Ask me anything about Game Theory - Page 3 - Poker Theory

ArBar · 07-18-2012, 08:17 PM

Quote:

Originally Posted by egj

Don't think this is correct.

For example, consider a strategy for two-person no-limit with stacks of twenty big blinds that says you fold KK to an open-shove. Although obviously stupid, this strategy is not dominated. There are some opponents (e.g., one who only open-shoves AA) such that it is correct to fold KK there.

Having said that, if you are playing GTO, then your opponent is not indifferent between folding and not-folding KK to an open-shove. Not folding will surely be +EV. (Well, I haven't proven that, but I'm not sure anyone will disagree.)

It is correct, and extremely easy to prove. If a strategy is strictly dominated that means some other strategy has a better payoff than it at all terminal nodes. So any mixed strategy playing it with a positive probability can be improved by playing it with a 0 probability.
The case you are describing isn’t a problem for it. It has to do with opponents’ types and your belief system, but it won’t alter the truth of the quoted statement.

Correct, but your opponent’s strategy is not completely described by your post. His strategy consists of much more than just what he does with KK facing an open shove.

Quote:

Originally Posted by Huggy

Do you know what ex-showdown equity is?

Nope. But if I had to guess I would say it’s equity once hands are realized.

Quote:

Originally Posted by SquirrelsUnite

TBH, I did expect you to be familiar the Mathematics of Poker as well as standard poker terminology. At the very least you should be familiar with the kinds of toy games people study and why they are interesting from a practical point of view.

By the [0,1] framework I meant representing players' ranges as probability distributions over the [0,1] interval, for one street (or half street) games. These games can often be solved analytically and the results are directly applicable to actual play (at least as long the initial estimation of ranges is accurate).

However the model is imperfect in the sense that it assumes player 1 faces the same range regardless of the hand he holds. This is of course untrue: our opponent can't hold a card we do. The most important case being when we hold a blocker to the nuts.

So the question is how do you extend this framework to create an exact model of the actual game but still preserve the power of analytical methods that allowed you to solve fairly complex games.

Now, based on your posts in this thread, I don't really expect you to have an answer for this. But this shows why it's dangerous to say "ask me anything about game theory". The kind of games poker players study are very specific. The main question we ask: "How can I create a toy game that's both solvable and useful from a gameplay perspective?". Or at least illustrates the structure of the game in some sense.

These question are much more about poker than game theory. At least the small part that I understand doesn't use any complicated mathematical machinery and completely avoids the complications of 3+ person games and non Nash-equilibrium solution concepts.

To extend it to account for blockers would be to adjust the probabilities based on where you are at on the game tree. It would make the results more accurate, but it would greatly increase amount of work required to solve.

ArBar · 07-18-2012, 08:19 PM

Quote:

Originally Posted by Paul Valente

False.

This thread is worthless. How about you just correct all these "incorrect posts" when you see them instead of starting a thread that at best will result in a cluster-****.

Cool story bro.

Quote:

Originally Posted by Paul Valente

And I don't think you meant that if we play GTO our opponent can just randomly press buttons and be indifferent, but I think that's what some ITT think you meant. That is obviously incorrect. Many deviations from GTO will result in loss of EV against a GTO opponent. (but not all deviations)

That’s probably because they don’t know what strategies are. Thx brah

yaqh · 07-18-2012, 08:38 PM

Quote:

Originally Posted by Ssslipnssslide

If we are playing GTO then our opponent is indifferent to taking any action since we are perfectly balanced right? Does this hold true for NL games when overbets are possible?

Quote:

Originally Posted by ArBar

Correct, if you are playing the strategy from a nash equilibrium, then your opponent is indifferent between their actions.

Quote:

Originally Posted by DarkMagus

Are you sure about this? I mean, surely an opponent can't be indifferent between playing or folding AA preflop...

Maybe you meant to say they are only indifferent for strategies that aren't dominated?

Quote:

Originally Posted by ArBar

Yeah only strategies that aren't dominated. Any mixed strategy contained a strictly dominated strategy is itself strictly dominated. Thanks for pointing that out.

Quote:

Originally Posted by egj

Don't think this is correct.

