do pio, GTO+, SPF, monker, etc all use the same algorithms? - Poker Theory

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do pio, GTO+, SPF, monker, etc all use the same algorithms?

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08-20-2019 , 10:45 PM

nightmaretilt

centurion

Join Date: Apr 2018 Posts: 182

Im not sure 'algorithm' is even the right word for this question, but do these different software all use basically the same type of code?

I guess Im not really referring to preflop necessarily, since only pioEdge and monker have this, so that could definitely complicate this question. Also monker works with plo which complicates the question as well. Mostly im thinking of NLH postflop solutions, and wanting to know if there is some difference in the DNA of these software??

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08-21-2019 , 12:00 AM

YouAreAwesome

journeyman

Join Date: Aug 2017 Posts: 345

subbed.

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08-21-2019 , 05:53 AM

getmeoffcompletely

old hand

Join Date: Aug 2012 Posts: 1,670

I'm pretty sure they all use some variant of CFR.

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08-21-2019 , 07:40 AM

just_grindin

Pooh-Bah

Join Date: Dec 2007 Posts: 5,263

There is a software forum where you might get better answers.

I assume the methodolgy is mostly the same in terms of the basic data structures they use and as getmeoffcompletely said they are likely using some version CFR to update the EV trees.

Where they might differ is in their game abstraction and what properties they use to determine which nodes to traverse.

See here for a description of pio's abstraction technique to get some idea of what's going on.

https://www.piosolver.com/blogs/news...the-whole-game

If your asking if there is a standard library they all use for designing the software I would doubt it, though I don't know for sure.

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08-21-2019 , 03:50 PM

EggsMcBluffin

MTTPIOExpert

Join Date: Feb 2019 Posts: 1,459

No, IDK about the last two but PIOs algorithm is proprietary

But they are all ultimately are intended to do the same thing, and I'm pretty sure in theory they're all supposed to converge to the same solution.

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08-21-2019 , 07:17 PM

YouAreAwesome

journeyman

Join Date: Aug 2017 Posts: 345

Quote:

Originally Posted by EggsMcBluffin

Is it possible there are multiple solutions? Has it been proven there is only one solution? I'm not sure. I've always thought there will be a range of solutions that all yield the same ev... but I could be wrong.

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08-21-2019 , 07:42 PM

ArtyMcFly

Carpal \'Tunnel

Join Date: Dec 2014 Posts: 13,256

Quote:

Originally Posted by YouAreAwesome

Is it possible there are multiple solutions? Has it been proven there is only one solution? I'm not sure.

Assuming the following conditions are met (and it's a 2-player game), there is a unique Nash Equilibrium when:

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* The players all will do their utmost to maximize their expected payoff as described by the game.
* The players are flawless in execution.
* The players have sufficient intelligence to deduce the solution.
* The players know the planned equilibrium strategy of all of the other players.
* The players believe that a deviation in their own strategy will not cause deviations by any other players.
* There is common knowledge that all players meet these conditions, including this one. So, not only must each player know the other players meet the conditions, but also they must know that they all know that they meet them, and know that they know that they know that they meet them, and so on.

Source: https://en.wikipedia.org/wiki/Nash_equilibrium

Since solver software effectively takes all those conditions into account, I don't think there is any doubt that heads up poker has a solution that is a unique Nash Equilibrium. There's always a best move and a best response and best counter-response etc, not multiple best moves/responses. (It's just confusing in that there are many mixed strategies that "add up" to make the equilibrium solution.)
The solver software would presumably crash (or get lost in a neverending loop) if there were multiple discrete solutions.

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08-21-2019 , 08:11 PM

YouAreAwesome

journeyman

Join Date: Aug 2017 Posts: 345

Quote:

Originally Posted by ArtyMcFly

There's always a best move and a best response and best counter-response etc, not multiple best moves/responses. (It's just confusing in that there are many mixed strategies that "add up" to make the equilibrium solution.)

Hmmm I thought there were multiple best responses. For example, check and bet often have equal ev. Similarly differing bet sizes yield equal ev in certain circumstances and I imagine differing ways of creating mixed strategies could also yield equal ev hence why GTO+ may give a different solution to PIO. I presume there is more than one global solution for NLH, unless of course, we are meaning the one solution includes all the differing strategies.

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08-21-2019 , 08:30 PM

whosnext

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Join Date: Mar 2009 Posts: 6,733

My first thought is that Arty's post is incorrect. Those are not sufficient conditions for the existence of a unique Nash Equilibrium.

