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EDIT:: Haha I wrote this like an hour ago and forgot to post, above post is more concise. The only thing I somewhat disagree with is that your M is shit, M=10, you still get 40 hands at this level (probably ~30 with blind increases) we can still be somewhat selective, but I'd say JJ is being fairly selective. Depending how you rank hands JJ+ is somewhere around JJ,QQ,KK,AA,AKs,AKo,AQs. Though with a wider range, we're maybe 3-4 betting here for better value, as with AA perhaps, to induce a reraise.
This should be in the SNG subforum.
I wouldn't say shoving is a bad move here..
I ran the odds on poker stove, and if you put his range of calling all ins at about AJs+, you come back with about 50/50 odds with him overall (if I'm including KQs, many tourney players at this stake over-value this a lot), which is only if you get called. However, I wouldn't say he will call for the majority of his stack with that wide a range, maybe AKo/s, TT+ you're still only behind 43/57, I would say UTG is significantly behind, so him calling isn't too big of an issue, and you have 750 chips to steal here with a significant raise.
Unless you have a good read on BB, and he will only reraise you with premium (ie. AA, KK, maybe AKs) then maybe a 3bb raise to 4bb total would prevent this, as you could fold to a shove, but 4 handed there is a lot of bluffing, so I would say his range is wider, and given your odds with shoving, even if you get called (minor %), shoving is still pretty even.
in which case, how you played it doesn't seem bad. I'm not sure if there's a better line.
Can't win em all. (:
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