The EV of Limping or Shoving LP with a Short-Stack (Full-Ring)
Wednesday, May 19, 2010 at 12:07PM The analysis here will discuss whether you should push all in or limp with a low pocket pair when the action is on you with a short-stack of 20BB in the SB or BB and 3 opponents have limp-called ahead. It was always my belief that you should limp here, but some comments inspired by BH made me want to go into the math of this scenario more. If you shove just how screwed are you?
Analysis A: EV of set-mining with low-pairs Late Position with 20BB:
Going forward let’s say specifically we are holding 33 in this spot. I’ve argued that it is more +EV in the long-run set mining in this spot with minimized variance, even with just 20BB.
I valued a successful set mine here at approximately +20.5BB (+4.5BB from the blinds and limpers and +16BB from amount expected to win). Let’s look at the approximate +EV of set-mining late with a short-stack based on 8 scenarios:
Scenario 1 lost .5 BB and folded.
Scenario 2 lost .5 BB and folded.
Scenario 3 lost .5 BB and folded.
Scenario 4 lost .5 BB and folded.
Scenario 5 lost .5 BB and folded.
Scenario 6 lost .5 BB and folded.
Scenario 7 lost .5 BB and folded.
Scenario 8 won back the .5 BB and WON +20.5BB.
In the first 7 scenarios combined you lose 3.5BB by calling and folding when you miss your set on the flop. Now we include scenario 8 and average winning 20.5BB when we hit. Overall you are profiting around 17 BB for every 8 scenarios here by set mining, with very little variance.
Analysis B. EV of Shoving with low-pairs Late Position with 20BB:
Now let’s do the same 8 scenarios only we shove all-in. I’m going to assume at least 3 out of the 8 times you will be called with 44-TT. This is based on my experience full-ringing at rig-stars. Though I really think it would be more like 5 out of 8 times, but I’ll assume 3 here for fun. Next I’m going to assume you’re called 3 out of the 8 times with a coin-flip situation (this includes someone getting tricky with a big hand like AK, or someone just clueless for that matter who decides to stack off with A5+ or whatever). For easy math we will use 50% equity. Now let’s assume that 2 out of the 8 times everyone folds around and you pick up the pot. So here we go:
Scenario 1. Shove 20BB. You’re called with 44-TT by LIMPER 3 or 4. You’re 20% to win. You lose -20BB. But remember we suck out 20% of the time so knock that -20BB down to -16BB.
Scenario 2. Shove 20BB. You’re called with 44-TT by LIMPER 3 or 4. -16BB.
Scenario 3. Shove 20BB. You’re called with 44-TT by LIMPER 3 or 4. -16BB.
Scenario 4. Shove 20BB. Coin-flip situation. +4BB Since we will include the 1.5BB in blinds and 3BB from the other limpers on top of our 50% equity.
Scenario 5. Shove 20BB. Coin-flip situation. Again, +4BB.
Scenario 6. Shove 20BB. Coin-flip situation. +4BB.
Scenario 7. Shove 20BB. Every-one pathetically folds. No one person had the courage to call!!! What a cowardly table you play on. This is an awesome situation. +4BB
Scenario 8. Shove 20BB. COWARDS!!! +4BB
Scenario 4-8 combined = +20BB.
Scenario 1-3= -36BB
Total combined = -12BB
I’m coming up with -12BB for the 8 scenarios when shoving, and this is being generous based on my experience.
Analysis C. Vacuum Analysis without actual stats
For fun let’s say we come up with some stats that say in a vacuum the players will fold around 5 out of 8 times which could be close to likely. Certainly not likely on my stakes and format, but perhaps close to likely if we took every full-ring poker situation in the 100NL online universe where we shove the limpers with our 20BB stack holding 33. Then let’s say 1 of those times you will run into 44-TT (Yeah right), and 2 out of those times you will coin-flip. This is the best possible scenario I could ever imagine shoving your 20BB short stack with 33 from SB with 3 limpers on a full-ring table. Here we go.
