grrrr... i'm going to have to start writing shorter posts because I just look like a tag along when you make my point right before me. Or at least, I'm going to have to hit refresh and see if you beat me to the punch before I post.

I also want to thank you for taking such an interest in the thread.

Trying to play more balanced has really transformed my game. I've had so much success in my game when I worked on shoring up some of these places I was being exploited. I think more people should work on it. You hear the constant drone of "don't worry about balance, don't worry about balance, don't worry about balance." It's just nonsense. Thanks for writing this thread. I wanted to do it, but I didn't think I could do the topic justice.

You very well are probably right.

Like I said, I was just quoting something I read somewhere. I usually don't make statements about things that I don't understand myself. But we were making lists of assumptions that we make when we talk about finding balanced strategies in poker, and I thought that was one I read.

I've never studied any of this stuff outside what I've done on my own really... like I never took a class. So the only thing I know about game theory is how it relates to poker.

I know you've mentioned stuff in other threads before about this topic, so please feel free to point out any other mistakes I might make.

I agree. There are very few players who don't make an attempt to steal blinds. You're just losing so much money in not at least making an attempt to protect your blinds. They add up over time.

And they aren't thinking, "I am exploiting this player's tendency to fold too much to blind steals" but if you fold too much, you're being exploited. Same thing on the flop. The villain isn't thinking, "the other guy who called my raise will fold way too much so I can exploit him by betting ATC." He's thinking, "I haz initiative, I cbet" But if you fold too much, it comes out to the same. Steals and cbets are the most common forms of exploitation.

Look, if you raise UTG and a reg from MP2 3bets you, then fold really, really wide. Villain isn't trying to exploit you. He's probably got a really freaking strong hand. But people steal and cbet so light that you have to fight back.

Yeah, I agree. It's not so much that I want to play balance, it's that I was on the wrong end of the exploitation in too many places. And it wasn't so much that the Villain was making a conscious effort to exploit me, they were just playing there normal game and by studying this stuff that I could make easy adjustment to exploit them.

I agree. There's no reason why we can't 3-bet for pretty wide value from the blinds. When a Villain is opening up a ton and assuming that we can play pretty well post flop, there's no reason not to go for some thin value from the blinds.

I'll probably write something on blind play some time. I think there's quite a bit of interesting spots.

And think about how HU players defend their blinds agains a Button open of 85%. If we're facing a Button who opens 85%, then we should be playing a similar Blind defense from the BB. Or at least exploiting him for opening so wide.

I totally agree. I think the most money to be made at micro limits exploiting other players tendencies is to open the Button a ton and c-bet a lot because a lot of players fold in both places too much.

I totally agree this is a spot where you're just not ever getting exploited. People aren't 3-betting UTG raises too light because they're trying to out level you. Just doesn't happen at the micros.

Hhhhmmmmm... not really right. But I'm not the kind to laugh either.

Now when the Button bets, he's going to be betting a very small range of his hands, but he's also going to be perfectly balanced with bluffs. So let's try and take what we learned from the other example.

Our goal with calling is to keep the Villain from being able to bluff too much. In other words, we want him to be indifferent to betting his bluffs -- i.e.. his Bluffs should have EV of 0.

Now what % of hands does the BB need to call with, so the Button has an EV of 0 with his bluffs.

So let's go back to the EV of Hero's Bluffs:

So as you can see, the BB needed to call 50% of the time in order for the Button's EV of bluffing to be 0.

So what does that mean here -- when he's betting a smaller range of hands? It means the same thing! The BB still needs to call with 50% of his hands. It was a bit of a trick question. Now just because the Button was betting a smaller range of hands, didn't mean that he was suddenly unbalanced with way too much value in his betting range to his bluff range. Look we can confirm this.

Ratio of Bluffs to Value hands in scenario 1:
50 Value to 25 Bluffs = Ratio of 2 to 1 value to bluffs.

Ratio of Bluffs to value hands in scenario 2:
10 Value to 5 Bluffs = 2 to 1 value to bluffs.

Let's confirm the Buttons EV when we still call 50%:
Button Bets a Bluff, BB calls, Button loses = .05 * .5 * -10 = -.25
Button Bets a Bluff, SB folds, Button wins = .05 * .5 * 10 = .25
EV of Button Bluff = .25 - .25 = 0

So nothing actually changes in terms of BBs strategy because the Button is still playing a balanced strategy, just not an OPTIMALLY BALANCED STRATEGY. (Which I'm kind of regretting not making the distinction in the original post). So the Button is just not betting all of his nutted hands-- he's checking a bunch back, so he's losing money by not getting as much value from his nut hands.

Let's try and guess what the EV will be in this scenario with this new info. So in Scenario 1, the BBs EV was equal to the percentage of total hands the Button checked back which were bluffs. It's my guess that it's going to be the same here. So the Button is checking back 45% of total hands which are bluffs.

