A Technical Question Regarding Blind Stealing
 

In reviewing an upcoming two plus two book, I have come across a statement that I believe to be incorrect (and if so will change). It has to do with how many hands are profitable raises on the button or small blind, given the tightness of the big blind. Playing Limit Holdem

Obviously, as a general rule, the tighter the big blind, the more hands you can profitably raise with. And vice versa. But what about if the blind is extremely loose? Is there some point where you can add back in some hands as profitable raising hands (assume you can't just call) that you would fold if he was a tad tighter? We can make this question a litter more explicit later on if need be.

Re: A Technical Question Regarding Blind Stealing
 

Seems like that might be the case if your outplay/positional advantage against the BB was very large.

I don't know for sure and don't off the top of my head know how to quantify it, however.

Re: A Technical Question Regarding Blind Stealing
 

Yes if a he's a calling station since if the steal misses yet you hit in a good way, you can profit from his wrong calls. Calling may be better against such a player (especially if passive) though, but I'm not sure about this.

Re: A Technical Question Regarding Blind Stealing
 

One would think so, especially if the extreme looseness preflop is accompanied by extreme passivity postflop.

Re: A Technical Question Regarding Blind Stealing
 

I believe this is likely.

I am fairly sure it is true for short stack no limit, where big little hands like Q6o might be unprofitable on the button against blinds defending 50% of their hands, but profitable against blinds defending 100% of the time or 20% of the time.

In limit you have the extra consideration of playability after the flop, but I suspect this does not perturb the underlying race sufficiently to remove this effect.

Re: A Technical Question Regarding Blind Stealing
 

[ QUOTE ]
Obviously, as a general rule, the tighter the big blind, the more hands you can profitably raise with. And vice versa. But what about if the blind is extremely loose? Is there some point where you can add back in some hands as profitable raising hands (assume you can't just call) that you would fold if he was a tad tighter?

[/ QUOTE ]

On pure hot and cold equity, no.

Re: A Technical Question Regarding Blind Stealing
 

Well, it's certainly the case if we consider that as the player approaches "extremely loose" and beyond, they are usually worse post flop as well. Obviously there are exceptions - especially as you get to high limits - but in general this is true.

If the opponent is very tricky and good - even if way too loose pre flop - I do think there are still hands you can add back in, but not very many.

Re: A Technical Question Regarding Blind Stealing
 

[ QUOTE ]
In reviewing an upcoming two plus two book, I have come across a statement that I believe to be incorrect (and if so will change). It has to do with how many hands are profitable raises on the button or small blind, given the tightness of the big blind. Playing Limit Holdem

Obviously, as a general rule, the tighter the big blind, the more hands you can profitably raise with. And vice versa. But what about if the blind is extremely loose? Is there some point where you can add back in some hands as profitable raising hands (assume you can't just call) that you would fold if he was a tad tighter? We can make this question a litter more explicit later on if need be.

[/ QUOTE ]

OK, well suppose we take the BB-on-the-button headsup case. I'll make the problem more explicit, as I suspect that arguments like "if he plays poorly on future streets, you can raise more hands," aren't what you're looking for. Hint: If the guy plays poorly postflop, you can raise every hand profitably.

Suppose that the BB is a limited nemesis; it will maximally exploit you, except that it is forced to vary its preflop strategy for the purposes of our problem. You can choose your preflop strategy as you wish, but starting from the subgame that begins with the flop, it will play optimally for the distributions and pot size that you have carried here.

Suppose that the BB plays the optimal preflop strategy. We don't know what this is, but your question seems to assume (and I agree) that it is right for the BB to fold at least a few hands, and it would be optimal for the SB to likewise fold at least a few hands on the button.

Suppose that the BB then moves his strategy toward extreme looseness by simply calling with all hands he would have folded previously, and you continue to play the full-game optimal strategy, ignoring his new strategy. How does this benefit your strategy? You gain value from your stronger hands - because he is calling with hands that are too weak.

Now consider the question of your borderline raise/fold hands. Can it be right in this new game to switch one from fold to raise? I maintain that it can't. Here's the argument:

Consider a hand X that is close to the border between raising on fold, but which is a fold in the full-game optimal strategy.

Suppose that the BB folds a set of hands Z playing the full-game optimal strategy. In order for this change to cause the SB to switch X from folding to raising, the new equity of raising X must become higher than the equity of folding it.

But we know that when the BB was folding with Z, he was giving the SB +1 unit each time he folded, and still raising wasn't profitable. Now in order for the SB to switch to raising, the increased equity from playing *postflop* against the widened distribution has to exceed the difference between the equity of playing out X, a marginal hand against the hands that the BB would fold.

This is virtually impossible because of the nemesis restriction on the postflop play. The SB can't make enough value from playing his weakest hand against an expanded postflop distribution to offset the +1 units he was getting from those hands that the BB was folding.

So then, no, there's no situation where you would back additional hands into your distribution as the BB tended toward extreme looseness. (this argument extends to situations where the BB plays only a few fewer hands as well.)

