[ QUOTE ]
[ QUOTE ]
It really seems like you ought to include some of the stronger draws such as:
Flush Draw + OESD + Pair
Flush Draw + OESD/Double Gutshot
Flush Draw + ISD + Pair
Flush Draw + 3Straight + Pair
OESD+Pair+BD Flush Draw

[/ QUOTE ]

[ QUOTE ]
I quite agree, but how the hell to I figure those odds out and then how do I add them to the other odds?

[/ QUOTE ].

Let's start with flush+OESD+Pair:
Clearly we want to have a pair with one of the hole cards. So the flop must contain: 1 of the 6 cards that pair with the hole cards.
In addition, there are three possible combinations of cards that make the OESD/Flush draw. That's a total of 18 possible flops that make that draw for you.

For the double-gutshot+flush draw, you need one of two combinations of values:
(For example, for 65 - you need 973 or 842) and you need exactly two of those three cards to be of the same suit as your hole. That makes for 2*3*3=18 possible flops that make gutshot+flush draws. Clearly none of these are OESD situations, so they're seperate from the ones above.

For an OESD+Flush draw, you need to get one of the three possible combinations of extra values, and an additional card chosen from the 8 unused values(we don't want the boar to pair) Exactly two of the three are suited, so we're looking at 3*3*3*8=72 possibilities.
Now, there are four pairs of values that give inside straight draws. (For 56 they are 23, 89, 37 and 48.) Now, for each of the values, there are 6 possible cards that make the pair with your hole (since this is Flush+IESD+Pair the two must both be suited) for a total of 24 possibilities.

We're really only interested in 3 straight draws that involve the cards in the hand, so there are two possible values (for 65, 7 and 4). For each of the two, you need to see one of 6 pairing cards, and one of the remaining 8 flush cards. (There are 10 cards that form a 4-flush, but 2 of them make for better straight draws.) That's a total of 96 possible hands.

Now, the OESD+Pair+BD Flush:
There are 3 possible pairs of values that make the OESD, and the remaining card must be chosen from 6 in the deck. In addition, since we're looking for exactly 3 suited cards, there are 6 suit combinations for each of the pairs. That makes for a total of 3*3*6=54 possibilities.
[ QUOTE ]
That said when figuring these odds out, how do you account for hand possibilites that meet these criteria, but were already figured in as part of the made hand odds? does that make sense?

[/ QUOTE ]

You have to make sure you don't count the same hand twice.

The draws above total to 282 possibilities.

With the 701 other possibilities, that makes for a total of 983 viable card combinations of 19600 which is close to 1 in 20.