Backdoor Flush

[Macedon]

OK, math is not my strong point, but I gave a shot at trying to figure the odds of landing a flush when you've flopped a backdoor (3-to a flush on the flop).

My calculations:
22.8:1 (against)
4.2% (for)

Please don't laugh if I'm WAY off.
Any math help will be appreciated.

[kyro]

Well, I got 23.02:1, but regardless it's 4.2 percent. Not very good odds are they?

[BradleyT]

But that might be enough to sway a fold into a call if you have say a gutshot straight draw also (4 outs ~16%).

[Macedon]

The odds stink.
The only way you should play the backdoor flush is if it gets checked around on the turn and you get a free viewing on the river.
Otherwise, you shouldn't bother.

[cartoonsoldier]

Most of the times, you can only draw to a back door flush draw if you have a pair, or two overcards atleast.

[Mike Haven]

you may be interested in reading this thread (http://forumserver.twoplustwo.com/showflat.php?Cat=&Number=626157&page=&view=&sb=5&o =&fpart=all&vc=1) in the SS forum

at one point i wrote the following, which i still believe to be correct, but some others disagreed:

every time we look at our hand we compare it with the hands we deduce our opponents to have

normally we can see that we have nine outs, or eight outs, or five outs, or whatever, for our hands to catch up and overtake the leading opponent's hand

when we have a backdoor flush or straight we can't use the conventional outs-counting method because the ten outs or eight outs we need to improve our hand to a four-flush or an OESD still leave us well behind even if we catch, and still leave us with only a draw

therefore we need to establish a sensible and realistic comparison between drawing to a standard finite draw and to one of these rather imprecise situations

looking at my previous calculations we can see that AT THE MOMENT OF STARTING TO DRAW TO A BACKDOOR FLUSH OUR EXPECTATION OF SUCCESS IS ALMOST EXACTLY THE SAME, IN MONETARY EXPENSE TERMS, AS THAT OF STARTING TO DRAW TO A TWO-OUTTER

whether we finish drawing to improve to the flush, as with whether we finish trying to hit our two-outter, is irrelevant

the backdoor flush's outs-value of 2 applies only at the moment we have to decide whether or not we have enough outs to warrant drawing to our inferior hand when comparing the bet to be made with the pot odds available

finally, let's use a specific example to prove that the 2 outs is correct (we have to wonder why the pot is so large, but, whatever!)

we have Ac2c and our opponent has AdKd on a flop of Kc9h6s in a 2-4 game

ignoring runner-runner twos we have only our backdoor flush as a winner

the pot is 50

37x46 = 1702 times we lose our 2 = 3404 loss

10x46 = 460 times we have to call 4 more and we lose 370x4 = 1480 loss

3404+1480 = 4884 total loss

90 times we win 50+4 = 4860 win

this is proof that the pot odds needed to break even over 2162 hands were 50 to 2 or 25 to 1, which are the same odds as an equivalent 1.8 outter on the flop
QED

summary:

a backdoor flush is worth an additional 2 outs (actually 1.8 outs, but i have rounded up because of the reasonable likelihood of winning extra bets on the river) in terms of the cost of drawing