simple game theory question

[PhlegmWad]

wow that's a good question - Im not sure that it's possible to define that ... my best guess is that it's between 1 and 4!

[jay_shark]

This is not a simple game theory question at all .
I don't even think any of the Putnam contestants can solve this problem in the alloted time .

This type of problem is already challenging when we restrict the game without any raises .

[Paxinor]

D&L is correct...

in game theory with no more cards to come there are basicly just pure bluffs and valuebets.

you will pick your worst cards to bluff at the pot and check behind medium strength hands...

basicly if the definition of pure bluff is that no worse card will call you then there is never a cap because you will always be bluffing at least a small portion.

if you define "pure bluff" to a special hand strengh meaning no pair or whatever the question is not really answerable because it depends on the flop and the action before...

[Yepitis]

Once you are reraised in a limit game why would you take it any further with no chance of winning?
If he has called and raised a couple of times why would he ever fold instead of just calling?
Unless you are saying he is on a bluff also and you both believe this and are both just trying to get each other to fold so you don't have to split the pot since neither of you can beat the broad.
I play low limit so I would never raise on the river and fold to one more bet no matter what I had. I would just use that fact I couldn't beat his 4 high as table image...heh.

[jstill]

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

shoot some examples Id say, itd probably be a more productive discussion

3 bet bluffing the river is somethin i rarely rarely do and probably never in HU where no one raise folds the river and everyone raise calls (depends I guess) 4betting the river on a bluff is not somethin ive ever done

the example theoretically has come up before of huge pot both players know eadh has nothing... the answer comes back if both are good they will call with the range of K Q hi hands instead of bluff reraising so going off for tons of bets in this scenarios would be sub optimal by both players

[SNOWBALL]

[ QUOTE ]

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

[/ QUOTE ]

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

[_D&L_]

[ QUOTE ]
Once you are reraised in a limit game why would you take it any further with no chance of winning? If he has called and raised a couple of times why would he ever fold instead of just calling?


[/ QUOTE ]

You are correct that most every human player would have entered "call down" mode at this point. But from the point of game theory, call down mode is not an optimal strategy. It acts as an overdeterrent to bluffing, and at the same time pays off big hands.

Game theory is about how you would play against an opponent playing the optimal strategy. Thus, u are correct, u wouldn't use these ideas versus a human.

A game-theory optimal player is balancing at least two considerations here. Minmaxing the EV of his opponent hands that beat him, and Minmaxing the EV of his opponents bluff hands. The more he folds, the less EV he gives to hands that beat him, and the more he calls/re-raises, the less EV he gives to bluffs.

An optimal player who is not holding the nuts would not enter call down or no-fold mode. He would always fold his hand some percentage of the time. He doesn't need to call with his hand 100% of the time to deter bluffing.

In fact, he can even make bluffing the prefered choice for a few of our really trashy hands (hands with virtually no call value), and at the same time deter us from bluffing with moderate hands (hands that get higher EV from calling, than bluffing).

Thus, against an optimal player we do continue to bluff some percentage of the time (in some cases, near zero), but never quite zero percent of the time.

Against a human player, this strategy of always coupling value bets with bluffs may not be needed on big pots. But it wouldn't keep us from stealing the human players money, we would just be less efficient at it.

Think of it as trading mistakes - we bluff at a person who always calls, but we have more value hands than bluff hands, thus his mistake is bigger than ours.

----_Dirty&Litigious_----

[jogsxyz]

[ QUOTE ]


Game theory is about how you would play against an opponent playing the optimal strategy. Thus, u are correct, u wouldn't use these ideas versus a human.


[/ QUOTE ]

If that statement were correct, you wouldn't be able to use game theory against a player who didn't know how to play.

[_D&L_]

[ QUOTE ]
[ QUOTE ]


Game theory is about how you would play against an opponent playing the optimal strategy. Thus, u are correct, u wouldn't use these ideas versus a human.


[/ QUOTE ]

If that statement were correct, you wouldn't be able to use game theory against a player who didn't know how to play.

[/ QUOTE ]

Yes and no. If your opponent doesn't now how to play chess, you can use the three-move checkmate to beat him. But that doesn't say anything about Kasparov's strategy other than a more efficient strategy might exist for this opponent.

A player that doesn't know how to play will do worse than a player using an optimal counter-strategy. So we still win versus bad player using game theory.

----_Dirty&Litigious_----

[jogsxyz]

[ QUOTE ]


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


[/ QUOTE ]

This is the garbage they teach in school.

If opponents were able to play anywhere near optimal strategy, this game is unbeatable. The rake is outrageously high.
Game theory is also about using best exploitive strategy against bad opponents. These bad opponents are oblivious to your strategy and will fail to exploit you.

Chess is a deterministic game. You don't need game theory for chess. In chess a good move against a good player is a good move against a weak player. You can't make this same statement in poker. In exactly the same situation it may be correct to call player A, fold to player B, and randomize against player C.