Can anyone tell me the odds of making these backdoor draws:

Flush?

Straight?

I have the information somewhere but cannot find it. I think it's about 22-1 against making a backdoor flush and 23-1 for the backdoor straight, but I'd like to have the exact odds. Please state your answer to the nearest tenth.

Given 10 hearts left in the remaining 47 unknown cards, the chance that turn and river come up hearts is 10/47*9/46 = 0.0416 = 1/24. Straights are a little more complicated based on the number of combos you need. If you have no gaps I think it comes out to about the same 1/24. Gaps are much worse.

Have you ever watched Linus waiting around for the Great Pumpkin? If all he's getting is a little candy, it is hardly worth it. If he's going to get a lifetime invite from Hef to the Mansion, he should wait every year.

Backdoor draws are a bit like that, to the nearest tenth.

Doug

Thanks for the useless story.

I'm back (from dinner). For straights, one issue is how many pairs of cards make your straight. If on the flop you have no gaps (three to flush) then three pairs of cards make the straight. With one gap, two pairs; and with two gaps, one pair. The cards that make the pairs can come in either order. So, on the turn there are 4/47 cards, and on the river 4/46.
4/47*4/46*2*3 = 1/22.5 = 21.5:1
The factor of 2 comes in due to the flexibility in order.
The factor of 3 comes in due to three possible pairs to make the straight (for zero gapper).

For one gapper: 4/47*4/46*2*2 = 1/33.8 = 33:1
For two gapper: 4/47*4/46*2*1 = 1/68 = 67:1

-- Matt

Yes, straights are much more complicated. It not only depends on the gaps, but the stretch of the cards, as 789 is easier to fill than 234. I just ran the 789 on my computer for 200,000 hands and a straight was made .044 of the time, which is 21.7-1. The 234 made a straight .029 in 200,000 hands, which is 33-1.

Very good. Thanks.

OK, I'll bite - why do you care to the nearest tenth?

Regardless of the number of decimals involved the answer is - "such a long shot that unless the preflop action included more than half the table for three or four bets and you know you can get through the flop for one bet only that it isn't worth putting any more money in."

Which, I'm pretty sure, was the point of the "useless story."

What if the pot is 20 bets, costs you 1 bet to call, and you have both 3-to-flush and 3-to-straight? Then throw away?

My story had humor and character. You should try to have both. R U a troll, or do these seem serious questions to you? Why would you demand that this group provide you answers you could find in a basic statistics textbook or on wikipedia and then attempt to grade the replies?

The practical answer is, you don't know the other hands well enough to care about the exact odds. You need a huge pot to even worry about a pure BD draw, or the BD draw is a second feature for a hand close to calling. Re-read my story and understand the wisdom in it.

Doug

imo

Now that we've done your homework for you...or something.....

Matt

That's a hard scenario for me to imagine because in order to meet the conditions you set out there would have to be heavy action preflop and then it gets passive on the flop.

But - if it's that big a pot and I was really confident of not facing a raise later then I probably peel with both backdoor draws particularly if the fd is to a big flush. My thinking would be that I'd give myself two outs for the combined draws and I'm getting 20-1 with good implied odds. I couldn't call it a bad fold either though.

I see this scenario often enough in live 4-8 play (I see). In fact, often when a pot is 3-bet, someone will 4-bet just to make it interesting. Then it gets checked through on the flop.

I think the point here is that you can play poker by rough guessing or you can play by trying to work with the pot odds, implied odds, reverse implied odds, opponent likely play, etc. I try to work the latter way, which is why I think this calculation is relevant.

ship this thread to the probability or beginners forum

this is the wrong forum for this "discussion"

OP you wont play enough hands in your lifetime to worry about the difference between getting 20:1 vs 22;1 on a backdoor draw so stop getting your panties in a bunch

I don't disagree that the calculation is relevant, I just don't think it's relevant to the nearest tenth. I think Doug made the point perfectly which is in order for this to even be a decision to ponder you need to be offered a huge potential reward. You're correct that there needs to be analysis of issues like this away from the table so that when you encounter the situation at the table you have confidence in what to do, but does know it to the nearest tenth change the decision? I say no because there is no way that in a game situation you will make decisions that finely.

Ed Miller covers the topic pretty well in SSHE. And . . . from several years ago, somewhere in 2+2 land, I just remembered that "people said" count the backdoors as 1.5 outs (each).

Backdoor draws can add value to other weak draws such as overcards or gut shots.

I would have replied immediately, but I didn't realize that my question got moved to this section.

First of all, I did not demand any answer. You better do some re-reading yourself. In the second place, you story still sucks. It was a poor attempt at humor. In the third place, you've got your nerve calling me a troll, you idiot. In the fourth place, read the following:

On page 103 of Small Stakes Hold 'Em by David Sklansky, Mason Malmuth, and Ed Miller, a backdoor straight draw of Queen-Jack-Ten is discussed. The following is stated:

"These draws come in 4.5 percent of the time, or are about a 21.5-1 dog."

Now if they use tenths when discussing backdoor draws and you say its foolish, then apparently you know more about poker discussion than they do. Maybe they should step aside and let you do the publishing on poker in the future.

You're almost as dumb as the guy with the stupid story. I asked a simple question, and you give me a sarcastic remark. Move your comment to the forum for imbeciles because I do admit that you are one step above an idiot.

Well, all I can say to you is

You're just another ass****.