Note: After rereading your OP, I think you're looking for a simple rule such as other respondents have given. So feel free to ignore the last several paragraphs of this post.
That said, are you certain you're not confusing probability and odds?
http://poker.wikicities.com/wiki/Odds
You seem to be confusing the
odds against a flush with one card to come (approximately 4:1) with the
probability of a flush with two cards to come (approximately 1/3). Although odds and probability are closely related, failure to distinguish between them will lead you to all kinds of estimation errors.
Your expression "1:3 chance" probably is intended to mean "a probability of 1/3", not "3:1 odds" (i.e., a 1/4 probability), but is likely to breed confusion. I would only use the colon for odds.
OK, the rest of this post is minutiae you probably don't care about. [img]/images/graemlins/smile.gif[/img]
[ QUOTE ]
From what I have read I am NOT looking for implied odds or effective odds.
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I beg to differ -- if this isn't a classic question on effective odds, then I don't understand effective odds properly. (EDIT: I just remembered that effective odds also accounts for the extra turn bet, so that's extraneous to your question -- still, your question is very much an effective odds question, or I don't understand effective odds.)
But if you're looking for the specific math:
Turn: 9 [img]/images/graemlins/spade.gif[/img] remain, 47 unseen cards.
River --
provided you didn't catch a [img]/images/graemlins/spade.gif[/img] on the turn: 9 [img]/images/graemlins/spade.gif[/img] remain, 46 unseen cards
Probability of a OR b (or both) =
P(a) + P(not a) * P(b)
In our case, P( [img]/images/graemlins/spade.gif[/img] on turn, river, or both turn and river) =
9/47 + (38 / 47) * (9 / 46) =
0.191 + 0.809 * 0.195 =
0.349
A probability of 0.349 can be expressed as 34.9% or "odds of 1.865 : 1 against".
(NOTE: My original post had a small error, now corrected.)