How come flop EVs tend to run really close to one another in trees with multiaction strategy profiles?

Are you able to talk about the concept of a GTO strategy "sacrificing" EV in certain parts of the tree in order to achieve a balanced strategy? I notice that on rivers (really in terminal nodes in general) you see a lot of situations where the solver wants to "Theory call" a -EV combo or even "theory fold" some marginally +EV calling combos in order to make the overall strategy unexploitable (is that what is going on in this screenshot?)




But in the non-terminal nodes you tend to see what you'd expect which is that the solver only choose the highest EV actions.



What I'm guessing is that the EV differences from "sacrificing" in other parts of the tree show only show up in the terminal nodes? Can you correct my understanding if it's wrong?

I apologize for the numerous ?'s, thanks in advance:

What is the definition of a Maximally Exploitative Strategy (MES)?

I'm trying to really understand how frequencies are bucketed amongst options in a strategy profile. Not necessarily for any particular hand but more of a general, abstract understanding about why the solutions looks the way they do

Is the Nash equilibrium produced by the solver unique for a given configuration?

In other words, if I keep all inputs the same (same ranges, stacks sizes, same options in the strategy profile, etc) is it possible to find a different strategy than the one found by the solver that is also unexploitable?

Hello if I want to take in mind the these days in poker and calculate for 100nl game with 5% cap and 5$ max rake.
What do I need to put in Pio
for 1000nl is 5% with 5 chips
for 200nl is what? and for 100nl is what?

For example all people are using starting stack 1k with 55 in pot
If we use 200 starting and 11 in the pot ?

I don't understand the question, can you be more specific? It's not clear to me what you are comparing.

The concept doesn't exist. The definition of the equilibrium is that no player can improve their EV by altering their strategy. That means that if you make not max EV action at some point it's not an equilibrium.

It's only because the solution is not perfect yet.
In the near future we will have a feature to make rivers more precise by recalculating on the fly (now it only happens when you load a small save) to mitigate that effect.
Notice that even on your screenshot the EV differences are relatively minor (in comparison to the pot size) and that you are looking at the very rare line to begin with (0.06% total).
Also please take note that the EVs are calculated against current solution (and not against exact equilibrium as we don't know what it is). The frequencies might already be almost perfect but the EVs will vary as even one small deviation (from the theoretical equilibirum) of one of the players will produce EV differences. The EVs provided are mainly useful as a sanity check. The closer they are for mixed actions the better the solution is.

Well, it's not always the case. In general the more frequent the line is the more precise the solver is going to be there (as mistakes in frequent lines matter the most for overall exploitability).
It's defined as a strategy that perfect adversary - one knowing our exact strategy in every spot and adjusting perfectly - would take.
In other words it's a strategy that can't be improved against us.
In perfect equilibrium both solutions are also MES'es to each other (although there exist many more MES strategies, all with the same EV but potentially different frequencies).


It's possible for many equilibrium strategies to exist. We even showed that on some toy games in the past. As long as the game is zero-sum (that is no rake and no ICM) all those strategies will have the same EV for both players. In practice it seems there is one equilibrium all the algorithms find so it's reasonable to assume there is just one for practical purposes. (again, without rake/ICM).


It's the easiest to multiply everything by 10. That means using cap of 50 and 5% for rake.
Sanity check is this: in 100NL game you pay max 5bb rake. You need to make it the same if you want to simulate it with higher blinds.

If i always want to use 1000 chip stack for 5% with 5% cap
100nl is 5% with 50 chips max
1000nl is 5% with 5 chips ?
That logic doesnt seem right, no ?
For 1k nl we pay max 0.5BB max rake
For 200nl we pay max 2.5bb rake
For 200nl 5% with 25 chips max ? Thats if we use always 5/10 in Solver
If we use smaller stacks in Solver For example starting pot 10 and starting stacks 200...
Can we use 5% with 5 chips max

Unfortunately it is. The rake is that high at 100NL.
Yes. If the cap is still 5$ then to simulate 200nl game you would use 25 rake cap with 5/10 blinds.

