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 Micro Stakes Limit Discussions of micro stakes limit Texas Hold'em

07-08-2012, 08:02 PM   #31
grinder

Join Date: Jun 2004
Location: Avon, CT
Posts: 604
Re: Terminology

Quote:
 Originally Posted by bellatrix Yes, the presence of draws complicates things. I could go on, but I would refer you to Chapter 19-20 of Mathematics of Poker. And even there, they don't fully go into it, they just send you on their way, because multi street games are not that easy to evaluate. Even the static case (where the hand values don't change) is horrible, imo. While on the river it is very easy and the hand either beats you or it doesn't you can kind of look at things quite linearly. On earlier streets it is difficult, because a hand that was way down in the hand ranking side could suddenly jump up by the turn of one card. Anyway, the example is not to tell you how to play, it's just to define some terminology.
Yes, multistreet games are pretty hard to evaluate. But the principle still holds: suppose you have an optimal strategy pair (x*,y*) for a multistreet game. Then it is pretty obviously possible to find a family strategies X' such that the expectation of x in X' vs y* is less than the expectation of x* vs y*, but y* is the best response to x. Such a family of strategies would certainly fit into the spirit of "balanced."

"Balance" isn't really a rigorous concept; at least we didn't really try to make it so. It's just a shorthand way of expressing that there are different ways of failing to achieve the equilibrium game value: 1) Doing things your opponent can exploit. 2) Doing things that just sacrifice value no matter what your opponent does.

In real multistreet games, things like card-removal and the Fundamental Theorem of Chasing define the parameters inside which street-to-street balancing has to take place. This is a very hard problem and if I knew how to solve it, I wouldn't tell you.

07-08-2012, 08:22 PM   #32
Pooh-Bah

Join Date: Jan 2009
Location: Ohio
Posts: 3,852
Re: Terminology

Quote:
 Originally Posted by Aaron W. Exploitable strategy = A strategy for which there exists a counter-strategy that does strictly better other counter-strategies. Yes, you can work out an ideal strategy. But if EV[calling] = EV[folding], then all strategies (fixed, mixed) have the same result, and you can do nothing to exploit your opponent. His EV (and yours) are both fixed. However, if EV[calling] > EV[folding], you can exploit your opponent by calling. You increase your EV, thus reducing his, and therefore you can take advantage of his play.
It seems to me that in almost every case there exists an ideal counter-strategy. If by "strictly" you mean "substantially", then I guess I see what y'all mean.

Seems like it's very rare to have a spot where EV(calling) = EV(folding).

07-08-2012, 10:50 PM   #33
Carpal \'Tunnel

Join Date: Sep 2002
Location: Henderson, NV
Posts: 21,433
Re: Terminology

Quote:
 Originally Posted by Cranberry Tea It seems to me that in almost every case there exists an ideal counter-strategy.
Yes. But there could be many ideal counter-strategies. And all such counter-strategies might yield the same EV.

Quote:
 If by "strictly" you mean "substantially", then I guess I see what y'all mean.
Strictly means strictly. But we're talking about an idealized concept here. In reality, "substantially" works better.

Quote:
 Seems like it's very rare to have a spot where EV(calling) = EV(folding).
That's because it's rare to find a villain that is playing a perfect bluffing/value betting ratio.

It's also a one-street situation in which raising is not an option, so it's also a particularly specialized scenario that is being used as an example to illustrate the situation. In a multi-street GTO situation, it's more complex because you've got "luck" as a third player. (Luck chooses the card(s) to come.)

07-10-2012, 11:54 AM   #34

Join Date: May 2010
Location: Murmansk,Russia
Posts: 937
Re: Terminology

Quote:
 Originally Posted by Aaron W. Villain is trying to mix up his plays to keep hero confused to the point that hero doesn't really have any good decisions (good measured relative to his other decisions). [This is balance.]
he is folding 100%...what is he mixing up? folding and folding?
------------
about 100% c-bet...maybe not such exact example but close...

Let’s assume that instead of being a TAG, you are a loose and maniacal player. You will raise preflop with any two cards, and your opponents know that about you. And when checked to on the flop, you will bet every time. If you play this way, then your range on the flop is extremely unbalanced.

You might say to yourself, “Unbalanced? If a guy can have any two cards at any time, isn’t that balanced? You can never put him on a hand.” This would be true, except for one simple fact. Most hands miss the flop. When you’re up against someone who can have two random cards on any flop, the vast majority of the time, your opponent will have a hand that most players would consider to be weak–no pair or one small pair.

So if you were to put this player’s hands into one of three buckets–weak, medium, and strong–you’d have a lot hands in the weak bucket, some in the medium bucket, and a relatively small percentage of hands in the strong bucket.

Any range that is unbalanced in this way is guaranteed to be exploitable, and the exploit is simple. You bet or raise frequently against the range.
http://www.notedpokerauthority.com/a...-bet-fold.html

Quote:
 Originally Posted by Aaron W. Yes. Your opponent is playing in a way that you can't figure out what he has, and it's done so perfectly that no decision you make can earn you more than any other decision.
you know why? because according to his strategy (folding 100%) you win the maximum you can...you cant win more

Quote:
 Originally Posted by Xhad GTO does not mean "guarantees 0EV" http://forumserver.twoplustwo.com/25...olding-103112/
ty,sir...now i do have a headache

07-10-2012, 12:09 PM   #35
Carpal \'Tunnel

Join Date: Sep 2002
Location: Henderson, NV
Posts: 21,433
Re: Terminology

Quote:
 Originally Posted by perplexed76 he is folding 100%...what is he mixing up? folding and folding?
Ahhhh... I see where you may be confused. I used the word "mixing" as a general term to mean "deciding upon a strategy." In general, you're right that it won't end up being a strategy that only has one decision. It's just that these examples are the ones that are easiest to think about.

Quote:
 Let’s assume that instead of being a TAG, you are a loose and maniacal player. You will raise preflop with any two cards, and your opponents know that about you. And when checked to on the flop, you will bet every time. If you play this way, then your range on the flop is extremely unbalanced.
You're taking the one-street analysis and pushing into a two-street game. That's problematic for the discussion. Trying to get "balance" in a multi-street game is very difficult in theory and in practice. As noted before, it's because the "third player" (luck -- the guy who picks the cards) is now in the game, and so "balance" must take into account his actions as well.

So pull back to the one-street game and think about it. If villain raises 100% of the time preflop, his range is perfectly balanaced. If he only raises blacks aces and 7 2, he's perfectly balanced*.

* This isn't quite true because his equity isn't 100% when he has AA and his equity isn't 0% when he has 72o. And this analogy doesn't take into account the calculation of equity based on pot size and whatnot.

But if you take the situation where he raises only two hands, he probably won't be balanced on the flop. If you have 55 (a hand in between AA and 72) and the flop is J74, you know you're 100% behind. But if the flop is J64, you know you're 50% ahead. This is because "luck" has made his move. This changes everything. If you want to think about "balance" in this game with respect to preflop play, you've got to take into account not just balancing the two cards, but balancing the different flops that can come out. (You probably will not be balanced on every flop. But that's not the goal. You want to have some sort of "overall" balance. And it will probably be a probabilistic strategy.)

(The c-betting example is specifically about exploiting villain's BET-FOLD. The FOLD part is what makes villain's range/strategy unbalanced, and the thing that you're trying to exploit.)

Last edited by Aaron W.; 07-10-2012 at 12:15 PM.

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