Hold'em Poker Puzzle (hand with most outs)

[Paul2432]

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If your hand must improve, ten is the most nut outs possible. For example, you hold As Ts, board is Ks Js 3c 2d. Nut outs are the four queens plus six non-pairing spades.
Paul

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Man, this problem is tricky. If outs that tie for the nuts count, and your hand must improve to a new category (not just kicker improvement), then my answer is 14.

You hold As Ts, Board Ah Qs Js Td. Your nut outs are Ad Ac Ks Kd Kc Kh 9s 8s 7s 6s 5s 4s 3s 2s. You could argue that Ad Ac should not count, because quad aces would be the nuts on those boards (I count them as nut outs because the ace in your hand blocks quads, I suppose you could say 9s, 8s are not nut outs by the same argument), and that the Kh Kd Kc should not count because the board plays.

Paul