For example, consider a strategy for two-person no-limit with stacks of twenty big blinds that says you fold KK to an open-shove. Although obviously stupid, this strategy is not dominated. There are some opponents (e.g., one who only open-shoves AA) such that it is correct to fold KK there.

Having said that, if you are playing GTO, then your opponent is not indifferent between folding and not-folding KK to an open-shove. Not folding will surely be +EV. (Well, I haven't proven that, but I'm not sure anyone will disagree.)

Quote:

Originally Posted by Paul Valente

And I don't think you meant that if we play GTO our opponent can just randomly press buttons and be indifferent, but I think that's what some ITT think you meant. That is obviously incorrect. Many deviations from GTO will result in loss of EV against a GTO opponent. (but not all deviations)

Quote:

Originally Posted by ArBar

That’s probably because they don’t know what strategies are. Thx brah

What distinction are you trying to make w/ your definition of strategy? I'm having a hard time seeing how the second quote above is correct without a pretty specific context.

Otherwise, thanks for the AMA.

ArBar · 07-19-2012, 01:26 AM

In game theory a strategy is a comprehensive plan of action. It's basically a complete if then book that you could hand to anyone and they could carry it out. It covers what you will do in every possible situation, even if that situation never arises in the game. So in poker it would tell you what to do in every possible combination of starting cards, position, bets/checks/raises, etc. So you get dealt KK, but your strategy isn't just to check/fold/bet/raise with KK. Your strategy tells you what you are going to do with KK and what you are going to do with A3s, 78o, etc etc for all possible hands.

egj · 07-19-2012, 02:15 AM

Most of the papers on poker I'm aware don't (explicitly) make use of terminology related to Bayesian games. So, for example, they will talk about "Nash equilibria" rather than "perfect Bayesian equilibria".

Although, at the same time, they will represent a game of poker in extensive-form (i.e., tree-form) with a "chance" player ("nature") who takes actions at random.

So are these papers all (implicitly) using the Bayesian framework even if they don't adopt that terminology?

If not - is there value in moving to the Bayesian framework? Is it useful to talk about poker in these terms?

This question is a bit vague but maybe you can make sense of it...

Huggy · 07-19-2012, 04:15 AM

ArBar this AMA would be much better had you read MoP

yaqh · 07-19-2012, 06:40 AM

Quote:

Originally Posted by ArBar

In game theory a strategy is a comprehensive plan of action. It's basically a complete if then book that you could hand to anyone and they could carry it out. It covers what you will do in every possible situation, even if that situation never arises in the game. So in poker it would tell you what to do in every possible combination of starting cards, position, bets/checks/raises, etc. So you get dealt KK, but your strategy isn't just to check/fold/bet/raise with KK. Your strategy tells you what you are going to do with KK and what you are going to do with A3s, 78o, etc etc for all possible hands.

I understand this, but it doesn't really address the issue people have with you saying

Quote:

if you are playing the strategy from a nash equilibrium, then your opponent is indifferent between their actions.

BobbiWings · 07-19-2012, 06:51 AM

Haha thats funny!

Bobito · 07-19-2012, 06:59 AM

Quote:

Originally Posted by ArBar

Well since I know game theory, and I know how to play NLHE. I would say I know how to apply game theory to NLHE.

The logical fallacy committed is sufficiently serious to make me question everything you write.

therightdeal · 07-19-2012, 10:29 AM

What is the easiest way to learn game theory and apply it to poker?

Zanardi · 07-19-2012, 11:04 AM

Q: I don't know anything about game theory. I am a complete beginner. I want to learn. What books should I begin studying?

Jerrod Ankenman · 07-19-2012, 02:49 PM

This thread makes me want to do "ask me anything about game theory."

Paul Valente · 07-19-2012, 03:20 PM

Quote:

Originally Posted by Jerrod Ankenman

This thread makes me want to do "ask me anything about game theory."

Please, please, please!

yaqh · 07-19-2012, 03:30 PM

Yea, I think you should do it

mperich · 07-19-2012, 03:32 PM

Quote:

Originally Posted by Paul Valente

Please, please, please!

Massive +1