Rather complex problem of odds
Here is a situation ––
you hold two spades, and two spades appear on the flop.
of drawing a flush on either turn or river are thus roughly 2:1.
The turn comes on a diamond.
The chances of you drawing your spade on the river are now....
4:1, or do they remain 2:1 ?
Simple logic dictates that the chances of drawing the spade on only one card are 4:1, yet since this is the second of two chances, the odds are surely higher in your favor, and seem to me to remain 2:1?
If I'm wrong and the odds are actually 4:1, demonstrate why, but I've been going through a few books (most recently Flynn's Professional No-Limit), and this problem is ignored, and the odds in this situation were understood as 4:1, thus ignoring the context.