7 card stud - Calcluating Probability for improving 1p - please help

[Pok Jung Kee]

Hi poker gods,

I am confounded by this one. On Mike Caro's site, assuming 0 dead cards (throughout the hand), he states that the probability for making 1p into 2p or trips is 52%, 60% if you consider improving to a boat. (I don't even care about that extra 8% right now)

When I calculate it, I come up with a number better than 100%, and I know from experience that the number is closer to 50%. LOL. Please help me. What is my fundamental flaw in calculating probability here.

Let's assume the following: 8 person table, headsup play from 4th street forward. Starting hand is AA9. (This could be any pair, any kicker)

3rd) So with AA9, I have 7 cards to improve and 10 unseen cards, so 7/42 to improve.
Any unhelpful card falls, say a 6.
AA96
4th) So with AA96, I have 3 more cards to help, so 10 to improve, and 12 unseen cards, so 10/40 to improve.
Any unhelpful card falls, say a 4.
AA964
5th) So with AA964, I have 3 more cards to help, so 13 to improve, and 14 unseen cards, so 13/38 to improve.
Any unhelpful card falls, say a 7.
AA9647
6th) So with AA964, I have 3 more cards to help, so 16 to improve, and 16 unseen cards, so 16/36 to improve.
And wouldn't you know it, on the river I do NOT catch any of those 16 cards. GRRRRR.

I add these fractions, since it's an "OR" condition I improve if A or B or C or D occurs, and when I add those numbers, (I round the denominators to 39 to simplify)
(7+10+13+16=46) so about a 46/39 chance = I should improve 120% of the time!!!

People steamroll my pocket Aces all the time in 7CS.

Odds-masters, please help, I know this is something small and stupid, but perhaps others make the same fundamental mistake in their calculations.

thank you,
Pok Jung Kee