I see that some high level NL games and coaches play/recommend now SB open limping range. Can anyone produce GTO analysis, which would support SB open limping or challenge otherwise my approach below in such way that limping is +EV? I acknowledge that my analysis below is very likely wrong but cannot see how.

Analysis:

Assume GTO type of approach and assume SB can raise hands > 50 % profitably, where "> 50 %" refers to better half of the hands (and same notation used for other part of the ranges later on). When doing the analysis I had in mind 100 BB NL cash game.

Lets see if the worst hand (marked as ~50 %) not raised (so the best hand to be limped) can be limped (so +EV) profitable (with some strong assumptions). If the best limping hand cannot be limped, I would argue there is no such range at all.

SB opens:

> 50 % -> raises (this part is not limped and thus not part of the analysis).
~50 % -> limps (vs. folds = EV0).

SB limps -> BB's action:
> 25 % & < 50 % -> calls (goes to post flop).
> 50 % -> raises & < 25 % -> (bluff) raises.

SB limps -> BB raises -> SB's action:
~50 -> folds.

EV = -0.5 BB * 75 % = -0.375 BB (happens 75 % of the time).

I'm quite sure SB cannot call the raise here with the limping range (~50 %) given BB's superior range. Calling with an inferior hand range against the position isn't good. Raising needs even more strength (all-in equity favors BB). So effectively BB can fine tune this range and get even better EV.

Post flop (pot = 2 BB; SB's range ~50, BB's range from 25 % to 50 %); assume SB's EV ~ 60 % vs. BB's EV ~40 %. This should be adjusted by taking account BB's positional edge.

Given the assumptions post flop EV for SB = 2 BB * 0.6 * 25 %= +0.3 BB.

So all in all SB's best limped hand seems to be a slight -EV (0.3 - 0.375 = -0.075) proposition in the analysis.

If the analysis is correct (?), SB's open limping range doesn't seem to be a profitable option. One thing neglected is that for the balance SB needs to limp some of the strongest hands, which tilts analysis more away from open limping.

This is your main issue and it's not true that it makes open limping worse. If BB is raising 75% then SB has a pretty big incentive to limp his stronger hands. BB can not raise this much (I think).

Thank you for pointing that out, it seems obvious now. I got the sign wrong. I read about balancing with slow playing but got carried away when doing the analysis.

The analysis goes a lot complicated if more balancing lines will be added but I think this will change the result quite a lot.

Note also that limping can cause the BB to raise hands that would never call an open. e.g. If the BB has a polarized raising range vs a limp, then it might include hands as weak as 72o or 93o. Being able to limp-reraise to pick up 3bb from trash like adds EV to the SB limper's strategy.