[bobbyi]

I would cap the flop and take a free card on the turn if I don't improve. If you don't get the free card, the flop cap costs you nothing in expectation anyway because you are going to end up with the best hand about a third of the time here and neither opponent is folding for one more bet as the cap protects you against BB raising again and driving the other guy out.

Most of the time, they will both check to you on the turn if you cap. On a QT2r flop, there aren't many strong draws available, so BB is likely to give you credit for a strong hand here rather than a draw and check the turn. Even if he doesn't give you credit for strength, he may try to check-raise the turn to protect his hand in this large pot. One way or another, you get a free card often. Since your jack high is worthless unimproved, you don't have to worry about a turn check causing you to get bluffed out on the river.