Scenario 1: You’re called with 44-TT by LIMPER 3 or 4. -16BB.
Scenario 2: Shove 20BB. Coin-flip situation. +4BB.
Scenario 3. Shove 20BB. Coin-flip situation. +4BB.
Scenario 4. Shove 20BB. Coin-flip situation. +4BB.
Scenario 5. Shove 20BB. THE COWARDS FOLD! +4BB
Scenario 6. Shove 20BB. THE COWARDS FOLD! +4BB
Scenario 7. Shove 20BB. THE COWARDS FOLD! +4BB
Scenario 8. Shove 20BB. THE COWARDS FOLD! +4BB
Scenario 1 equates to -16BB. The rest of the scenarios combined will yield around 28BB of profit based on the 8 scenarios combined.
This would mean +12BB based on the sample size, even if in our perfect vacuum world we only ran into a 44-TT hand 12.5% of the time. But going back to the first example our set-mine profit still turned out to be +17BB.
So overall I’m calculating at least a +5BB EV by CALLING for the set in this situation, as opposed to jamming. This +5BB is a huge number, and that is still assuming the best case scenario I can imagine for shoving here, which would be facing utter domination only 1 out of 8 times.
Looking at this analysis in a vacuum:
A logical factor to consider here would be the % of times that your opponents are in fact dealt 44-TT. I could research this and get the exact numbers, but I won’t since I’m at work right now and all poker is blocked. Also I think it would be somewhat of a waste of time. Getting caught up doing analysis in a vacuum is a great way to become totally out of touch with the actual situation. I think this the kind of thing that many people go wrong on. I think this is why David Sklansky can’t win a tournament to save his life. The math wiz David hasn’t won a World Series bracelet since 1982, yet large circles still worship his books and theories. Why hasn’t he won more? Because in a vacuum his plays are correct. Fine justify all of your plays in a vacuum if that makes you sleep at night.
Furthermore, my vacuum analysis above was when I calculated with the massive assumption that our opponents will fold 5 out of 8 times to our shove. Honestly, my original analysis “B” sums up my actual beliefs (-12BB per 8 situations), while the vacuum analysis “C” was just being nice (+8BB per 12 situations). Analysis B was where the opponents will fold around 2 out of 8 times. Shoving here becomes a negative EV play, I can’t justify it any differently. Keep in mind 3 limpers ahead of you is a VERY rare situation on PokerStars full-ring games. Their ranges favor holding hands like 44-TT. To push you need to absolutely have a sick almost out of this world HUD read on all 3 limpers. I’d say that no short-stacker at full ring 100NL stakes is good enough to make this push profitably.
I didn’t mean to pick on the 33 hand. This was just a starting point for me. I think each hand will have a slightly different result. I still personally would feel comfortable set mining anything under pocket 88 here based on a variance and EV perspective.
In conclusion if you’re holding a low pair in the SB with a short-stack on a full ring table and have 3 limpers ahead of you FOR THE LOVE OF GOD LIMP. Calling is the way to go.
I’m open to any thoughts on this analysis. Especially from FK and BH who brought this particular discussion up and got me interested on justifying my out-look. I wouldn’t be surprised if I made a few mistakes in their, I’m no David Skalnsky by any means.
Either way this was a good exercise to waste an hour of my useless work day.
-bag
Reader Comments (6)
I complete the SB here with 33 - rarely do I push any small pairs as part of my short stacking strategy.
Before I type anything else I'll say I use things like Pokerstove and HEM far less than I should so I am not throwing out anything as a math based absolute. Ok... back to my reply.
I don't push small pairs. I fold them to raises (no set mining value at all) and from early position I'll limp them and fold to a raise for the same reason. Open jamming is suicide and raising 3X out of position is bad, too. If folded to me on the button my decision will then be based on the stats of the SB and BB. I probably fold the baby pairs there and wait for better shove spots. Maybe that's a bit weak.
