I would shove this hand always. That way you put more pressure on them since they need to call for their tournament life, and also it discourages the BB from flatting when your hand plays quite bad postflop at this stackdepth.

I also don't see how you can exclude higher pairs from his range when you get shoved on less than 10bb.

I haven't played NL tournaments for ages, but when I used to grind SnGs I was shoving my entire opening range in this spot and 33 was comfortably part of that. Very few hands are excited about inducing extra action here (inc 33) and I didn't wanna telegraph my monsters by doing anything different with them (although I'd sometimes min-raise or limp AA, KK, and even QQ 'cas people were awful and didn't notice the absurd tell).

That said, I can well believe that tourny strategy has moved on a thousand miles since I last played these (and I wasn't even that good a SnG player to begin with) so you might wanna take what I say with a pinch (or a pound) of salt.

Thanks for responses, guys!

I have thought about this play a lot today and I came up with conclusion I had to either fold this hand or shove it in the first place.

As min-raise, indeed, show a great strength, he could think of it as a weak steal attempt (which I think he did and moved in with a decent hand). Pushing the threes right away would generate a better effect on his mind than did just a min-raise. You know, keep him guessing, plus, I assume I would gain extra fold equity as others would see - that guy is moving with any pair. From that we would got greater value out of monster hands too - as they would think I am moving in with any pair, but instead we got a monster. Any thoughts?

Offtopic about monsters - it depends on positioning and actions of other players. In early position I consider a call instead of min-raise or all-in as most of the players will read it as a great strength anyway and we will use value of the hand. By calling we allow to players positioned later to re-raise us, therefore, we gain extra value of hand. In most cases we also can do re-raise and about 80% of time opponents will shove with 99+ or AJ+ (especially suited). Best pay offs come of the 5-6BB players as they are realizing - I am going to be blinded out anyway and will push way worse hands than we hold AA-QQ.

def 33 will play better as a shove here.  As played its prob fine but thin.  Your getting late game so there is some Icm consideration too.  We don't want to always shove our entire range but here especially vs randoms we want to shove our +ev hands that don't have blockers, we would rather min raise our blocker hands that we can min fold.  Hands like Axo and JTo.  Hands like A5s and JTs have a little more equity and since we have to min/call, then we should feel they play better as a shove. Def min raise the top of your range if there is no one there to exploit you (even sometimes if there is). But ya this spot is about blockers and how you play them imo.