Balancing Bluffs vs Balancing Strategy

[jogsxyz]

[ QUOTE ]
It's not only likely, it's proven. (von Neumann and Morganstern, and then Nash proved the existence of equilibria in games with more than two players). I don't really understand your comments about "different games" - the turn and the river are part of "in every sequence" from my comments above. To specify a strategy for the game, you must specify an action in every possible sequence, from preflop through all possible flops, turns, and rivers, and all betting sequences with nonzero realization weight (ie, any sequences you allow to happen.)

jerrod

[/ QUOTE ]

In hold'em the relative pot equity of the two players change with every street. Does the proof includes games with a randomizing mechanism that changes relative pot equity?

Isn't changing the relative pot equity the same as changing the rules of the games? Thus a new game.

[leaponthis]

[ QUOTE ]
Isn't changing the relative pot equity the same as changing the rules of the games? Thus a new game.

[/ QUOTE ]

No. The game doesn't change. It is the situation that you find yourself in that you base your strategy on. So to be optimal the stragety must consider all possibilities for each situation (street). It is not the individual hand that gets modeled in total, it is the individual situation (preflop, flop, turn and river) of each hand that is modeled.

leaponthis

[Jerrod Ankenman]

[ QUOTE ]
Jerrod, Jared...this is getting confusing... [img]/images/graemlins/smile.gif[/img]

Anyways, this is about Jerrod's example of betting the turn with the "correct mix" of hands. I know how many pair-combinations I play in certain positions and I can ballance it by adding as many other combinations like 2-suited-card or offsuit-cards with max-stretch. Unfortunately I have no idea how often those 4-card draws and those made hand monsters come up on the turn, so all that knowledge doesn't help. If I bet everything just as it shows up, I am almost certain to have an incorrect mix.

It would have been nice to see some stats tables in the book and maybe one of example of how the ballancing is done, but that's of course missing....too bad I am not Brian Alspach.

[/ QUOTE ]

Well yeah, if we knew how to find "the correct mix" then we could easily find the optimal strategy. So we guess in an informed way, with an eye to making our distribution reasonable no matter what cards come on later streets. This isn't hard in holdem because you can easily mix together draws and made hands in all sequences. It's not so easy in stud, where if your board is 952 rainbow you just can't have much of a drawing hand. i don't know what the answer there is; mostly I just try to play a lot of hands in the same way so that I'm not very readable.

jerrod

[Andrew Prock]

Just to clarify, the zero sum result only holds if mixed strategies are allowed. e.g. there is no pure equibrium strategy for the game matrix:

31
24

But as Jerrod mentioned earlier, the mixed aspects of the strategies tend to be at boundaries. So if you have a mixed strategy for KTo, you're probably going to have a pure strategy for KJo and K9o.

- Andrew

[SA125]

Do you recommend reading it? I don't have ranges for it but, if you ask for some limits, 20-40 thru 50-100?

[seemorenuts]

"When is the point at which we stop playing the hand differently and start playing it Sklansky-optimally?"



When you but hopefully not your opponents know that the current hand is the last you'll ever play. [img]/images/graemlins/laugh.gif[/img]

[bbbushu]

Authors,

i've got the book and have been reading it over (i'm thankful for the first chapter btw, i am taking full advantage of the refresher micro-course...) but i predict a fairly major issue with it that maybe this thread can help me flesh out.

while the book is loaded with somewhat intimidating-looking math, i believe i'm fully capable of processing the information and understanding the concepts but i think i'll have some trouble with the application to actual play. i play limit hold 'em (almost exclusively shorthanded and HU, if that matters) so i'm assuming whatever applications you guys make in the NLHE case study will be only partially useful for me. i understand this might be addressed in the book and if you feel i'll figure it out simply by reading the rest of the book, feel free to say so. i understand that the book is NOT a "formula" for winning hold 'em, etc. but i might struggle applying the ideas, themselves, to the play of hands.

another question that may be answered later in the book: does a player hafta choose between optimal and exploitive strategies while playing? can they be used to compliment each other or are they mutually excusive (and possible counterproductive when combined)?

thank you for starting this thread, it has already helped me out.

bbbushu

p.s. leaponthis, please don't reply to my question.

[Alan3]

If you are playing an optimal game without taking into account how your opponent is playing then you are playing an equilibrium stategy and breaking even before the rake. Playing at equilibrium means you force your opponents to break even no matter what action they take (unless they make mistakes by making dominated decisions -- like calling a bet on the river with the nut low). Playing optimally does not offer your opponents the opportunity to make mistakes (except for dominated decisions which are always availble no matter how you play). In order to offer your opponents the opportunity to make mistakes, you must deviate from the balancing point of optimal equilibrium -- you must tilt. To do so profitable requires that you tilt in a direction that exploits the direction in which your opponent is tilting, but in doing so you open yourself up for exploitation by another player.

This is all just theory for me though. No one really knows what an equilibrium strategy looks like in most forms of poker (two-player Kuhn poker is one form in which we do know what equilibrium looks like). But I suspect that most of the top players, Sklansky included, have a good internal approximation of equilibrium and can recognize when people deviate from it, and how to expoit those deviations.

[Alan3]

Brandi,

I've had some experience with always being called down to the river in micro limit games. Two bits of advice that have worked for me:
- Play the odds: Do not feel you have to win every hand. TPTK wins a lot of the time. If you occassionally get sucked out on by two pair then so be it.
- Jam early, jam often: Focus on getting all of your chips in while you are ahead. If they are folding only when they are behind when you jam then reduce the bet and figure out how much they will call when they are behind.

This will increase your variance so make sure your bankroll can absorb some large hits. Also, since they are calling everything all the time, they should be giving you excellent implied odds to play more hands.

But then I've never played at the stakes you described so there is a good chance I do not know what I am talking about.

[D.L.M.]

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"