Half an out?

Let's say you flop a 3 flush and can only win if you make your flush. The probability of getting there is:

(10/47)*(9/46) ~ 0.042

If you had 2 outs the probability of catching on the turn would be:

2/47 ~ 0.043

Even though the probability of catching is roughly the same the 2 outs are better. This is because you do not have to pay for a river card in the two out example. The value of a BDFD depends on what the turn action is going to be. If you knew your opponent would check the turn a BDFD would have a value of 2 outs. If you knew your opponent would make a large all-in bet on the turn your BDFD would be worthless.

I checked this on cardplayer.com where they have an odds calculator. Say you have 78 suited (hearts)against top set with a board of Kh, Qd, 2c so you only win with running hearts that do not pair the board. You are a 3% chance to win on the turn, but if a heart comes you increase to 16% on the river.

Does that answer your question. I am sure you can play around with other hands and determine that.

If you're all-in on that flop though, how many outs can you say that you have? It's gotta be less than two since the profibality of catching two outs on just the turn is the same than as if you hit your hearts on the turn and the river.

its equivalent to 1 adding about 4% to ur all in equity if i remember correctly

It is not accurate because you can make your flush but your opponent can make a full house.

I count one out to the river.

If my opponent is cont. betting, I rarely (just to mix up my game) call him (with Axs and one on the board) and if I hit fourth to flush on turn I take lead of betting or raising.

I don't remember the title of the book that I read by David Sklansky, but if I can remember correctly he designates a backdoor draw as exactly 1.5 outs. Therefore, if the flop is 1093 with one of your suits and you have 75 s0000ted, you have 3 outs because you have a backdoor straight draw and flush draw (assuming your pair is no good). Hope this clears anything up.

I allowed for the full house in my answer. How do you count one out to the river? I am giving an example of top set against running cards of a suit.

I am sure someone can play around with an odds calcualtor and put in various situations and come up with different scenarios.

The question is worded oddly? Maybe it should be what is the chance you will win with a back door flush as your only outs?

I count one out, because you have 4,2% chance you make your backdoor flush as counted DrVan above. And I roughly count 4% for each out (up to 7 outs, then I remeber accurate % for 8, 9, 12 and 15 outs). I dont understand, why Sklansky counts 1,5 outs, but as far as I remember Harrington counts 1 out. Accurately one out (making your hand on turn or river) means 4,2553% which is very very close to your chances making your backdoor flush.

If you are asking, what is your chances against set, its little less. It depends, if you hold suit of the card on the flop, which gives your opponent set or not. He can have either one or two ways to make his full house if you make a flush. In your case, he has two ways (Qh, 2h), so you actually have 8 not 10 "backdoor" outs, so your chances are 8/45 x 7/44 = 2,83%.

I thing you should be aware of these added outs only in limit games, where they can turn your play from correct folding to correct calling.

10c2/47c2 ~ 4.16%

Let x be the number of outs.

The probability that you don't hit if you have x outs is

1 - x*(x-1)/(47*46) ~ 0.041628122

Solving for x and using the quadratic equation we get x ~ 46.021972

Therefore, the number of outs is ~ 47 - 46.021972 = 0.978028 outs. We can simply round this number up to 1.

I don't know the exact math, but Dan Harrington in HOH gives 1.5 outs for bdfd, and 1 out for bd str8 draw.

1.5 outs is overstating the true number of outs. Even if we use the conventional 4X rule, then we have 1.5%*4 = 6%

It is a routine check to see that the probability of hitting a flush with a bdfd is 10/47*9/46 ~ 4.16%

Divide this number by 4 and we get about 1 out.

Is it that different to say 1 or 1.5?
Now how many outs does a open ended straight draw have against top set?

Now the board pairs on the turn, how many outs? Zero.

The question is not how many outs does the Back Door Flush have, the question is what is the win % of the hand?

If the turn brings another suit, the back door flush has more outs. If the turn does not bring the desired suit, there are zero outs.

Losing players make bad calls and say, "but I had outs.." Losing players...

Again, it is not the right question to ask.