question about JJ

[rci97]

This might be a stupid question, but... Play was down to 6 handed, blinds 25 - 50. I was one of two shortest stacks, with t650. UTG (big stack ~ t2000) calls, UTG + 1 calls, action to me). BB was other large stack with ~ t1650).

I had JJ. My thinking was that there was already t175 in pot. If I make a normal raise of say 250, I'm almost pot committed but there are so many overcards to my jacks that can flop. I push all - in. No callers. Would any of you played this differently? Did I minimize the value of this hand by "only" winning what was already in the pot? My thinking here was that I was playing survival and wouldn't mind a call by two overcards or of course would love a call by Ax from one of the larger stacks (this was at $5 PP so you never know what kind of hand you can get a call from). Thanks for your input.