low M shove range given call range?

[bogey1]

In any tourney, but particularly turbos, you get into low M shove modes at some point. I'm at work, book is at home, but I recall HoH talking about "any ace" as good enough to shove when you get an M < 5.

I'm trying to look at his backwards and figuring what to shove based on villian calling ranges. The "any ace" thing seems bad with weak aces if you're in EP or even early MP. Pairs and bigger aces are the bulk of the calling range, which leaves you about 25-30% to suck out.

But, something like J8s does much better against that range. You're only 60:40 against a big ace, even better against small aces and coinflips with smaller pairs.

Is there a tool to work the math backwards? If I put in a calling range of A6+,22+,KQ, what are the best "underdog" hands to shove with?

[bogey1]

Ok, I got pokerstove (had no idea it was free, duh) and ran some numbers. This all assumes we got called, but that should be ok as the fold equity in a shove is the same regardless of your hand.

Against a calling range of: 22+,A2s+,KQs,QJs,A2o+,KQo

A2o = 35.496 (ewwww)
A2s = 38.972
74s = 35.541
74o = 31.925
A5o = 38.990

A crappy ace against that calling range is equivalent to crappy suited and barely connected. Also worth noting suitedness helps quite a bit when shoving crap (not so much if not shoving crap, at least as a % gain over unsuited).

Weak aces start to look decent at A7o.
A6o/s = 39.466/42.694
A7o/s = 42.100/45.150

Now, looking at true suited connectors:
76s = 39.096
87s = 39.980
98s = 40.829
JTs = 43.066

So, I guess what I'm finding is when desparate, small aces really, really suck. You're better off pushing barely connected suited cards. Connected really matters though.

T5s = 35.760
Q7s = 37.410
T7s = 39.005

Probably not a shock to a lot of people, but it helped clarify things in my mind. I'm not shoving micro aces (<5) anymore from EP/MP. The calling range just crushes me. However, shoving T7s looks pretty good in comparison.