This is a situation from a home tourney. There were roughly 15 people left on two tables where 6 places would be paid.

SB posts 500, BB posts 1000 and then:
UTG-BTN (5 players avg stack 10-12K)
SB 24000
BB 7000 (Hero) Ad2d

UTG-BTN fold
SB raise to 3000
BB ?

Unfortunately, I don't know a lot about SB's play when effective stacks are under 10BB. He's neither a nit nor a maniac, but that's about all I can say.

In the actual game, I pushed as I thought SB's raising without pushing could be a pretty wide range. Really, I'm so geared towards the push/fold game (I play a lot of SNGs) that a mere raise when I'm under 10 big blinds often confuses me. By pushing, I'm a dog to pairs and aces, but I'm ahead of other stuff in his range. I have to post 500 next hand. There's also the possibility that I may have some fold equity against his steals.

What would you consider a slightly tight, average, and slightly loose raising range to be for SB in this spot? When is my shove good? When is it bad?

im shoving Ax, 22+, J10, Q8+, K8+. it beats their 50% of hands range and ur need to double.

Well, you reached the same conclusion I did, so I'm glad about that. I agree that I need to take a shot at doubling, and think that I should push here with only a slight edge. But it's not clear to me I'm ahead of half his range -- as that's essentially my question.

I just put this into SNGWiz using chip equity mode (not ICM). It gives the following, based on how I model SB:

loose (open/call 36%/36%): EqPush t7678, EqFold 7000, DiffEV +678 Recomendation: PUSH
average (open/call 30%/30%): EqPush t7225, EqFold 7000, DiffEV +225 Recomendation: PUSH
tight (open/call 24%/24%): EqPush t6526, EqFold 7000, DiffEV -474 Recomendation: FOLD

Top 36%: 22+, A2+, K5+, K2s+, Q9+, Q8s+, J9s+
Top 30%: 22+, A2+, K8+, K4s+, QJ, Q9s+, JTs
Top 24%: 22+, A2+, KJ+, K9s+, QJs+

Note that pushing risks 7K to win 4K immediately, or if called to win 9K. So, if villian always calls, my implied pot odds are 7-9 and I need 43.75% equity for this to be profitable. Said differently, I just need to beat my EqFold=7000. Or maybe I want a little bit of an edge on the "there will be better spots later" theory. But that edge would probably be small, in the 100-200 range.

The open ranges seem modestly reasonable I guess, although I tried a few things from the SB point of view and it recommends PUSH a lot. I find it surprising that it gives call ranges equal to open ranges, basically saying I have no fold equity at all. Shouldn't I be expecting an outright steal here a decent fraction of the time by SB? Or is it just true that even when stealing, SB still calls because I'm short?

Also, wouldn't we expect villian to push a lot of hands here? When I'm in the SB in a spot like this against a BB with under 10 blinds, I don't really ever just raise, I either push or fold.

I put this in SNG Wizard, but from BB's perspective, again using pure chip equity (no ICM). It recommends pushing just about ATC, based largely on the fold equity being so good. Note, it only considers push/fold, not raise. Based on how you model BB, you get:

very tight (call 7%) EqPush 20752 EqFold 19500 DiffEV 1252 Recomend: PUSH 100%
tight (call 14%) EqPush 20670 EqFold 19500 DiffEV 1170 Recommend: PUSH 100%
average (call 17%) EqPush 20682 EqFold 19500 DiffEV 1182 Recommend: PUSH 100%
loose (call 21%) EqPush 20730 EqFold 19500 DiffEV 1230 Recommend: Push 100%
very loose (call 28%) EqPush 20782 EqFold 19500 DiffEV 1282 Recommend: Push 98.2%

For the record, "loose" top 21% does include A2s. Top 21% is 33+, A4+, A2s+, KJ+, KTs+. Also, if SB has junk like 23o, this improves the chances BB will have a "top 21%" hand (eg to 22%). This is the "bunching effect".

For example, if SB has 23o against a loose BB calling 21%, pushing is +EV:
78% BB folds giving SB 21000 chips
22% SB calls and BB is a 28-72 dog against top 21%:
* 28% SB wins and SB has 28000 chips
* 72% BB wins and SB has 12000 chips
Total equity of BB call is .28*28000 + .72*12000 = 16480
Total equity is .78 * 21000 + .22 * 16400 = 20006
Total equity of folding is 19500
DiffEV is +506 chips when SB steals with 23o here. Wow!

This is really interesting. SNGWiz loves stealing as the SB, but doesn't incorporate it into it's opponent models as BB. That's a rather eye opening conclusion for me.

Anyway, given that stealing is so profitable for SB, as BB, we should expect a thinking SB to be doing this more. So I do think A2s is a good push here. But again, this analysis is against SB open pushing, not open raising 3K. I still don't understand what raising vs pushing means here. Maybe it's a trapping move?

Anybody care to comment on how wide should SB open in blind vs blind contest against a BB with 7BB's left (after posting)? My analysis above shows you can shove if BB plays tight, but each time you do so you encourage them to widen up too. So if you had to pick, what would you go with.

And still I'd like to hear theories on raise vs push with a big stack vs a short stacked BB.