Flush Draw Question

[EasilyFound]

This is counter intuitive to me, so I ask. I'm using pokerstove to calculate the winning % of a flush draw/2 overcards to a pocket pair. The winning % when I hold two cards of the same suit is 54%, but the winning % when I have one card of the same suit and the flop is three of that suit is 52%. I would have thought that it would be the same. Why not?

Here is the cards I was using for both examples.

#1. A [img]/images/graemlins/diamond.gif[/img] K [img]/images/graemlins/diamond.gif[/img] vs. Q [img]/images/graemlins/heart.gif[/img] Q [img]/images/graemlins/spade.gif[/img] and flop of 2 [img]/images/graemlins/diamond.gif[/img] 7 [img]/images/graemlins/diamond.gif[/img] 9 [img]/images/graemlins/spade.gif[/img] = A [img]/images/graemlins/diamond.gif[/img] K [img]/images/graemlins/diamond.gif[/img]d being 54% favorite

#2. A [img]/images/graemlins/diamond.gif[/img] K [img]/images/graemlins/club.gif[/img] vs. Q [img]/images/graemlins/heart.gif[/img] Q [img]/images/graemlins/spade.gif[/img] and a board of 2 [img]/images/graemlins/diamond.gif[/img] 7 [img]/images/graemlins/diamond.gif[/img] 9 [img]/images/graemlins/diamond.gif[/img] = A [img]/images/graemlins/diamond.gif[/img] K [img]/images/graemlins/club.gif[/img] being a 52% favorite.

(Numbers round up or down where appropriate)

[jay_shark]

Lets list the different ways pocket queens can win :

1) The flush draw in both cases goes unimproved and pocket queens wins by either unimproving or improving to a better hand .

2) Case1) . Any three ,aces or kings , can pair the board but the pair of queens improves to a set .
Case 2) . Any three aces or any TWO kings pairs the board but the pair of queens improves to a set( the qc) . Notice that if the Kd hits the turn , then the queens cannot win any longer.

3) Case1) Pocket queens wins with two pair . The turn pairs the board with the exclusion of any diamonds . In total there are 8 good cards for pocket queens .
case 2) Pocket queens wins with two pair but this time there are 9 good cards for pocket queens with the exclusion of any diamond .

4) Pocket queens improves to a full house .
5) pocket queens improves to quads .

Notice that 1,4 and 5 have the same chance of occurring in either case . It's only part 2 and 3 that require a bit more thought .

Do you see why pocket queens would rather face off against ADkC ?

[R Gibert]

In both, there are 9 outs for a flush.

In #1, there are 6 outs for a higher pair.

In #2, there are 5 outs for a higher pair,
since the Kd is already counted as an out giving a flush.

[EasilyFound]

[ QUOTE ]
In both, there are 9 outs for a flush.

In #1, there are 6 outs for a higher pair.

In #2, there are 5 outs for a higher pair,
since the Kd is already counted as an out giving a flush.

[/ QUOTE ]

Man, I should have been able to figure that out myself. Thanks.