I'm attempting this using the same basic model ([0,1] game) as in my BB defense post. Again, I don't intend to restrict this to short-stack strategy, although the stacks in the models are at most 24 with blinds at 1/2. My intention really is playing like this with full stacks, but I do also think it's relevant for short-stacking.

First off, a full model where SB is allowed to limp or raise or limp re-raise and BB is allowed all of the same options is so complicated that I'm not sure I even CAN do it. Nor am I sure that it's necessary because I think there are advantages to keeping your ranges sufficiently open that it's not at all clear when a board hits you.

I'll start with the relevant [0,1] games that I have solved (I think):

First one is the one from BB defense post. SB is allowed only to fold or raise to 8, and BB can fold call or shove for 24. Solution in [0,1] game:

SB raise: [0,42.7%]
BB value shove: [0,6.7%]
BB call: [6.7%,26.7%]
BB bluff shove: [26.7%,30.0%]
SB call shove: [0,13.3%]

Second is where SB can't start off with a raise but can limp re-raise to 24 if BB raises to 6 (I've made BB's raise a little smaller, simply because I like to keep my own raises a bit smaller when I have position). Solution:

SB limp: [0,67.0%]
BB value raise: [0,16.0%]
BB bluff raise: [92.0%,100%]
SB call raise: [3.0%, 33.5%]
SB value limp re-raise: [0,3.0%]
SB bluff limp re-raise: [33.5%,35.3%]

Finally, one where no re-raise is allowed (which makes it too complicated for me to solve) but where SB can raise to 6, limp or fold. BB can fold, call or raise, also to 6. Solution:

SB "value limp": [0,6.3%]
SB value raise: [6.3%,18.8%]
SB weak limp: [18.8%,62.5%]
SB bluff raise: [62.5%,68.8%]
BB call raise: [0,37.5%]
BB value raise: [0,25.0%]
BB bluff raise: [75.0%,100%]
SB call raise: [0,6.3%] and [18.8%,37.5%]

There's one thing that all of these games have in common and that I think is very much worth noting: It's a mistake against any opponent for SB to be giving up on any but bottom 1/3 of all hands.

Now, I'll look at a few fairly common mistake for BB in the games that I've played anyway, and what I think that means for adjusting SB play with combinations of limps and raises.

1) BB calls raise only on top 20%. Against this player, I think SB should raise all top 2/3 hands and never limp.

2) BB never bluff re-raises. Here, SB should play only JJ+ and AK to re-raises. Maybe PPs for set value, but the required stack depth to make that work may not be there according to some recent posts around here.

BB may also be too tight on his value re-raises. We've been talking about 99+, AJ+, KQ (or alternately 77+ and AJ+ if you don't like KQ) as the proper range, but if BB only value re-raises JJ+AK, you may want to play tighter still in SB.

3) BB raises a limp >25%. I think this is a very common mistake and really one of the main reasons why I started working on this whole thing. In light of the [0,1] game analysis, I think this is a pretty decent recipe against this type of player (with full stacks behind):

Value limp re-raise top 7% 3/4 of the time. Raise these hands 1/4.
Bluff limp re-raise 22-33 and SCs 3/4 of the time. Raise them the other 1/4.
Raise 7%-14% always. This is most of the middle pairs and trouble hands.
Randomly (50-50) raise or limp 14%-67% except for the limp re-raise hands.

If BB slows down and starts raising your limp too seldom (20% or so), then you should be more inclined to raise all of the top end and limp the bottom end--switching roughly to raising top 1/3, limping middle 1/3, and folding bottom 1/3.

Thoughts?

too many numbers for me to read. I think you obscenely over-analyze. Keep attacking from the SB til BB does'nt want to be spanked anymore then adjust your own play.

ah... i mean, personally, i hear ya bk, feel is absolutely an important part of my game; poker is a game of patterns, and if you feel someone's pattern is off in some way or another (like they're raising you more than you normally get raised), i generally try to pick a spot to play back at them, picking up the chips i've been folding by mucking my bb every fucking time to them.

but you know, meester ferguson has a different approach, heavily analytical, running models very similar to ais's and he's quite a player. i guess what i'm trying to say is that you guys are talking to each other in different languages about the same fricking shit.

i think...

