Help me better understand Game Theory

[LockLow34]

This is a theoretical hand:

Assume MP is an unknown player

Hero is UTG with
A[img]/images/graemlins/spade.gif[/img]K[img]/images/graemlins/spade.gif[/img]

Preflop:
UTG calls, MP raises, BB calls, UTG raises, MP calls BB calls

(Pot 4.5 bets)
Flop:
J[img]/images/graemlins/spade.gif[/img] 8[img]/images/graemlins/heart.gif[/img] 4[img]/images/graemlins/spade.gif[/img]

BB checks, UTG bets, MP raises, BB calls, UTG raises, MP raises, BB folds, UTG calls

(Pot 9.5 bets)
Turn:
7[img]/images/graemlins/heart.gif[/img]

UTG checks, MP bets, UTG calls

(Pot 11.5 bets)

question:
With what frequency should one bluff on the river to make calling or folding neutral EV for MP?

[Rozez]

Is it 8 percent of the time?(100/12.5BB) I' m not sure [img]/images/graemlins/confused.gif[/img] Please reply.

[Jerrod Ankenman]

[ QUOTE ]
This is a theoretical hand:

Assume MP is an unknown player

Hero is UTG with
A[img]/images/graemlins/spade.gif[/img]K[img]/images/graemlins/spade.gif[/img]

Preflop:
UTG calls, MP raises, BB calls, UTG raises, MP calls BB calls

(Pot 4.5 bets)
Flop:
J[img]/images/graemlins/spade.gif[/img] 8[img]/images/graemlins/heart.gif[/img] 4[img]/images/graemlins/spade.gif[/img]

BB checks, UTG bets, MP raises, BB calls, UTG raises, MP raises, BB folds, UTG calls

(Pot 9.5 bets)
Turn:
7[img]/images/graemlins/heart.gif[/img]

UTG checks, MP bets, UTG calls

(Pot 11.5 bets)

question:
With what frequency should one bluff on the river to make calling or folding neutral EV for MP?

[/ QUOTE ]

Ok so first of all there isn't an easily derivable "game theoretic" answer for this question.

1) It's a multiplayer game and therefore is subject to collusive equilibria.
2) Even though it becomes headsup later in the hand, the previous action heavily impacts any analysis of how the hand should go.
3) Any question about how often you should bluff doesn't pertain to a specific hand, but to a distribution. Game theory isn't about playing mixed strategies with every hand on every street.

You didn't supply a river card, which of course is of prime importance in determining the action on the river. As the hand has played out, it seems that even if you tried to approximate some type of pseudo-optimalish strategy, the MP guy would never fold a hand better than AsKs, so you should never bluff the river with this hand.

Jerrod

[Rozez]

[ QUOTE ]


You didn't supply a river card, which of course is of prime importance in determining the action on the river. As the hand has played out, it seems that even if you tried to approximate some type of pseudo-optimalish strategy, the MP guy would never fold a hand better than AsKs, so you should never bluff the river with this hand.

Jerrod

[/ QUOTE ]

OK, if we think about it this way, I would be alerted on the flop because MP has shown much strength so far. Given his preflop play, he could have a hand like a set of jacks which would mean trouble for the hero's flush draw.
I know it doesn't make a lot of sense oversimplifying this example so much but I'm a newbie so I'm gonna ask anyway. What if MP could possibly fold for a single bet?(Obviously he won't but you get the idea) What would be the optimal bluffing frequency in that case? This topic interests me.

[Jerrod Ankenman]

[ QUOTE ]
[ QUOTE ]


You didn't supply a river card, which of course is of prime importance in determining the action on the river. As the hand has played out, it seems that even if you tried to approximate some type of pseudo-optimalish strategy, the MP guy would never fold a hand better than AsKs, so you should never bluff the river with this hand.

Jerrod

[/ QUOTE ]

OK, if we think about it this way, I would be alerted on the flop because MP has shown much strength so far. Given his preflop play, he could have a hand like a set of jacks which would mean trouble for the hero's flush draw.
I know it doesn't make a lot of sense oversimplifying this example so much but I'm a newbie so I'm gonna ask anyway. What if MP could possibly fold for a single bet?(Obviously he won't but you get the idea) What would be the optimal bluffing frequency in that case? This topic interests me.

[/ QUOTE ]

I think you miss the point. Normally no hands, or just one specific hand, in the distribution of hands have a bluffing frequency. All the rest are played with pure strategies (either check all the time or bet all the time). You have a bluffing frequency with ALL your hands which determines how many hands are checked and how many are bet. But to determine that you need to know the overall solution to the game as well as what the river card is.

Jerrod Ankenman

[Rozez]

Are you saying that "What is the optimal bluffing frequency" is actually the wrong question because a bluff in this situation has no chances of being successful? It seems to me that this hand could have some bluffing potential if you're up against a player who thinks it's right to fold on the river when you "know you're beaten". There is a small possibility that this could work, if the river is a scare card like a nine or a ten. Of course, this is quite far-fetched since you'd have to be against a type of non-observant opponent who doesn't have a clue about pot odds and who is always scared about everything.

I would just like to hear some basics about game theory and how it relates to bluffing.
Rozez

[EvilDrSluggo]

[ QUOTE ]

I would just like to hear some basics about game theory and how it relates to bluffing.
Rozez

[/ QUOTE ]

http://www.amazon.com/exec/obidos/tg...ce&s=books

pp. 186-219

[Rozez]

Thanks for the tip! [img]/images/graemlins/smile.gif[/img]
Rozez

[Rozez]

Now, after some reflection, I finally realized that my thoughts are quite controversial. I got lost in my last post when I started to babble something about knowing your opponent. Isn't game theory supposed to be used in situations where you either don't know your opponent or he is much better than you are?
I think I'm following you now Jerrod. Or am I?
Rozez [img]/images/graemlins/ooo.gif[/img]

[MaxPower]

You need to make the odds against you bluffing the same as the odds that he is getting from the pot.

So if he is getting 12:1 (to simplify) and there are 9 cards that make your flush (assuming an ace or king is not an out), you would need to chose .75 cards to bluff with. Since this is impossible, I suppose you could choose one card to bluff with and then flip two coins. If they both come up heads check, otherwise bluff.

Also this wouldn't be neutral EV for your opponent, it would be negative EV. Its just that his EV would be the same no matter what he does.

That is theoretical. In reality in a hand like this, your bluff will almost never work unless your opponent is on a draw (which he isn't). There would be no need to use a game theory approach when you have a good idea of what your opponent has.