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08-21-2019 , 09:12 PM

#10

just_grindin

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Join Date: Dec 2007 Posts: 5,263

I agree with whosnext I thought the criterion finite game with most of the stuff Arty gave guaranteed at least one Nash Equilibrium, but did not gurantee it was the only Nash Equillibrium.

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08-21-2019 , 10:14 PM

#11

statmanhal

Pooh-Bah

Join Date: Jan 2009 Posts: 4,987

Referring to the same source Arty used, the following is stated (my emphasis)

Nash's Existence Theorem

Nash proved that if we allow mixed strategies, then every game with a finite number of players in which each player can choose from finitely many pure strategies has at least one Nash equilibrium.

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08-21-2019 , 10:47 PM

#12

YouAreAwesome

journeyman

Join Date: Aug 2017 Posts: 345

Quote:

Originally Posted by statmanhal

Heh, so back to square one. There's definitely one solution, but there may be more. However if solvers produce differing but correct outputs then there's most probably >1 global solution. (e.g. a solution that has more or less mixed strategies than another but overall creates the same ev).

I'm confident that at some stage in the future, just as in chess (Stockfish vs Alphazero etc), GTO+ vs PIO vs Pluribus vs etc. will occur.

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08-21-2019 , 11:38 PM

#13

nightmaretilt

centurion

Join Date: Apr 2018 Posts: 182

the way I understand: there is a true, singular nash strat which yields max EV, but commercial solvers just find the nash solution within the input parameters provided to hero/villain

as ben sulsky said, solvers effectively run upscaled toy-games for us, and provide a nash solution. But the true nash strat does not have forced input parameters

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08-22-2019 , 01:56 AM

#14

nightmaretilt

centurion

Join Date: Apr 2018 Posts: 182

this thread has some similar questions. https://forumserver.twoplustwo.com/1...stion-1722295/

in this thread someone says that pio might not converge to rock bottom equilibrium, which might make it spit out slightly different solution than gto+

if we assume that there is only 1 true 'perfect' nash strat (which might be incorrect), i wonder if these software are doing the same thing in different ways, or maybe there some widely used CFR code. i really have no idea what im talking about btw

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08-22-2019 , 03:54 AM

#15

plexiq

veteran

Join Date: Apr 2007 Posts: 2,554

Quote:

Originally Posted by ArtyMcFly

Assuming the following conditions are met (and it's a 2-player game), there is a unique Nash Equilibrium when: ...

Nah, that's a misinterpretation. Here's the actual description from your link:

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If a game has a unique Nash equilibrium and is played among players under certain conditions, then the NE strategy set will be adopted. Sufficient conditions to guarantee that the Nash equilibrium is played are:
ArtyMcFly's quote...

This section doesn't make any statement whatsoever about when unique NEs occur. IF a unique NE exists then the quoted conditions are sufficient for players to actually adopt that unique NE.

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08-22-2019 , 07:02 AM

#16

just_grindin

Pooh-Bah

Join Date: Dec 2007 Posts: 5,263

Quote:

Originally Posted by YouAreAwesome

I am guessing the solvers' solutions can't be used as evidence for multiple nash solutions.

The variations are likely from the way they abstract the game, the conditions they use to stop the simultations, etc.

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08-22-2019 , 11:25 AM

#17

NMcNasty

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Join Date: Feb 2004 Posts: 3,990

I'm pretty sure the multiple equilibria thing only really applies to strategically irrelevant choices.

Example: Board runout is AQKTJ rainbow (rakeless). It doesn't matter if you pot/call, half-pot/call, or even check/call, all will satisfy Nash as long as neither player folds.

Not sure if multiple equilibria actually exist where one strategy set say 3bets JTs 35% where another only 3bets 15%.

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08-22-2019 , 12:05 PM

#18

whosnext

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Join Date: Mar 2009 Posts: 6,733

I've always distinguished 2-player poker from 3+player poker for this issue.

I would be surprised if 2-person poker has multiple (non-degenerate) Nash equilibrium and I would be surprised if 3+person poker does not have multiple (non-degenerate) Nash equilibrium.

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08-23-2019 , 05:53 PM

#19

mojo6911

veteran

Join Date: Feb 2008 Posts: 2,979

I know for a fact that GTO+ and Pio don't use the same algorithm. Pio can't solve to 0 nash EV, but GTO+ can. Monker definitely doesn't because it uses abstraction and buckets for multiway.

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