As it stands it's also a few too many numbers for me to remember, but I'll just list some things that I've learned from the analysis as well as excession's remarks in the other thread.

1) It's a mistake against any player to give up on any top 2/3 hand. Against a player who actively defends his BB, I think a lot of people do give up on too many of these.

2) If you're raising a top 43% and a shorty shoves even 1/4 of the time, you should always call. I also really liked excession's step from [0,1] game to real poker by factoring in subsequent developments.

3) You really should be re-raising (for value) 99+, AJ+ and KQ from BB against almost any SB raise.

4) It's not a sin to limp in SB.

4) is really the whole reason why I went through all of these calculations. If you're going to limp sometimes and raise sometimes, you've got to have some mix of very strong hands in there on the limp. And you have to have some idea of when you want to limp-call, limp-fold, and limp re-raise. It's really the ability to limp in SB that imo requires a more complex strategy.

Ais...while math is poker...and you can define the correct way to play any situation thru math, nobody ever will, because there are always way more variables than you can/will give credit for esp bvb. But it looks like a nice guideline to be used when you are completely without reads.

Well, I felt kind of obligated to put the game-theory in there to show where I was coming from, but it no doubt leads more to confusion than anything else.

Here's basically my plan for SB with full stacks (here, too, I'd be interested in pursuing some of excession's short-stack thoughts further, but first full stacks). The assumption is also that everyone has folded to you in SB.

Starting (without reads yet): Raise any top 2/3 hand. If you get a call or re-raise, then play accordingly and now you have the hypothesis that we're getting too many calls. If fold, keep going with this (raising 2/3 and never limping) as long as it's working. "Working" is defined as "BB folds >2/3 of the time."

If BB is calling more than 1/3, then we try another strategy: The complex limp strategy, and that was my main reason for looking into these games--namely figuring out how properly to play limps from SB. And I'll take a stab at it not with [0,1] game but with poker hands.

Value limp re-raise: TT+ and AQ+ (4.7%). But also raise these 1/4 of the time, limping 3/4.

Bluff limp re-raise: 54s-JTs, 53s-J9s, 22-33 (5.1%). I'm actually suggesting this more often than prescribed because for one thing, these hands do well against monsters (in contrast to [0,1] game) and for another, I don't think many people make this play, particularly at lower levels, so your fold equity is probably higher than one might expect. Here, too, we limp 3/4 and raise 1/4.

Value raise: 44-99, AT-AJ, KT-KQ, QT-QJ,JTo, A2s-A9s (14.8%). We raise these 3/4 and limp 1/4. If limped, these are all limp-calls.

Random raise or limp: All other top 2/3 hands. On these, we're raising half the time and limping half the time, and they're all limp-folds.

I think this is a good strategy for beating excessive raising to limps.

There are 2 mistakes your opponent can now make to adjust to this strategy: 1) Backing down too much with raises (<25%), or 2) Folding too often to raises.

In case 1), our adjustment is to go to simply raising top 1/3, limping middle 1/3, and folding bottom 1/3. Villain is no longer sufficiently attacking our limps.

In case 2), we revert back to simply raising all top 2/3 hands.

To summarize:

If you're raising top 2/3 and getting called too often. Then it's tempting to tighten your raising range from SB. What I'm saying is that that's not the best way to adjust but instead to adopt a limp strategy that no realistic opponent is ever going to grasp for a VERY long time just by playing with you. I mean, it's hard to grasp (or even remember) when it's laid out explicitly.

I don't know just how much EV is getting lost if you simply fold some portion of top 2/3, but I'm convinced that it's definitely some. And the best strategy I can come up with as counter isn't to start folding hands that are worth something but rather to enter what I'll call the "complex limping strategy."

wow that last post is stunning.

Made my day..

Aisthasias could you do this same strategy upside down for the BB??

Thinking about this, their has to be a dominant strategy for every position and if opponent differs from that we'll make money from a Sklansky POV