Have I made a mistake?

[VivaLaViking]

Assume the flop leaves you with 10 outs.

Your probability of improving your hand by the river is:
[1 - (37/47)(36/46)] * 100 ~= 38.4%
Your probability of improving your hand immediately on the turn is:
(10 * 100) / 47 ~= 21.28%
After not improving on the turn your probability of improving in the river is:
(10 * 100) / 46 ~= 21.74%

Why does this math indicate that the probabilty increased for the river draw over the turn draw?

[mosdef]

because you've calculated the probability GIVEN THAT you missed on the turn, not the probability of hitting your card on the river regardless what happened on the turn.

[VivaLaViking]

Thanks, so the math looks OK to you?

[Jacob_Gilliam]

there's one less card in the deck on the river, so the odds of you hitting increases slightly.

[LetYouDown]

Odds of catching at least one of your 10 outs by the river:

1 - C(37,2)/C(47,2) = ~38.4%

[VivaLaViking]

Thanks All. For a moment I thought I was crazy. Wait a minute, it may be correct but that doesn't mean I'm sane.