trivial. Both solutions still have same EV+-error.
The next thing to do would be to add 1 bluff hand in OOP range and node lock the bet 100% and look at the solution for IP player. Then try node locking 1 value hand in OOP range and node lock bet %100. (Better to just remove the check option from this tree). And study the solution for the caller.

A funny thing is earlier when I node locked one more bluff hand and found Nash OOP bet slightly less and IP called %50 and when I node locked 4 more bluff hands and tried. (my deep understanding of fractions) OOP checked a little more and IP still called at %50. We should have just removed the check.

I would slowly build on this example and mess with it.

Both solvers work great. Trivial. Cause remember the solution is OOP bet %100 and it will not matter what IP does. Calling %50 and folding %50 is trivial. Try locking different call frequencies. The EV for OOP will always be the same. IP is indifferent to calling or folding.

Yeah, MDF makes sense for the %50 I got when adding random bluffs and solving without locking %100 bet

Maybe quirk isn't the right word but GTO+ doesn't require me to manually remove the check option for OOP to get to the 50-50 call solution for IP. In fact it is there in GTO+ but it doesn't show OOP strat to be 99.99% as in Pio. Also when I look in Pio at the individual combos for OOP, none of them show less than 100 bet% even when the total bet% 99.99%. I assume this is just a rounding thing.

Again, I understand we are indifferent, I am only trying to understand how the two programmes work. I know the correct solution in my example is for OOP to bet 100% which is why I set it up that way. What I want to know is why Pio doesn't reach 100% when I allow a check option while GTO+ does reach 100% when I leave a check option open and both trees should be solved at the same distance. Could some sort of internal rounding preferences be a cause of this?

Got a bit thrown off when you said "GTO+ calls at 1/2 which is what I would except if indiff"
Ask the coders for the inner details, the code is closed source so know one knows but them.

i think in your example the "correct" frequency is not 50%, as you expect, but any frequency between 0 and 50% are all valid. the reason is that the aggressor cannot respond exploitatively to a low calling frequency.

Yep, both solutions in original post are at nash equilibrium since no defending strategy by IP can make OOP bluffs -EV.

Basically OOP's range is at the boundary of what is too strong for MDF to apply for IP. Removing 0.01 bluff candidates from OOP will force IP to fold range when OOP bets. Adding 0.01 bluff candidates to OOP will force IP to defend using MDF (and OOP will check 0.01 combos of bluff candidates to guarantee his bluffs are not -EV).

It's because PIO doesn't solve till perfection. Even if for a certain hand betting has higher EV than checking, PIO will still check it 0,01% of the time, as long as the difference in EVs isn't too big. Therefore it will be betting 100% of value hands on this river, and only 99,99% of bluffs (it will still check 0,01% of them). Because of that it will be underbluffing.
That's how I understand it.

If you click the "force OOP bet" button, it will solve the spot correctly.