I don’t remember any details of the stack distribution on the other table but I remember that villain was 5th or 6th in chips and that I was 11th of 17 players remaining. Rather significant pay-jump at 13 players and the jumps start getting large at 5th place. Since I don’t have precision stacks for the other table (or the average stack at the time of the hand), the results may be a little inaccurate. I’m close enough that the %EV of some hands might change by 0.01 but that’s unlikely to change the shoving or calling ranges.

PokerStars – 3000/6000 Ante 750 NL – Holdem
Hand converted by PokerTracker 4

BTN: 33.93 BB
SB: 31.88 BB
Hero (BB): 18.84 BB
UTG: 9.48 BB
UTG+1: 9.5 BB
MP: 27.96 BB
MP+1: 23.75 BB
MP+2: 6.94 BB
CO: 10.94 BB

9 players post ante of 0.13 BB, SB posts SB 0.5 BB, Hero posts BB 1 BB

Pre Flop: (pot: 2.5 BB) Hero has K 7

fold, fold, fold, fold, fold, fold, SB raises to 31.88 BB and is all-in, fold

SB wins 3 BB

This particular hand felt like a trivial fold, but I marked it to run through ICMizer to see how far from a call it was. Turns out it is right on the border vs a Nash range (although definitely still a fold) but miles away against the 50% range that I think it is wise to assign this villain.

These are the results:

Calling Range vs 72%

Calling Range vs 50%

These ranges may not be surprising to players who’ve done a lot of work on ICM calculations, but I was surprised by how poorly some hands were doing. Unless I felt my edge at the table was relatively small or non-existent (which does still happen in some fields, especially if I’m not quite playing my A-game), I would always be looking to fold the 0.02 EV hands and probably anything <0.05 EV. I’m not certain, but I think an argument could be made for folding anything <0.1 EV in situations where we don’t have fold equity.

Let me know if the links don’t work for you and I can post a description of the results. I plan to highlight some takeaway points after I recover from the shock of realizing how poorly I understand the effects of ICM. 

EDIT: Just for curiosity sake, I decided to look at a 38% shoving range for the SB. Unlikely to be the case, but if this were their range (vs. known nits this would be a reasonable expectation), it is amazing how tight we want to be calling. 

Calling Range vs 38%

What the hell KQs?!? I thought we were friends.

You and me both brotha, lots (and lots, and lots) of ICM work needed in the near future.

I meant to include this in the original post, but here is the Nash Equilibrium in terms of chipEV:

Villain shoves 56% – their shoving range is 16% tighter when they can’t apply ICM pressure! We can profitably call with 35% of hands.

ChipEV at Equilibrium

The numbers in the chart are in terms of bb won rather than EV%.

It’s worth mentioning that I still don’t want to call the really marginal +chipEV hands. I would be looking to fold anything winning <0.25bb (maybe even <0.5 bb). I would for sure be folding K3s, T9s, and Q9o. I would also strongly consider folding K4s, Q8s, JTo, K7o, maybe even 22 and J9s.

Even if we fold all of those hands, we still want to call 29.9% when there is no ICM pressure. With my vague knowledge of ICM, I was drastically underestimating how much our calling range changes in the endgame scenarios.

A Nash Equilibrium is a state where neither player can benefit from unilaterally adjusting their strategy. When we talk about Nash shoving ranges, we’re describing a range that can’t be exploited – the best villains can do against it is to call the range that makes up their half of the equilibrium. Any deviation from defending that range will win fewer chips in the long run. When taking ICM into consideration, any deviation from defending the optimal range will win less money in the long run.

The 16% tighter range is the 56% range. I was highlighting that the SB is actually supposed to shove looser (the 72% range) when BB’s strategy has to account for ICM. The 35% range that we can call according to chipEV has nothing to do with ICM, it was included here to show how dramatically our optimal calling strategy (in the first analysis) changed due to ICM. The ranges from the earlier post are the ICM calling ranges.

SB isn’t shoving 30+bb. Their stack is 32bb, but BB is the effective stack with a little under 19bb. I’m not sure what you mean by ‘most villains.’ Less seasoned players shove many different ranges, but I expect most regs at >= $11 (at least on Stars) to be shoving slightly tighter than but relatively close to Nash small blind ranges if they aren’t employing a more nuanced strategy (limping or raising small with some hands). I expect the better regs to shove more or less exactly Nash. This is much less the case when taking ICM into account but, for straight-up chipEV, most regs will know <20bb SB ranges like the back of their hand and won’t be shy about pulling the trigger.

That being said, if you believe a certain player or even population is shoving much tighter ranges, you definitely want to call tighter. We can exploit their overly tight shoving ranges by calling tighter when they do shove and getting more walks/free flops when they don’t.