Yes. The only downside of using smaller blinds/stacks is that chips are not divisible so you will run into some rounding problems when it comes to bet sizes (for example 50% pot bet with a pot of 11 is going to be 6 not 5.5). That's why it's convenient to multiply everything by 10 or 100.

Hey there!

I have a somewhat related question to the one that was asked recently regarding {board}, when running scripts.

Would it be possible to add a possibilty with an update to have another automatic naming option like {board2} or something, where the output of the script filenames is:

Q73ss
QT2sss // QT2 mono

instead of

Qs 7s 3d
or
Qs 7s 2s

This should be somewhat easy to implement and would make the results from the scripts so much more userfriendly.

Thanks a lot in advance!

The problem with this idea is that those are not unique.
For example Q73ss might be:
Qs 7s 3h
Qs 7h 3s
Qh 7s 3s

and of course there no guarantee there won't be a flop like Qs 7d 3d which is strategically the same as the last one from the list above but still it's possible to request those in the script. To implement this idea one needs a way to resolve name conflicts in such cases. Maybe it's just easier to write a tool to change names of the files once they are created. It doesn't have to be related to the solver in any way.

I interpret this to mean that the frequencies generally converge faster than the EVs do. Is that correct?

Does the solver also calculate the equities against the current solution?

What is the definition of "equity" that the solver uses?

Qs 7s 3h = Q73f
Qs 7h 3s = Q73g
Qh 7s 3s = Q73h

hi, i recently purchased pio solver edge and i have problems running some of the sims

most of the post flop sims run good but when i try to run a complicated post flop sim or a pre flop sim i get the message:

"ERROR: add_all_flops not enough memory; needed 430778 MB;
available: 10079 MB" for example

i have a new laptop computer that i recently bought:
16GB RAM(15.9 GB usable)
930 GB free on "D"
165 GB free on "C"
system type: 16-bit Operating System, x64-based PC
processor: intel(R) core(TM) i7-8750H CPU @ 2.20GHz, 2208 Mhz, 6Core(s), 12 Logical processor(s)

from what i have looked in the System requirements the computer that i bought should be strong enough to run this software(also what the person that i bought from him the computer told me when he looked at the requirements).

so does my computer is strong enough to run complicated post flop sims and pre flop sims and i have some problems in the settings or should i buy a new computer ?

It's hard to compare the two but it makes sense to think about it this way.
Small differences in frequencies along the way to the river may result in quite a big EV difference.

We use it this way:
"equity" = "all-in equity" that is EV assuming check-down to the end.
"EV" = how much you win or lose on average assuming both players follow the solution from here.

You can see both in the browser.
43GB big postflop tree is really just too big. Are you using like 5 bet sizes and 3 raise sizes everywhere?

The computer is good enough to run postflop spots (although won't be too fast as it's a mobile CPU). The problem is that it's always possible to build a bigger tree so there is no amount of RAM that is enough for all trees.
Pio already uses very little memory in comparison to other known algorithms. It's just that you are going overboard with the number of bet sizes. Please also use a cap as well (we really should have made it default). One way to make the tree much bigger than it should be is to use a small bet size on the flop and then a small raise size so it creates endless bet/minraise/minraise/minraise... chain.

You could in theory build a machine to solve trees as big as well although we don't recommend it because even if you are able to build those trees they will take a very long time to solve.

hi, sorry if this is a dumb question but i was watching a video with sauce analyzing pio and he brought up some menu where you could see the evs for every runout and suits. where can i bring this up? i cannot recall which video or what time i watched it, thank you

It's in the top menu: analysis -> Runouts EV comparison
You can also use a shortcut: ctrl + H
Try it on the turn or river.