So we're going to guess that the BBs EV is going to be:

Guesstimate BBs EV = .45 * 10 = 4.5 bb

Let's see if we're right.
BBs EV of Calling:
Button Bets for Value, BB calls, Button wins = .1 * .5 * -10 = -.5
Button Bets as a Bluff, BB calls, Button wins = .5
------------------------------
Buttons EV of Calling = 0 (Just like in scenario 1, since the Button is still balanced between value and bluff hands, the BB is indifferent to calling)

BB EV when Button checks Back:
Button Checks back Nuts, BB loses = .4 * 0 = 0
Buttton Checks back Air, BB wins = .45 * 10 = 4.5

BBs TOTAL EV:
BBs EV of calling = 0
BBs EV of Folding = 0
BBs EV when Button Checks = 4.5
----------------------------
BBs Total EV = 4.5

Yeah, we were right!

Can we guesstimate, the Button's EV then without doing an EV calculation. Sure. We know that poker is a zero sum game, so we know that the two players EV needs to add up to the pot before betting.

Buttons EV = Pot (before bets) - BBs EV
Buttons EV = 10 - 4.5 = 5.5


SCENARIO 1 SCENARIO 2
Buttons EV = 7.5 Buttons EV = 5.5
BBs EV = 2.5 BBs EV = 4.5

As you can see, the only thing that was different in Scenario 2 is that the Button didn't value bet as thinly. And as such he lost value EV. And he couldn't' make it up with his bluffs because we were defending enough. So even if the Button decided to bluff 100%, his EV would of still been 5.5. And if we used your strategy the EV would be exactly the same, the Button would make ALOT more on his bluffs, but we would lose EXACTLY the same amount on his value hands -- because you're not calling as much. But the EV being the same has nothing to do with how you constructed your range, it has to do with the fact that Button's range was still balanced even if it wasn't optimally balanced.

---------------------------------------------------------------------------------------------------

SCENARIO 3
Let's assume exactly the same as Scenario 2. The Villain is a nit who doesn't feel like he can value bet thin. But what we didn't know about him, is he thinks everyone else is a nit, so he thinks he can always bluff people. So he value bets exactly the same as in Scenario 2. But he Bluffs 100% in this scenario.

Let's look at his range:

TOTAL RANGE -- HAND DISTIRBUTION:
Nut Hands = 50 combos
Air Hands = 50 combos

BETTING RANGE:
Value Hands = 10 combos
Bluff HAnds = 50 combos

CHECKING BACK RANGE:
Value Hands = 40 combos
Air Hands = 0 Combos

Now how would our two different BB ranges have stacked up against this particular Button. If we were using my balanced calling range of 50%... the Villain's EV would have been the same as in scenario 2... Buttons EV 5.5.

Now what would the Button's EV be against your range?

Calling Range (based on NJD77 guess):
Calling 6.6%
Folding 93.4%

EV of Button:
Button bets value, BB calls, Button wins = .1 * .066 * 20 = .132
Button bets value, BB folds, Button wins = .1 * .934 * 10 = .934
Button bets Bluff, BB calls, Button Loses = .5 * .066 * -10 = -.33
Button bets Bluff, BB folds, Button wins = .5 * .934 * 10 = 4.67
Button Checks Back Value, Button wins = .4 * 10 = 4
-----------------------------------------------------------------------
BUTTON'S EV = 9.406

Now obviously 9.406 this is higher than the 5.5 with my range. Now of course, I obviously changed the scenario where the Button was bluffing 100% against your hands. But with my range, his EV would stay exactly the same because my range is balanced so it can't be exploited by the Villain bluffing too much.


So what's the point? What we learned is that if we wan to play balanced we DON'T change our strategy based on the Villian's strategy. An optimally balanced strategy ends is fixed. We would only change it if we wanted to exploit the Villain which would be higher EV. So an optimally balanced strategy is not dependent on the Villain's actions.

So if we go back to your question of pre flop. We don't need to change our strategy if our strategy is the optimally balanced one... regardless of what the Villain does. What exactly is a balanced strategy defending from the blinds depends on a few assumptions, but I think this might help wrapping your head around it.

I think you did a good job of understanding it. It's BEST to play unbalanced exploitative poker to take advantage of your opponent's leaks if they don't adjust and start exploiting you. But the reality is that most Villain's don't adjust when you're exploiting their leaks.

There's so much going on in this thread that I can't keep up, but here's an easy explanation of this confusion.

The cliffs are, Villain defends 15% of the time, but with a 33% range. Let me explain.

55% of the time there is no steal, and thus no need to defend. 45% of the time we attempt to steal. Villain decides to defend with his top 33%. So two thirds of our steal attempts are successful, which accounts for 30% of all hands (66% * 45%). A third of our steals are defended against, which accounts for 33% * 45% = 15%.

So we have the following distribution:
55% no steal attempt
30% successful steal
15% resteal

So we have accounted for all 100% of hands.

(As usual it is assumed that our hand and villain's hand are independent, i.e., card removal effects are neglected.)

Ty Cangurino. Just another point though (I'm not going to let this one go until I'm completely convinced! ), because I don't think your post above is correct (I've bolded where I think it's wrong) :

In HEM, the stat of 3b to BTN Steal of 15%, isn't an OVERALL stat, it means:

15% of the time that the villain faced a steal from BTN, he made a 3b-resteal. He obviously can't have an option to 3b if he doesn't even face a steal, so this stat doesn't consider all hands, it only considers the times he actually faces a steal.

