counting outs with an example

I am sure this question should me in the FAQ section, as it must be asked all the time. However, I would like to get a fresh answer to how many outs you can add for a back door flush draw. I have read that a back door flush gives you two outs.


Please help me understand this hand:


Heads-up AdKc vs. QsJc


Flop [Ah Qd Jd]


AKo has Ac, As, Ks, Kh, Kd, Tc, Td, Ts, Th to improve on the turn to beat the 2-pair. While QJ has only four outs to improve to the nuts and will tie if both a king and ten fall on the turn and river. This tie assumes that it is not exactly the Kd and Td.


Here is where I need help counting outs, if one of those cards misses the turn. AK can still win if a smaller card hits the turn and then pairs the river. It can also improve if two diamonds hit the turn and river. With the overall potential to be the absolute nuts, how many outs does AK have to win? What am I missing in this analysis? Thank you.