simple game theory question

[nickabourisk]

The main author Martin Zinkevich (who came up with the new method) has since moved to work for Yahoo so unfortunately, he's not here anymore. The others, however, are all still here (although the Godfather and creator of the group, Darse Billings, is about to move to work for Full Tilt Poker). I attend their weekly Poker Group meetings.

Regarding the second question, on the next paragraph, he mentions exactly what you are talking about (what he meant by four betting rounds was that on each street, there is also betting, as some research previously has omitted one round of betting due to computational resource constraints):

[ QUOTE ]
Early poker abstractions [2, 4] involved limiting
the possible sequences of bets, e.g., only allowing three bets per round, or replacing all first-round
decisions with a fixed policy. More recently, abstractions involving full four round games with the
full four bets per round have proven to be a significant improvement [7, 6]. We also will keep the
full game’s betting structure and focus abstraction on the dealt cards.

[/ QUOTE ]

[Paxinor]

@ nickaboutrisk:

i just briefly looked over the paper but what is really new about and superior about that solution?

is it correct that you trade memory that a LP Solution needs with CPU power, but you won't reach a really optimal state because it is just an approximation (of the optimum of the approximated game)?

there might be the advantage that you calculate a sequential nash equilibrium that you won't always get if you use the Koller algorithm but i don't know (just flew through the pages of your paper) but there is a paper somewhere how to correct that...

anyways it doesn't perform really better than the Koller algorithm so therefore its not really a progress?

[jogsxyz]

[ QUOTE ]
the discussion about the maximal strategy is at least as theoretical and unpractical as talking about the optimal strategy


[/ QUOTE ]

Not really. The OP's question is about a controlled environment. Only one street and static relative equities.
These solutions are known and solvable.

With less than 10bbs in NL the jam or fold charts are solutions to the headup game. The key is to reduce the complexity of the problem.

[Paxinor]

yeah i got that allready

i am just saying that if people mention that equilibriums have no practical sence in "real poker" and mention the concept of the maximal strategy they are also wrong because in todays poker its more about "keep the edge, don't let the villain adjust" and not about max strategies meaning exploiting his as hard as you can

i know that there are solutions for lots of pokerlike games and tourneysituations

and i know that its the key to abstract the game in lossless way to compute the nash equilibrium and i know that all that wasn't OPs question which has allready been answered and relies heavily on the definition of "pure bluff".

anyway i really think that all academic work so far has not focused enough about those abstractions because todays game theory solving is mostly done by computer scientists and not by economists and in computer sience its more about the algorithm than the acutal solving of the game so there has to be put in some serious research about correct abstraction since those Linear Programming Stuff is kinda shooting birds with cannons without abstractions..

all those guys trying to solve the game have different motivations than "solving the game"

basicly since koller's paper about the sequential form of games in 1995 there hasn't been a major breakthrough even though computers have evolved massivly.

[jogsxyz]

[ QUOTE ]
yeah i got that allready

i am just saying that if people mention that equilibriums have no practical sence in "real poker" and mention the concept of the maximal strategy they are also wrong because in todays poker its more about "keep the edge, don't let the villain adjust" and not about max strategies meaning exploiting his as hard as you can

[/ QUOTE ]

Any true student of the game should learn nash equilibriums for one street games. But that doesn't mean he should follow them religiously. When opponents deviate even only slightly from optimal, often but not always, students would do better by using best exploitive strategy.

[ QUOTE ]

anyway i really think that all academic work so far has not focused enough about those abstractions because todays game theory solving is mostly done by computer scientists and not by economists and in computer sience its more about the algorithm than the acutal solving of the game so there has to be put in some serious research about correct abstraction since those Linear Programming Stuff is kinda shooting birds with cannons without abstractions..

all those guys trying to solve the game have different motivations than "solving the game"

basicly since koller's paper about the sequential form of games in 1995 there hasn't been a major breakthrough even though computers have evolved massivly.

[/ QUOTE ]

Those are just the wrong authors. RGP has threads by poker players. Ferguson, both Chris and his brother Tom, Weideman, Chen, Ankenman all contribute about the micro aspects of the game.
Still waiting for a paper on the two street, dynamic game. Don't think anyone has solved it yet.

[Paxinor]

first: i of course know you should adjust to an opponent to exploit him if he plays weak. this has been said OVER AND OVER by various posters including me. i am just saying that its highly inpracitcal to exploit him maximaly because max strategies usually are very extreme (the example where preflop 3bet with every hand made earlier) and the opponent will adjust so its more about "keeping the edge without the opponent adjusting" as i said before. so exploit him, but not as hard as you can...

and no these are not the wrong autors...

the papers of ferguson, weidman chen und ankenman are very very basic models

there are forms of pokers that are already solved (2 streets and more). you are really behind, the group the guy has postet a paper from are far further, there is also gilpin and sandholm who have solved a form of poker called "rhode island poker" which is a simple hold'em

basicly if you want to solve big games you need that koller algorithm, and you'd have to solve it with linear programming

ferguson and the others haven't really developed something new, these [0,1] models are known since 1944 and they are even solvable by hand.

sience is really WAY AHEAD of this.

there are multiple solutions of pretty big dynamic games

[jogsxyz]

http://www.cs.cmu.edu/~sandholm/RIHo...roceedings.pdf

This paper only gives an overview for solving RI holdem.
There's no micro details.

Ferguson explains the painful step-by-step process.

-----------------

On this exploiting thing on the final bet the call/fold
decision is completely extreme exploitive. If the
bettor overbluffs even slightly, you should call
100% of the time(assumes you actually hold a hand
that can beat a bluff). If the bettor underbluffs,
you should fold 100%.
It's only best to use optimal strategy(mixing calling
and folding) against an unknown opponent or a very
strong opponent capable of mixing his strategy.

[jogsxyz]

[ QUOTE ]
http://www.cs.cmu.edu/~sandholm/RIHo...roceedings.pdf

This paper only gives an overview for solving RI holdem.
There's no micro details.

Ferguson explains the painstaking step-by-step process.

-----------------

On this exploiting thing on the final bet the call/fold
decision is completely extreme exploitive. If the
bettor overbluffs even slightly, you should call
100% of the time(assumes you actually hold a hand
that can beat a bluff). If the bettor underbluffs,
you should fold 100%.
It's only best to use optimal strategy(mixing calling
and folding) against an unknown opponent or a very
strong opponent capable of mixing his strategy.

[/ QUOTE ]

[Paxinor]

there is other exploiting than just calling a bluff on the river which happen every 50 hands...

there is also often exploitable spots in preflop play or flop play (fold to often) that makes it the maximal strategy to raise 100% of your hands. you dont want to do that because your opponent will adjust very fast...

@ gilpin and sandholm papers: go to gilpins homepage, there are 3 papers with technical reports and proofs and everything, you can even play the optimal solution.

[admiralfluff]

Haven't read all the responses, but I don't see how there could be a theoretical cap. If there were, than the last bet made would be exploitable.