Probability of completing a flush draw

[Zangief]

I've been thinking about this for the last few days and wondered what others thought about this.

The situation in question is when you have 2 suited cards (let's say As 9s) and there are 2 of your suit on the flop (let's say 3s Ks 8d).

Everything I have read about this has suggested that you have 9 outs to make your flush on the turn card, giving you a 9/47 = 19% chance.

While in the best case it is true that no one else would hold any of your suit, I think it is not accurate in the average case.

In a 10-handed ring game, there are 20 cards dealt to the players. On average, there will be 20 cards / 4 suits = 5 cards of each suit dealt out. Since you hold 2 spades, on average there will be 3 spades dealt out to the other players.

So, on average, you really only have 9 - 3 = 6 outs to make your flush on the turn card, giving you a 6/47 = 13% chance.

Does this make sense to anyone else? Or am I breaking correct probability calculations with my "average" thinking?

It just seems to me that having 9 outs for the flush is really the best case, where in poker we really want to rely on the average case. And I'm trying to figure out what that average case is.

Has anyone seen this covered elsewhere?

Thanks.

[dalecooper]

You overthought it and came to the wrong conclusion. There are 47 cards you haven't seen, including your opponents' hands; 9 of those are spades. That's 9 outs in 47 cards. If you wanted to go about it the way you are proposing, you would account for not just the missing spades but also the missing cards your opponents hold, so your outs are 6 in 29, which works out to be basically the same percentage and therefore gives you the same calling odds.

[Zangief]

Yes, I think you're right. Thanks for helping me figure this out.

[bspahn]

yup i agree.
Zangief - you're on UB right, do you have ultimate buddy? Whats your exact handle..

[mimmons775]

off the flop if you have 4 to a flush you have about a 35 percent chance to hit the flush draw with the turn and river to come, if you hit your flush draw on the turn you have about a 17 percent chance to hit it on the river.

[ttanaka]

I like it when Zangief body slams Dhalsim.

[TylerK]

I like it when Zangief body slams Dhalsim.

My cat's breath smells like cat food.

[Zangief]

I like it when Zangief body slams Dhalsim.

My cat's breath smells like cat food.

I like it when Zangief piledrives Ralph Wiggum.

Zangief - you're on UB right, do you have ultimate buddy? Whats your exact handle..

I just installed UltimateBuddy. My exact handle on UltimateBet is the imaginative "Zangief0" (that's a zero).

I assume you're asking because you're convinced I'm a fish?

{This post has been removed}

[Zangief]

(sigh)

the flush draw

every poker players nemesis

I do find that I play hands trying to defend against flush draws more often than I am playing a flush draw myself. But isn't a flush draw a tool for everyone to use? I know I enjoy it when I semi-bluff with one, get a caller, and hit the flush on the turn ....

amazing this topic came up... yesterday i had 23 flush draws on the flop... just one card away...

I was 1 for 23 all yesterday with making them... I think I defied odds