Hi, I'm thinking of buying basic license. I have a notebook I7 7700HQ 2.8ghz x64bits, 16GB RAM. I don't plan to change notebook for a while so I would like to know if with it I would be able to run trees with 3 bet sizes on the Flop. Thank you

It always depends on things like betting structure on other streets, stacks etc. but in general you shouldn't have a problem.
For example this
https://gyazo.com/c48520947d5416e7af9392e8db480c73

already very big 100bb BTN vs BB tree with 3 bet sizes on the flop for IP, donkbet included for OOP and 2 bet sizes on the turn and river for both players is 5.5GB.
This is already quite large so it will take a while to solve but if you don't care about solving time you can add more bet sizes still.

Hi, is it possible to use PIOsolver to building preflop opening/calling range?


I mean situations like UTG open, MP folds, CO folds, HERO is BTN.
I know probably what is UTG's opennig range but that is not enough. In game are SB and BB still. How to solve this situation? Thanks

thanks for your reply

Normally, I wouldn't include donk sizes (maybe only on the river) but if I should use the X / R option on each street
When you talking about stack sizes, I have to assume that with smaller stack sizes as 40bb, 30bb it will take less time / ram?

is there a way to shrink cfr files and still be readable from pio?

Hi, imagine a situation if I open from SB. I want to find out what is +EV open.
I know villain's range. I know what he call's what he 3bet's. But how to solve it in PIOsolver?

I build a tree where is range of villain. But I can not divide tha range to 3b range, calling range to Piosolver knows how villain play and how.

How to solve it? Thanks

Hi,

Sorry if this a noob question. I am trying to use the text interface to get the EV of a hand. However, calc_ev returns a different value to that one showed in PioViewer. I read that we need to add the money invested by the player to be added to arrive at the correct EV shown. However, this is flop when it goes check and i am checking the value for check for IP player. Here is a screenshot for reference:

https://gyazo.com/578e052b89f196c2ea788d6ffb6f7621

Please help.

Hey so yesterday I was trying to run some icm sims on pio.
I currently have piosolver preflop edge
I looked in my tree building and I couldnt find the icm structure button so I updated the software. After updating this software I was able to use icm with the "icm structure button.
https://gyazo.com/3bddde531279ca620ef27bc78335c650

While doing this I saved some trees to look at later and decided maybe I should try and run some sims on my friends pc since his is faster. I took the license and deactivated my account on my main pc. Since reactivating it back on my new pc my button for icm structure has disappeared.
https://gyazo.com/8d05c8b43179c98ef836dd49caa726e7

I have tried updating/force updating but to no avail.

further more the trees I saved yesterday I cant even open anymore since deactivating license and reactivating with this error message

https://gyazo.com/f31f18c656e919319eccff7b6c88c630

If someone could be of help to me it would be very much appreciated.

many thanks!

It's not possible to solve at the moment.


Yes, because there are less possible lines in the tree in such case.

No way to do that. We could try compression or not saving EVs but it doesn't seem to be very popular request so it's unlikely to happen in the near future.
The values are translated using a formula defined in Tools->Configuration->Date presentation - other

The default is to display EV at given point (so fold is always 0) while the solver internally returns EV of the whole line (so if you call 100 on the flop and then fold on the turn the EV of that fold is -100). While those values are just a different way to say the same thing most people are used to looking at EV at given point while for programming purposes it's easier to have EV of the whole line. You alter this formula to have EV in % of the pot for example.

The values on your screenshot look completely different though. Are you sure the solver is not running and wasn't running between calling that command and looking at the viewer? Another thing is that you shouldn't use calc_ev_pp, just use calc_ev and parse the values if you are developing a tool.

All the symptoms point to you still running an old version. You can verify that by going to "about" in the top menu or looking at the bottom bar which displays engine version.
The current version is: 1.10.24.3 for the viewer and 1.10.21 for the engine.

The best way to make sure you are running the newest version is this:
-run the installer, notice the installation folder location
-go to that folder
-DO NOT remove any files from there and run PioViewer from that location

What is likely happening is that you have a shortcut to the old version on the desktop and the old one is installed somewhere else on your computer.

Thank you for your help. It was a mismatch of IP/OOP when using the calc_ev command causing the values to be different. I wonder why this param exists instead of deriving the same from the node. Thanks again so much for helping out.