Balancing Bluffs vs Balancing Strategy

[jjacky]

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The only thing that really needs to be randomized are hands that require mixed strategies, and there are quite likely to be very few of those.

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do you think this statement is also true preflop?

i imagine, that the number of holdings that require mixed strategy on the current street decreases more and more (that is beacause the information revealed by ones own actions gets less and less important). what do you think about that?

[bbbushu]

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One obvious example of this is the "arms race" on the turn in high limit LH games online. What developed there was a tendency after the sequence rc; kbrc; b? on two-flushed boards for people to semi-bluff raise liberally on the turn (including all flush draws, straight draws, and other weaker draws such as small pair+gutshot and the like).

The exploitive response to this that I observed was for original bettors to three-bet liberally, including hands as weak as middle pair in this sequence, because the number of semi-bluffs was just far too high compared to the number of value raises (as these players wouldn't adjust their value raise thresholds to balance). Against a properly balanced strategy, three-betting this liberally is a disaster. This also shows a clear example of why, contrary to some players' assertions, playing optimally or in a balanced manner isn't about equalizing all your opponent's actions -- just the ones that are on the borders.

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this is a terribly interesting post to me, but it generates a few questions:

a) how does the player in position decide what constitutes a proper balance between raising the player in the blinds' turn bet as a semi-bluff and for value?

b) how can we figure out which situations (or, i guess, sometimes hands) are at the "border"?

thanks,
bbbushu

[emerson]

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David,

It bothers me a little when you say "It might be better to play a hand differently almost every time from the way it should be played if it was the last hand of your life. For the sake of future hands. "

Game theoretically you should play the hand unpredictably if it's the last hand of your life as well. The reasoning has nothing to do with future hands.

Is this just an effective way of explaining game theory to people that you use because it's effective even though it isn't correct?

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That's only true if your opponent knows it is the last hand of your life. If you have been randomizing all along, and your opponent doesn't know this is the last hand you will ever play, why not just play optimally? Your past randomization was sufficient to make the assumptions upon which he will base his decisions less accurate. You have no need for the advertising value of the future.

[emerson]

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For two-player zero-sum games,

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Heads-up Holdem poker as spread online or in b&m casinos is not a zero-sum game. For it to be a zero-sum game both blinds would have to be equal. That is not how the game is played. In Casinos there is a small blind which is some increment below the big blind. This fact makes the game a non-zero sum game.

leaponthis

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I think he means zero sum on balance. You each play an equal number of small and big blinds. This is zero sum (ignoring the rake).

[emerson]

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Thanks for posting that link... I was reading the thread wondering what zero-sum was all about.

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It means the winnner's net + the loser's net is always equal to zero. There is no premium.

A tournmant where all entries are returned in the prizes is zero sum. If less than the full amount of entries is paid out it is negative.

[emerson]

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I strongly belive that in general you cant mix up you hand how you play it too much past the flop. so basically to deception purposes most of "mixing it up" is done preflop or on the flop, after that you should general make the play that is "correct" mathematically. however i believe that if you have two personalitys or two or more"styles" and you constantly randomize jekal and hyde then you have accomplished your game theory needs, becuase your opponent will never know if hes plays optimally against your mistakes. cause hes not sure whos hes playing Jekal or hyde. and maybe you can have happy medium between the two.I BELIEVE WE CALL THIS "CHANGING GEARS IN THE BIZ"

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And not the turn? You do not think that when acting first in a heads up pot, with a hand you believe to be the best, that you should sometimes check, and sometimes bet?