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[QUOTE="RammerJammer, post: 328399, member: 2090"]
Ultimately, the puzzle itself doesn't make any sense, because calculation of outs in game play is based entirely upon the number of cards it would take for [I]you[/I] to make [I]your best possible hand [/I] from the pockets and board already dealt.  What your opponent may or may not have doesn't enter into the "outs" equation at all.

Ignoring the impossibility of knowing what my opponent has, this hand presents 5 potential winning hands greater than my current top pair of Aces, but three hands are very dangerous, one is marginal, and one is strong.

2 pairs Aces & K's = 3 outs
2 pairs Aces & 7's = 3 outs
2 pairs Aces & 4's = 3 outs
[B]2 pairs Aces & 2's = 3 outs[/B]
[B]Set of Aces         = 2 outs[/B]

The only hands I'd really shoot for here would be the set or the hidden deuce, so of the [B]14 hand-making outs[/B], I would really only base my bet or check on [B]5 outs[/B], which put my odds of making a decent hand on the river at 10-to-1.  Anything I bet here would have to pay me ten times the wager (if I won the pot) to justify placing it.  Of course, all of this is exclusive from the consideration that I may ultimately win the pot with top pair.
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