[AKQJ10]

I'm glad it sounded like SheridanCat's reply helped you; I'm just going to pick a nit here.

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I think I understand drawing odds. If I have pocket aces, and one is a spade, and the flop hits 567 all spades, then I have to draw to the flush to be sure I have the nuts.

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If the flop is 5 [img]/images/graemlins/spade.gif[/img] 6 [img]/images/graemlins/spade.gif[/img] 7 [img]/images/graemlins/spade.gif[/img] and you have A [img]/images/graemlins/spade.gif[/img] A [img]/images/graemlins/club.gif[/img], you can never have the nuts by the river. The nuts on that board is 9 [img]/images/graemlins/spade.gif[/img] 8 [img]/images/graemlins/spade.gif[/img], or if you have it, 8 [img]/images/graemlins/spade.gif[/img] 4 [img]/images/graemlins/spade.gif[/img]. It's unlikely you'll make an ace-high flush and lose, but you don't want to be the person who goes 20 raises on the river and pays off the straight flush! You could also make a flush on the turn but see the board pair on the river. Both possibilities of losing with an ace-high flush are worth noting, though not obsessing over -- if you make your ace-high flush, you probably have the best hand.

Moreover, on a 5 [img]/images/graemlins/spade.gif[/img] 6 [img]/images/graemlins/spade.gif[/img] 7 [img]/images/graemlins/spade.gif[/img] you still have a very strong hand with AA. Although you may be losing to a flush, straight, or two pair, none of those hands is guaranteed to be out against you. Furthermore the flush redraw makes your hand very strong, so even if you are behind, you still (per your OP and the subsequent corrections of the math) have about a 1/3 chance of drawing out. If you're losing to a flush, of course, that's two less spade outs left in the deck, but a lot of hands like 9 [img]/images/graemlins/heart.gif[/img] 8 [img]/images/graemlins/heart.gif[/img] or 6 [img]/images/graemlins/diamond.gif[/img] 5 [img]/images/graemlins/diamond.gif[/img] should bet aggressively on this flop, so even if you feel the betting makes it likely you're behind, you can't assume you're behind to a flush.

Anyway, I just felt these considerations were worth pointing out. The big picture issue is, you're interested in your probablity of winning the pot, not your probability of making the stone-cold nuts. With AA even on such a highly-coordinated board, and even if you don't improve, there's a decent chance you're still ahead so your decisions should reflect that consideration.