How many outs?

How many outs does a backdoor flush draw count for assuming both of your cards play.


What about a backdoor straight?


How do you calculate this?

Suppose you have 9s-3s and get a free play in your big blind. The flop is: As-Th-2d, giving you a backdoor spade flush draw. The probability of both the turn card and the river card being a spade is: (10/47)*(9/46) which is 4.2%.


I believe Roy Cooke has stated that a backdoor draw is equivalent to about 1 extra out.

4.2% = 22.8 to 1 = 2 outs

I think this is incorrect. The odds are 22.8-1 against completing the draw on the next two cards, just about the same as the odds of hitting one particular card on EITHER the turn OR the river. So the backdoor draw is equivalent to one extra out. You may be thinking of the odds on turning a set when your pocket pair misses the flop. In that case, the odds are 22.5-1 against hitting either of your two outs on the turn, but if you are committed to stay to the river (as you would obviously have to do to complete a backdoor draw) the odds would only be 11.9-1.

i understand what you are saying, but i think that you are missing the point that you HAVE to look on runner-runner draws as a single "unit", or a single two-card draw, or else there is no point in making an estimated equivalent outer in the first place - you might as well, more correctly, say you have a 10-outer for a 4-flush


if the turn is your required suit then you will always try for the rivered flush, ("always", for all practical purposes)


if the turn is not of your suit then you won't (by definition) be trying for the rivered flush - but you have to understand the "unit" of the two-card draw is still "there", (whether you try for it or not)


so, once you accept that this is correct, then the odds for this two-card "unit" of a runner-runner draw are 23 to 1, or the same as a single card "unit" for a 2-outer


you should also note, however, that once you do hit your turn 4-flush, (as you will, 10 times in every 47 tries), for the purposes of calculating whether or not you should go for the river flush you have to forget the now historic 2-outer estimate altogether and turn it into a new 9-outer!

Excellent points Mike but I believe you are overlooking one important detail. You have to pay additional money on the turn to see the river and complete your draw. I believe this is why Roy Cooke discounts the 23-to-1 shot from two outs to one out because of this fact. However, I am just speculating.


I believe David Sklansky has stated that backdoor draws can sometimes turn a fold into a call especially if you have both a backdoor flush draw and a backdoor straight draw in conjunction with other outs usually.

thank you, Jim


yes, i see what you mean - the money does have an effect on the issue


after a number of calculations and experiments i am fairly confident that it averages out as a 29 to 1 bet, (3.33%), taking the second bet into consideration


1 out is 46 to 1; 2 outs are 22.5 to 1


so if i am right, a runner-runner flush should be regarded as a one and a half outer, tending towards a 2-outer, for pot odds calculation purposes


c. Mike Haven 8th May 2002

i didn't bring in the fact that two of my suit will put a pair on the board


that could swing it back to the one and a half outer tending towards a one-outer, perhaps depending on what cards are in the flop, and that might be why Roy gives his figure