[pzhon]

Once you get check-raised all-in, you have a relatively simple problem, believe it or not. Determine your opponent's range for raise/calling and then check-raising you all-in, determine your equity against this range, and then see if you have the odds to call.

I think a lot of players would play this way with JJ, AQ, and AK, and maybe AJs. If you think this is your opponent's range, you can count the combinations of each hand: There is only one AJs hand possible, there are 3 JJ hands, 8 AQ hands, and 6 AK hands. You dominate 8 of these, tie 6, and are crushed by 4 of these. It looks like you are ahead of this range, so if that is your estimate, then you have an easy call regardless of the pot odds. Other estimated ranges may give you a different answer. If you think your opponent is unlikely to play this way with AQ or AJ, you might count 4 wins out of 11, which would let you call getting 7:4 odds, slightly worse than 2:1.

You should be very cautious about stacking off with one pair in a limped pot, or a pot with a single raise. You should not be as afraid to get your stack in with AK flopping TPTK in a reraised pot. You don't often have more than one pair on the flop, so if you are willing to fold the best one pair hand to a single raise, you will be very vulnerable to aggression. It may still be right by a lot to fold if you think your opponent would not take advantage of that vulnerability.

Professinal No Limit Hold'em has a lot to say about this, although I think it is missing some key ideas, which might show up in later volumes.

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does the fact that i have the nut backdoor FD make enough of a difference to warrant a call when i would otherwise fold?

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Sometimes it is a plus, and an extra 3-5% equity can be worth a lot when you are trying to figure out if you win 25% of the time. Here, it is not necessarily a plus. The reason is that you are blocking some possible flush draws like K[img]/images/graemlins/club.gif[/img] Q[img]/images/graemlins/club.gif[/img] and K[img]/images/graemlins/club.gif[/img] J[img]/images/graemlins/club.gif[/img]. That may decrease the proportion of your opponent's range you beat.