Unexpected shove

It's a Bodog SNG 10-seat single-table tournament, with the standard 3-place payout structure (50%/30%/20%). We're down to three-handed, and I'm in the big blind with a stack of 5935 when the hand starts. Small blind is the short stack with 1320. Button is the big stack with 7745. We all post antes of 25, and the blinds are 100/200, making the pot 375 before the cards are dealt. Button now has 7720, small blind has 1195, and I have 5710 left. We have been playing at this level for quite a while, and though I haven't been watching the clock, I expect the blinds to go up to 200/400 (still with 25 ante) after this hand or maybe the next.

Button open-shoves, SB folds. I have Ad-Kc.

What should I do?

The most obvious consideration is that SB is likely to go out soon. He has only six big blinds left now, and will have only three if the level jumps next hand. Moreover, he's by far the worst player here. When we first got into the money, he had luckboxed his way to about 10,000 in chips, compared to about 2500 for both me and the other player. He and I have picked away at him little by little, so that the SB now has almost nothing left.

The button is comparable in skill to me, though somewhat more reluctant to play after the flop than he should be. I've been able to steal more than my fair share of pots because of his timidity. He has not opened with a shove since we got into the money, so it's an extremely unusual move for him. He's a conservative player, probably a little too conservative. If he bluffs, it's a meek, one-barrel affair, then he shuts down. He has done lots of limping since we got to three-handed--including once with Q-Q--only occasionally raised, never shoved pre-flop.

I don't think he would do this with A-A, K-K, or Q-Q. He would instead open for a more normal-sized raise. I also don't think he would do this with a small pair. Furthermore, I can't see him doing this with the classic "trouble hands," such as K-Q, K-J, etc. Finally, I rather doubt that he would do this with A-K. His pattern would be more towards a standard opening raise, then play straightforwardly after the flop with a bet if he hit, giving up if he missed.

It has taken us three levels to whittle our former big stack down to where he is (the first eliminations went unusually rapidly in this game), so I've had more time than usual to watch these guys play short-handed. On that basis, I'm reasonably confident that the button's range here can be limited to a pocket pair between 7-7 (maybe as low as 6-6) and J-J.

Which means that if I call, I will be a slight underdog, but basically close to a 50/50 proposition to double up. If I call and win, I'll have 11,995, or 80% of the chips in play. If I call and lose, I'm out in third place. If I fold, I'll still have my 5710, which is 38% of the chips, with a near lock on at least second-place money and a decent chance of taking first.

What's the right play?

I'll give you about 24 hours, then post what I did.