Re: $15 MTT with 77 on button allin or call?
If you have already a caller from UTG i would just call 77 too, as it is likely that UTG has a pocket-pair himself.
the main question in these situation is if you can get the implied odds you need if you hit your set.
you have odds of 1:9 to hit your set, so on the first betting round, where you invest 300 in the pot you have to get out at least 2700 if you hit your set to break even.
on the second betting round, where there is already 2100 in the pot and you need 600 to call, you have to get 3200 from your opponents if you hit.
i think a second approach here would be to push preflop on the second round, which i would consider with 99 (ev. 88 on a loose table).
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