Jerrod

Re: A Technical Question Regarding Blind Stealing
 

David are you assuming that the only variable is tightness of the blinds? i.e. are you assuming that there is 0 correlation between extreme looseness and postflop ability?

Re: A Technical Question Regarding Blind Stealing
 

[ QUOTE ]
This is virtually impossible because of the nemesis restriction on the postflop play.

[/ QUOTE ]

Jerrod's solution implies that an opponent with suboptimal pre-flop selection plays in an optimal way from the flop to the river.

I doubt that this combination of pre-flop idiot and post-flop genius is that common in limit practice (NL is a different story). Actually the other way around is much closer to reality. People usually have a pretty good idea of what to play pre-flop and struggle on the later streets.

There may be some rare cases where expert players intentionally get out of line pre-flop to project an image or to exploit a specific opponent, but I wonder if this is enough to make a rule out of the exception.

Theory of Restricted Choice simply tells us that the odds are 2:1 for a suboptimal pre-flop defender to be simply a bad player overall [img]/images/graemlins/wink.gif[/img]

Re: A Technical Question Regarding Blind Stealing
 

[ QUOTE ]
In reviewing an upcoming two plus two book, I have come across a statement that I believe to be incorrect (and if so will change). It has to do with how many hands are profitable raises on the button or small blind, given the tightness of the big blind. Playing Limit Holdem

Obviously, as a general rule, the tighter the big blind, the more hands you can profitably raise with. And vice versa. But what about if the blind is extremely loose? Is there some point where you can add back in some hands as profitable raising hands (assume you can't just call) that you would fold if he was a tad tighter? We can make this question a litter more explicit later on if need be.

[/ QUOTE ]

When taking into account his post flop play someone who defends 100% with a call but c/f when he doesn't hit a pair or a decent draw (say gutshot+) will simply fold the flop for one bet. You would certainly want to have the pot as large aspossible when he folds for that bet so iowuld imagine that any2 from the sb would do there.

Re: A Technical Question Regarding Blind Stealing
 

[ QUOTE ]
[ QUOTE ]
This is virtually impossible because of the nemesis restriction on the postflop play.

[/ QUOTE ]

Jerrod's solution implies that an opponent with suboptimal pre-flop selection plays in an optimal way from the flop to the river.

[/ QUOTE ]

I answered this problem because I thought it was the theoretical problem David was asking. If we're supposed to guess at how well our opponent plays postflop, then I will guess "badly" because that's how most opponents play.

[ QUOTE ]
I doubt that this combination of pre-flop idiot and post-flop genius is that common in limit practice (NL is a different story). Actually the other way around is much closer to reality. People usually have a pretty good idea of what to play pre-flop and struggle on the later streets.

[/ QUOTE ]

How can you say that people have a pretty good idea of what to play preflop and also characterize calling with all hands in the big blind as pre-flop idiocy? They aren't that far apart.

jerrod

Re: A Technical Question Regarding Blind Stealing
 

I also took the question to want to know just how variations in BB's preflop strategy affect our strategy, not how variations in BB's postflop strategy affect our strategy. And I think Jerrod's analysis is spot-on.

Re: A Technical Question Regarding Blind Stealing
 

David:

I'm not sure what you're asking. Are you looking for empirical information or apocryphical(our best guess)?

I assume that in your base case analysis, the Button's decision to raise or not raise is based on the following factors:

1. % that SB/BB will fold * amount of blinds (always a 0 or +ev)

Plus/minus

2. EV if you have to play the hand (either a +ev or a -ev).

The obvious point being that it is still profitable to raise with certain hands even if there is a -ev in step 2.

It seems that the entire analysis really revolves around these two points.

Your basic premise boils down to the following: as SB/BB get will defend with fewer hands, the +ev in step 1 declines, and the mix of hands in step 2 must be adjusted so that the -ev in this step is doesn't exceed the +ev from folding.

As SB/BB plays fewer hands, we have two variables that work in the opposite direction: First, the ev in step 1 decreases because there is a lower chance of successfully stealing. Second, for at least some subset of hands, the ev in step 2 increases because on average SB/BB will have progressively weaker hands.

So, for any given hand, the question comes down to whether it's worth raising with that hand given the lower +ev in step 1.

You start out by saying that as SB/BB play fewer hands, Button should raise with fewer hands. In essence this says that the Marginal Negative EV change for step 1 exceeds the Marginal Positive EV change for step 2.

As SB/BB plays more and more hands, it's possible that the difference in the marginal changes may narrow, or even cross over, so that at some point the range of hands increases. But this is largely a modelling exercise.

So, I come to my original point are you looking for something empirical or apocryphical.

If empirical -- I'm going to punt this one, you have far better tools than I.

If apocryphical -- except in extreme cases, where you can seriously outplay the blinds post flop, I suspect that the lines don't cross and you won't add back hands.

Re: A Technical Question Regarding Blind Stealing
 

That's good enough for me. It was my opinion too. And I'm deleting the comment from what I think so far is an otherwise great book.

