Thanks for doing your homework, Zackzarack!
I think the key to this hand is to put both of your opponents on ranges. Remember that whenever you get called after raising, as a general rule we should put our opponents on a range of hands that has more "middling" cards.
(Why? Because if they have very high cards AK/AQ/JJ+ etc we would expect them to reraise us)
So, when SB and BB call us we should put a lot of 89/9T/JT/QJ/KJ/QK hands in their range as well as perhaps some lower suited connectors and small pocket pairs. Lets give them both this range {44/55/66/77/88/89/9T/JT/QJ/KJ}. Now we can work out how much equity we have against those ranges on this particular board:
http://www.PokerStrategy.com
Operation completed... 6,051,906 games processed in 0 seconds.
Board: 9cjctd
Dead:
Equity Win Tie Loss Hand
Player 1: 24.938 % 24.586 % 0.916 % 74.498 % AsKc
Player 2: 37.531 % 35.279 % 4.715 % 60.006 % 88-44, KJs+, QJs, JTs, T9s, 98s, KQo, QJo, JTo, T9o, 98o
Player 3: 37.531 % 35.279 % 4.715 % 60.006 % 88-44, KJs+, QJs, JTs, T9s, 98s, KQo, QJo, JTo, T9o, 98o
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So as you can see we only have around 25% equity against their combined ranges, before anyone acts, once we have seen the flop.
Now the good thing for us is that we have position; so they both act first. When one of them shoves directly into us (even though we were the first to act as the preflop aggressor) and another one calls, that gives us a lot of information. In fact it tells us that both players consider themselves to be at the top of their range.
So we can probably exclude hands like 44/55/66/77 from their ranges. Once we do that our equity falls to 20%.
as kurrkabin says, our various gutshots and over cards and backdoor draws are all "illusions". Because very often when we hit those hands it actually improves our opponents ranges even more.
here I think we should just let it go on the flop and be thankful that our opponents made it so easy for us by " telling us" so clearly that they have strong hands. If they had both checked to us we might have been tempted to bet and then we would have lost even more. It goes without saying that SB's shove is terrible here, but that doesn't help us because we have to play against their ranges rather than their actual hands.
Well done for posting - this is the key to improvement!