Did I make the right move?

indeed a hard one. utg 5h with 13 BB’s holding 66 is quite difficult, it really feels too weak to shove and to strong to fold. and shortstack also means raising or limping is rarely a good idea either. below 10BB’s i would defenitely have shoved. but i honestly have to say i don’t know which action i would prefer here. i might have leaned towards shoving because of the tight table image.
as played, with this flop i would shove for 100% sure. the problem is that he called with a hand that should have folded. but with almost all hands that should be in his range you are having him crushed. even if you knew what he holded you still got 10 outs (3,6 and 8) and according to the rule of 4 and 2 it means you still got about 40% chance to win right now.

another thing around the bubble is as warlock already mentioned is the ICM, and ICM is the biggest in the bubble stage, which means losing chips count stronger then on any place in the tournament.
the flip side however is that it also means that people know about this (at least they know about the difference of cashing or not) and tighten up (too much) a lot. which means you should play looser instead. so the bubble really a bit double edged. but in general, a big stack allows you to loosen up and a small stack to tighten up.

don’t know if it helps, but i once made an explanation of ICM once in a forum. but my thread is mostly about the math behind, but it can help you understand it by knowing that.

hope this helps.

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