[scottwire]

The main problem is this:

Now, again correctly speaking, of those 16 cards out-of-play, the expected number of Spade 's is 1 in 4, or the expected number of Spade 's left is actually 5, not 9 which gives you only a 5 in 30 chance of drawing a Spade or 16.7% which is 3 percentage points less of a chance to draw a flush.

If 16 cards are out of play of 46

You want

9/46 = x/16


16*9 = 46x

144 = 46x

x = 3.13 cards out of those 16 in people's hands will be spades

Not 1 in 4 like you said