In other words, lets take a typical 100 hands where we are in the BTN and we have the option to open steal from the BB.

55 times we don't steal, so BB doesn't face a steal = 55 hands
45 times we steal and we face a 3b 15% of the time = 6.75 hands
45 times we steal and we are successful 85% of the time = 38.25 hands

So the distribution of these 100 hands should be:

55% no steal attempt
38.25% successful steal
6.75% resteal

Or am I wrong again???

But you were stating that this is the correct amount. It has been said before that in order for you not to profit immediately from your steals they have to resteal at least one third of the time. This means they have a range of 33%, even if you only steal 45%. That's what I meant by "15% of the time, but with a 33% range".

If they only 3-bet 15% of the times you steal, then your calculation is correct. Things get a bit more complicated since you face two players in the blinds. But even if both of them 3-bet 15% you show a slight profit.

With all due respect, this doesn't define anything. Who tells us what we can expect?

EV is the average of all possible outcomes, weighted by their respective probabilities.

One more problem is that payout happens only at the end of the hand. Thus we can't say what the expected outcome of a certain action is if there is money behind. We can only determine the EV of our strategy against the strategies of our opponents. Whether cold-calling SC's is +EV or -EV depends on our post-flop game among other things.

Of course this raises the question what a strategy is. Shameless plug: Intro to Game Theory

Why speak of "ranges and tendencies" here if everywhere else in this thread you speak of strategies?

So we can call a strategy exploitative only if we know which opposing strategy it is attempting to exploit.
Increase compared to what? Increase compared to any other strategy? Well, he can always find the strategy which maximizes his EV against our strategy. If this best strategy is not better than any other strategy it means that all strategies have the same expectation, so our balanced strategy can't win. So this can't be what you meant.

Increase compared to a balanced strategy? This would be a circular definition.

Increase compared to a game-theoretically optimal strategy? This is theoretically reasonable, but practically useless until we find said GTO strategy.

This doesn't make sense to me. If he is playing exploitatively, which strategy is he exploiting? And why would he improve by switching to balanced play? By definition, exploitative play is maximizing EV.

Likewise unclear.

All completely correct and fair points. But my goal wasn't so much to be thorough with the definitions, but rather give the reader an idea of the major points of the terms which were going to be important for the rest of thread.

And I look forward to reading your cotw.

Completely fair... I should have been more consistent. Yet at the same time, I wanted to show people how they could use game theory practically, so I wanted to also use terms we use all the time on the forums. But I shouldn't have gone back and forth using them interchangeably. I sent it to a couple people to read before I posted it... I obviously should have sent it to your first!

This is not how I use the term. I just use the term exploitative strategy as a strategy which defines all other strategies other than game theory optimal balanced. This is why I call them two sides of the same coin.

So in the first game of Roshambo, Geo used a strategy of only playing rock because he's a geologist and just like rocks (not really trying to exploit us... but I call this an exploitative strategy). And at the end, there's a more traditional leveling strategy which is consciously exploitative.

A game theoretically balanced strategy... which is what I tried to explain in the proceeding sentences. I obviously should have put this sentence later so it wouldn't be so confusing.

Yes ... as we talked about earlier in the thread, I was using the terms gto balanced strategy and balanced strategy interchangeably. I explained my reasoning for doing so earlier.

I used exploitative strategy as an umbrella term to define every strategy outside of an GTO one.


I appreciate your input. But I think it's important to remember that the goal of the post wasn't to rigorously define the terms (but I really regret not taking more time... especially at least putting optimal before balanced strategy).

What are your thoughts on the Abstract. Do you think this is a good approach to winning at poker?

I'm still wrapping my head around the abstract

My take on the whole matter is the following: We need to know optimal play in order to a) use it as a default against unknowns and b) recognize where opponents deviate from it, opening themselves up for exploitation.

Ok, I'll have to have a look at that. For me, a balanced strategy is not necessary optimal, since e.g., you may have the correct bluff/value ratio, but you're betting to few hands, or you use the wrong bet size.

"Exploitable" might be less confusing.

http://www.twoplustwo.com/magazine/i...os-balance.php

The whole point of the abstract and the entire thread was what you wrote here....



I guess I could have done a better job explaining.

Yeah, this is what I wrote later in the thread. My whole point for not using the term optimal was that people use it so much when explaining exploitative play... but I should have used something for the clarification to imply it.

nice thread

This is def one of the best cotw ever. The discussion is amazing too. This is great insight and really makes you think of the big picture instead of "what to do with KK on A high flop in 3bet pot OOP". Thank you very much sir!

this post is Fantastic. thanks very much for writing it. I will definitely be bookmarking this COTW.

Nice post. The link between Roshambo and Poker wear it perfectly.

nice post


ship it!

Nice COTW.
But I think a balanced strategy = BE poker.

I'm glad you enjoyed it and appreciate the compliment.

This is a common misconception that I've seen some very good players say but if you'd like to explore it, we could. Maybe you could explain why you think that, since I've only heard it used as a blanket statement as if it's self-evident.