okay, lets assume that you dont calculate equities for v-betting and bluffcatching. How do you calculate that Nash table ?
Notifications
Clear all
I don't know. To find the answer, you should probably go into scientific papers, starting with the Nash original paper. At any rate, it is probably impossible for a human to do it. The best we can do is using guesses and approximations.
Originally posted by kavboj84
okay, lets assume that you dont calculate equities for v-betting and bluffcatching. How do you calculate that Nash table ?
easiest way to do it is with linear programming
There is no "easy" way. Remember that the Polaris robot was developed at a big reputable university. They wouldn't mind to do it if there was an "easy" way. The Polaris robot still doesn't employ true GTO since it is provably beatable (see Boomers posts above).
@redsquirl
What do you mean here? Linear programming is a programming technique (about which I know basically nothing), not an algorithm for finding GTO.
Originally posted by YohanN7
What do you mean here? Linear programming is a programming technique (about which I know basically nothing), not an algorithm for finding GTO.
there are many different algorthms and methods. most of them (that i know of) require an understanding of linear programming.
finding an equilibrium strategy in poker is an optimization problem. linear programming is used to solve many different kinds of optimization problems, in economics, in game theory (obv), or stuff like finding shortest paths on maps, etc.
Ok
Out of personal interest, I'd like to see some of these algorithms. Could you provide a link to get me started?
@red:
I'd really like to see that how this can be achieved without using equity calculations. What ever method you use I cant bypass the usage of Equity. Even with linear programming what can you look for ? EV-s of lines / hands ? EV still uses equity as a variable. Otherwise how can you differentiate AA from 32o ?
Also it would be mesmerizing to see hand analysis in Solver. ♦
Originally posted by kavboj84
@red:I'd really like to see that how this can be achieved without using equity calculations. What ever method you use I cant bypass the usage of Equity. Even with linear programming what can you look for ? EV-s of lines / hands ? EV still uses equity as a variable. Otherwise how can you differentiate AA from 32o ?
Also it would be mesmerizing to see hand analysis in Solver. ♦
what do you mean by solver?
anyway, equity is kinda in there, but throughout EV calculations of all possible lines.
@Yohan, a very easy to understand algorithm is called counterfactual regret minimization, you should try to give a look at it, UofA has some papers regarding it, specifically the one in which they outline how they created polaris.
Originally posted by YohanN7
Out of personal interest, I'd like to see some of these algorithms. Could you provide a link to get me started?
this site shows a relatively simple example. they look at a 13-card poker game (2 through A, there's only one suit) with only a single street of betting.
the source is in matlab (if you wanna get into it more deeply, a free alternative to matlab is octave, the two languages are quite similar)
edit: http://www.cs.cmu.edu/~ggordon/poker/
Originally posted by YohanN7
@JLeitmotiv and redsquirl Thank you.What a wonderful thread this has become!
I had recently taken a look at the code that redskwerl sent you, and something should be said. Although it is indeed a nash equilibrium, it is NOT an admissible strategy. He says it himself (although you might miss it, that's why I say it) that the actual bluffing ranges make no sense intuitively. This model is solved exactly in Mathematics of Poker (bet capped to 1, [0,1) model), so I recommend you take a look at both solutions to see the differences between them. Try to see if you find any other one!
Originally posted by JLeitmotiv
Originally posted by kavboj84
Also it would be mesmerizing to see hand analysis in Solver. ♦
what do you mean by solver?
Solver is an Excel tool which is used for optimization tasks. It is commonly taught in university operational research courses and thats where I encountered it as well.
Originally posted by JLeitmotiv
Originally posted by YohanN7
@JLeitmotiv and redsquirl Thank you.What a wonderful thread this has become!
I had recently taken a look at the code that redskwerl sent you, and something should be said. Although it is indeed a nash equilibrium, it is NOT an admissible strategy. He says it himself (although you might miss it, that's why I say it) that the actual bluffing ranges make no sense intuitively. This model is solved exactly in Mathematics of Poker (bet capped to 1, [0,1) model), so I recommend you take a look at both solutions to see the differences between them. Try to see if you find any other one!
How do you define an admissible strategy? (I unfortunatly don't have Mathematics of Poker)
Originally posted by YohanN7
How do you define an admissible strategy?
a strategy is admissible if it's not dominated by other strategies
Originally posted by redskwerl
Originally posted by YohanN7
How do you define an admissible strategy?a strategy is admissible if it's not dominated by other strategies
Thanks. Fortunately, dominated strategy is defined in the linked page.
Question: Is it known whether several admissible strategies may exist? (Several Nash equilibria may apparently exist.)
It's a long time ago since I dealt with matlab. With a bit of luck, I'll be able to implement the required stuff by myself. I'm enough of a lunatic to have developed my own matrix manipulation library 