simple game theory question

[SNOWBALL]

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depends on the player... some players some boards going 5 bets would be -EV other players or boards not so

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this is a game theory question, so I am assuming no opponent modelling, which is to say we are playing unexploitably/optimally b/c we assume opponent is doing the same

[jogsxyz]

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Playing heads up limit hold em - how many bets max can it be optimal to go without the nuts on the river?

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There's no one size fits all answer. It depends on the board on the river.
---
You: KsQs
Board: QdJs8s, 4c, 2s

You would be willing to maybe put in the 2nd or 3rd raise.
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You: AhKs
Board: KdJs8s, 4s, 2s

Doubt that this hand is worth any raises.
---
You: AhJs
Board: QsJdJc, 4d, Qh

Opponent bets into you after being passive. This
is a crying call.

[jogsxyz]

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A. Game theory is about how you would play against an opponent playing the optimal strategy. ....

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B. Game theory is a branch of applied mathematics that is often used in the context of economics. It studies strategic interactions between agents. In strategic games, agents choose strategies which will maximize their return, given the strategies the other agents choose.

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Quote A and quote B are not the same. Quote A is wrong.
Game theory is finding strategies to maximize returns, not restricted to finding NE. Often the best strategy is NE, but not always.

[Paxinor]

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

everybody talks about "blabla max strategy blabla equilibrium against donkey no good bla"

but often the strategy which is max exploiting is usually very extreme and players adjust to it the next couple hands.

(folding to 3bets more than you should and therefore making it plus ev to 3bet alone so you should raise every hand)

because you will play more than one hand against an opponent he is able to change strategies that go against your favor. this strategy is hidden and therefore it bears threat...

thats why in pracitce keeping "the match under control" is important, therfore not exploiting every single mistake...

this is somewhat like the optimal play.

of course no one has calculated a sequential nash equilibrium... but in theory there exist one and that is a pretty important thing to know how the game really works...

[nickabourisk]

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You haven't a clue what's Nash equilibrium for hold'em. No one knows it.

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This is something that can be solved by computational game theory (at least within some epsilon). However, computational resources are not at the stage yet in which the game of heads-up limit hold'em can be solved (a game with about 10^18 states). However, the most recent work in this area has solved an abstraction of the game with 10^12 states and then uses the solutions from that game as approximate solutions to the full-scale game.

Regret Minimization in Games with Incomplete Information

Check out the work done by the University of Alberta Computer Poker Research Group. I just started my Master's there in Computer Science. Their most recent pseudo-optimal heads-up bots are playable at Poker Academy and recently competed against Phil Laak and Ali Eslami in a Man-Machine competition.

[jogsxyz]

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Regret Minimization in Games with Incomplete Information


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Do you know these profs?

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four rounds of cards being dealt, and four rounds of betting,

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Poker players usually say four streets of cards being dealt with three raises each street.

[jogsxyz]

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Playing heads up limit hold em - how many bets max can it be optimal to go without the nuts on the river?

Same game - How many bets max can it be correct to go with a pure bluff on the river?

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the first player bets.

The second player's action vector looks like this.

|______________call_______________|________fold___ ___|

When should the second player raise?

|_____raise___|_____call___________|___fold_______ __|br|

This pure bluff raise looks spectacular when it works.
But the math says never bluff raise from the fold area.

|____raise____|____call_________|br|________fold__ _____|

The bluff raise from the tail end of the call area does
better.

If that's what you meant by pure bluff, never pure bluff.

[_D&L_]

[ QUOTE ]

This pure bluff raise looks spectacular when it works.
But the math says never bluff raise from the fold area.

|____raise____|____call_________|br|________fold__ _____|

The bluff raise from the tail end of the call area does
better.

If that's what you meant by pure bluff, never pure bluff.


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jogsxyz, Snowball is asking a gametheory question. All of your advice categorically runs contra to gametheory. You don't bluff a hand that gets +EV from calling on the river.

In gametheory, on the river, u only bluff raise from the "fold area" - or more precisely, hands that do not show a call value greater than zero - no where else. The math says that...and its completely contra to your advice.

----_Dirty&Litigious_----

[_D&L_]

Hi nick,

Will you be focusing on poker-related research while earning your degree? Working with the poker research group in Alberta?

If you are...i got a problem or two i could use some input on [img]/images/graemlins/smile.gif[/img]

----_Dirty&Litigious_----

[jogsxyz]

[ QUOTE ]
[ QUOTE ]

This pure bluff raise looks spectacular when it works.
But the math says never bluff raise from the fold area.

|____raise____|____call_________|br|________fold__ _____|

The bluff raise from the tail end of the call area does
better.

If that's what you meant by pure bluff, never pure bluff.


[/ QUOTE ]


jogsxyz, Snowball is asking a gametheory question. All of your advice categorically runs contra to gametheory. You don't bluff a hand that gets +EV from calling on the river.

In gametheory, on the river, u only bluff raise from the "fold area" - or more precisely, hands that do not show a call value greater than zero - no where else. The math says that...and its completely contra to your advice.

----_Dirty&Litigious_----

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Just do the math. Bluffing from the call region is higher EV than calling from the fold region.