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