One thing I like to caution people of is this: If you end up using Pokerstove to arrive at what you think is the optimal strategy you must make sure that the hand ranges you assign your villains are very accurate.
I'm not sure how much limping behind you'd see with 77-TT but maybe it doesn't affect the results too much. I'll limp behind with 22-66 or 22-77 but with medium pairs I like to raise/jam to isolate and define my hand and take the lead on the flop. You can end up check-calling a couple streets to realize someone limped with AA or KK... or flopped a set or junky two pair ... etc.
FK,
I didn't think you would personally be shoving small pockets here with a short-stack. Some of the comments just motivated to do some basic math behind how unprofitable shoving here would actually be. I myself became curios.
Oh PokerStove. Let me say I think it is an incredible tool, especially for someone just starting off. You absolutely SHOULD know how certain ranges interact with one another if you want to take your thinking process to the next level.
If anything I've been using PokerStove MORE than I should. I completely agree with your caution against relying to heavily on PokerStove. I'm leaning towards actually never using it in very border-line situations anymore. You're the master, you understand the format, stakes, and feel of the situation. Just because you plug in a certain range and Stove recommends "51% equity" does not mean, ok sweet I'll automatically make the border-line play. When in fact you know based on the opponent and feel that he is way ahead of your range at the time. For anyone reading this don't use PokerStove to justify going against your feel when in very tough border-line situations, trust me you will hate yourself. Stove is just another tool at your arsenal, it is not the be all or end all.
A stat of particular concern to me is 3-betting and 4-betting. You may have 500 hands on an opponent, but maybe he happened to only be in 40 3-bet situations in those 500 hands. If this is the case, I certainly would be damn careful relying to heavily on making a play on this range with only 40 hands. You would be usually be better off trusting your read based on experience and the feel of the situation.
As a short-stack I am rarely limping with anything, but there are certain situations where it is profitable (like the one discussed in this post). With pairs like 77-TT I'm almost never limping. An exception may be around the blinds with several limpers ahead of me. Sometimes I might pick up something that spooks me and stops me from JAMMING all of my chips in. Even in this situation it is very rare that shoving will be the wrong play. However, you really aren't giving up a ton of EV by limping here.
Anyways much thanks for the input as always,
-bag
Bag,
Nice reply.
In terms of the 3 and 4 bet ranges I think even a small sample size allows you to tell what type of opponent you're up against. A lot of players only 3 bet with premium hands.
Then you have your CardRunners diciples who do it with a wider range like suited connectors and premiums.
And then you have your third group who plays reckless and does it with a very wide range.
I thnk just being able to see a few holdings where the person 3 or 4 bet can be a nice little guide - especially if you're able to see the stats of the person they did it against.
So many people are afraid to pull the trigger and 3 bet light that once you find opponents who can do it you have exploitable spots.
FK,
I small sample size certainly helps, I just wouldn't take it as a be all or end all. The 3-bet is extremely complex. I would use caution and probably add a few percentage points higher to their 3-bet% especially with a small sample size, just to be safe. I would rather be a little conservative then stack off an entire stack and feel stupid about the play.
I've never got into CardRunners so I wouldn't know anything about their 3-bet habits, but I hope to God they are 3-betting me frequently with suited connectors. That would be a huge mistake based on my range as a short-stack. I play hands for more heads up equity, and suited connectors are not the hands to go to war with when you are dealing with heads up equity.
I generally think the more 3-betting the better. As long as you're comfortable and assigning ranges correctly it is fine. Speaking of 3-betting I just mentioned the topic in my post I put up a few minutes ago. I've not been 3-betting enough.
CardRunners advocates 3-betting and squeezing with suited connectors a lot - probably from CO/Button and also from the blinds.
I myself usually mix it up from the blinds.
I see. A+