Re: A Technical Question Regarding Blind Stealing
 

[ QUOTE ]
How can you say that people have a pretty good idea of what to play preflop and also characterize calling with all hands in the big blind as pre-flop idiocy? They aren't that far apart.

[/ QUOTE ]

I am characterizing the player described by your model. Your player plays 100% perfect post-flop, but for some reason cannot get his pre-flop play right, because he plays "too many" hands by definition. For me this describes a mixture of pre-flop idiot and post-flop genius. It's of course a totally unrealistic assumption/model, but that should be obvious.

Re: A Technical Question Regarding Blind Stealing
 

Jerrod,

Out of curiosity, is your use of the term "nemesis" a standard one in game theory discussions in general or poker in particular? Or are you just using it as a more colorful connotative term for someone whose play would be described as "maximally exploitive" (and with "limited nemesis" thus being used to put a limitation on the exploitation as to the stages of a multi-street play hand)?

Re: A Technical Question Regarding Blind Stealing
 

[ QUOTE ]
Jerrod,

Out of curiosity, is your use of the term "nemesis" a standard one in game theory discussions in general or poker in particular? Or are you just using it as a more colorful connotative term for someone whose play would be described as "maximally exploitive" (and with "limited nemesis" thus being used to put a limitation on the exploitation as to the stages of a multi-street play hand)?

[/ QUOTE ]

Nemesis is a technical term from game theory. A nemesis against a strategy X is any member of the set of all strategies that maximize value against X.

I personally like to use the term in poker discussions as well to mean the devious super-opponent who will automatically exploit your strategy and adapt to any strategy changes you make. This is a very useful idea in making people understand what playing optimally means.

But strictly speaking, a nemesis is a strategy that exploits maximally.

jerrod

Re: A Technical Question Regarding Blind Stealing
 

[ QUOTE ]
That's good enough for me. It was my opinion too. And I'm deleting the comment from what I think so far is an otherwise great book.

[/ QUOTE ]

You shouldn't delete it, you should add an editor's footnote that you disagree.

Re: A Technical Question Regarding Blind Stealing
 

If a player is loose and a calling station, I would just value bet every street if I thought I had the best of it and fold otherwise. But this is w/ low stakes w/ weak players. High stakes wouldn't work because other players would see what you are doing and plan accordingly.

Re: A Technical Question Regarding Blind Stealing
 

DS are you all working through the stox book before SSNL or are you working on the limit book and mason on the Nl book

Re: A Technical Question Regarding Blind Stealing
 

I would tend to think that yes more hands become playable again. If the play is a poor postflop calling station and you connect you can gain back with these hands. Also, if he folds postflop if he doesnt connect then bluffs work well and some more hands may be profitable. If he is a strong postflop player then his looseness probably wont allow you to get off with playing more hands profitably.

Re: A Technical Question Regarding Blind Stealing
 

Take one extreme case, the jam/fold game. Let's say the big blind has announced that if you go allin, he will call without looking at his cards. Obviously, he is being way too loose. The "optimal" raising system goes out the window, and you rely solely on EV calculations, looking at which hands are +EV vs. any two cards, given the blinds.

Where ordinarily you might raise with suited connectors, now you must throw them away; and whereas, if blinds were deep enough, you might muck A2, now you raise with it. So it's a mix of both; some hands go out the window and some hands are added.

Re: A Technical Question Regarding Blind Stealing
 

I'm assuming both players are of equal ability post flop. ie. best hand pre flop wins. (obviously sometimes a player will fold the best hand post flop, but this will even out because both players are equal post flop).

If BB folds 100% of the time you would obviously raise every single time.
If he calls 100% of the time (never re-raises) you should raise whenever ahead, according to the fundamental theorem. The button should therefore raise 49.9% of all hands. (is this correct?)
If there is no point where you add hands, this implies that you should never, against any opponent, raise less than 50% of the time, regardless of his preflop play (and still assuming equal ability post flop). Is this correct?

Re: A Technical Question Regarding Blind Stealing
 

Is there a way to mathematically express situations where what you lose in fold equity you gain in pot equity, or no?

Re: A Technical Question Regarding Blind Stealing
 

[ QUOTE ]
Now in order for the SB to switch to raising, the increased equity from playing *postflop* against the widened distribution has to exceed the difference between the equity of playing out X, a marginal hand against the hands that the BB would fold.

This is virtually impossible because of the nemesis restriction on the postflop play. The SB can't make enough value from playing his weakest hand against an expanded postflop distribution to offset the +1 units he was getting from those hands that the BB was folding.


[/ QUOTE ]

To do better than folding out the BB, playing X has to give the button an average pot equity (vs. Z) of over 3 small bets in the 4 bet pot that results after BB calls. This is indeed a lot to ask.

It's a little more complicated than that, because of shania considerations -- adding X to his raising range makes all of SB's other raising hands play better, because his hand becomes a little harder to read. But SB's range is already pretty wide, so he doesn't gain a lot this way. By the same token, X is a fairly lousy hand, and I agree that it won't do well enough against Z, a collection of terrible hands.