A Technical Question Regarding Blind Stealing

[David Sklansky]

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.

[SplawnDarts]

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.

[Jim14Qc]

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.

[andyfox]

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

[Piers]

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.

[Gabe]

[ 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.

[The Dude]

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.

[Jerrod Ankenman]

[ 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

[PartyGirlUK]

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?

[Shandrax]

[ 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]