Edited on 08 Oct 2009 17:04 by
jdnorway
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Posted: 08-Oct-2009 16:50 by jdnorway
I assume you're being serious here, as your tournaments section indicates that you are new to the game.
In this section you're unlikely to receive a serious response to such a question. Try the beginner section for questions such as this one. This section is for questions about poker that extend beyond individual hands - hence Metagame.
I'll leave my evil, sarcastic sidekick to the side and answer your question. In your example you have a flush draw and a straight draw. Depending on the bidding, you may also have overcards you can hit to go ahead, though this may be deceiving (you may be up against hands like KJ or QJ, so if you hit an overpair, one of the others hits 2 pair).
Hence, you can expect to have the nuts (dismissing another player having Axd) if the following cards hit:
9 outstanding diamonds (13 minus the 4 you already see)
3 non-diamond aces
3 non-diamond nines
That means you have 15 outs + 6 semi-outs.
There are 47 unknown cards available for the turn and 46 unknown cards available for the river. The chance of you hitting on either the turn or the river is calculated by figuring out the exact opposit - what is the chance that you miss. The chance that you miss both turn and river is:
(47-15)/47 * (46-15)/46
The first expression is all 47 cards on the turn, minus your 15 outs, divided by 47. The second is the same for the river.
32/47 * 31/46 = 45.9 % - there is a 45.9 % chance that you miss all your outs. Hence, there is a 100 % - 45.9 % = 54.1 % chance that you hit.
It turns out that if you take the number of outs (in this case 15) and multiply by 4, you end up with a number that's pretty close to the right answer. If you have 9 outs (normal flush draw, no straight), you have about a 36 % chance of hitting. This is the easy way of doing it that most people use.
This way of doing it is right for about 1-12 outs, and starts deviating after that. In your example, if all king or queens were also outs, you would have 21 outs, but you would not have an 84 % (21 x 4) chance to hit. The right percentage would be:
100 % - 26/47*25/46 = 69.9 %
You don't often have 21 outs, so don't worry about this, just be aware that the actual percentage isn't outs*4, that's just the shortcut for calculating it.
Gl at the tables.
also: http://tinyurl.com/yan5fm4