Drawing to a back door flush

There's probably a very simple, straight-forward answer to this question, but for some reason it doesn't seem so obvious to me. Is drawing strictly to a backdoor flush wrong EVERY time?

I'm not a loose player, and i wouldn't consider this play at any time. However, recently I've been trying to sharpen the calculating aspect of my game. So, if i'm correct, the odds of drawing a backdoor flush is 17:1, which means that if you want to make this a profitable play, you have to extract 16 times the amount you put in the pot from the rest of the table. But how can you get those odds when there's only 9 other players at the table??

So here's an example.

You hold AhKh, you raise preflop, 5 people call.

10 bets in the pot.

flop is 9h 7s 2d. For the sake of argument, you know with 100% certainty that someone is holding a set of 9's. Thus, the only way you can possibly win (besides runner runner A's or K's, which is so unlikely it shouldn't be considered?) is with your nut flush, which will win almost 100% (given that the board doesn't pair up).

So, you estimate that it will cost you at least 7 bets (2 preflop, 1 flop, 2 turn, 2 river), which means that you have to have a 120 bet pot [your 7 + (16x7)]. Obviously, there's no way you can get this many bets.

So, the conclusion seems that it is NEVER a profitable play to strictly draw for a back door flush.

Is this correct? Did i calculate the odds appropriately? Are there other factors I'm not considring? This question is probably more about my thought process than drawing to a backdoor flush. Any comments would be appreciated, even if it's just a "you're right," or "you're wrong."

Thanks in advance!!

i believe your odds are incorrect


it is 37 to 10 to turn a fourflush = 3.7 to 1 = 21.28% of the time


it is 37 to 9 to river a flush = 4.1 to 1 = 19.61% of the time


so 19.61% of 21.28% of the time you complete your backdoor flush


which is 4.17% of the time


which is 23 to 1 (not 17 to 1 as you thought)


also, you have not taken into consideration the fact that if you don't hit your fourflush on the turn your investment in that pot is ended


EXAMPLE


if you have a pot of 14 sb


you can call with 1sb (as you're getting better than 3.7 to 1 to draw for fourth flushcard)


pot is now 15sb


if you hit your fourth flushcard you draw again


pot is at least 17sb (someone has bet 2sb) (so you are getting more than the 4.1 you need to call with your 2sb)


if you draw your fifth flushcard and win you take down a 19sb pot (even if no further bets)


3sb was your investment so your profit is 16sb when you hit your backdoor flush


if you don't turn a fourflush you have lost 3.7 x 1sb = 3.7sb


if you do turn a fourflush but don't river a flush you have lost 4.1 x (1sb + 2sb) = 12.3sb


total loss is 3.7sb + 12.3sb = 16sb when you don't hit your backdoor flush


conclusion


against one opponent you can chase a backdoor nut flush with 14sb in pot after the flop


this isn't a highly likely scenario so you can use these general calculations as a base to see how different numbers of opponents affect the result - you will find that you can chase a backdoor nut flush in some situations - but you can expect to lose a lot of the time, adding to your variance

Mike,


I think you came up with a number that is too low. It seems to me that that should be the about the number if there was going to be no further betting after the decision to stay in.


There are 2162 combinations of turn and river cards. On the turn, you will miss 37 out of 47 times, or (1702 out of 2162 combinations start with a miss) these each cost 1 small bet.


If a card of your suit comes on the turn, you will miss on the river 37 out of 46 times, or 370 out of 2162. these each cost 3 small bets.


A card of you suit, giving you a flush, will appear the remaining 90 out of 2162 times.


You will spend 1702 small bets on the flop.

You will spend 1110 small bets on the turn.


You need to recover 2812 small bets the 90 times that you make your flush, or 31.25 small bets each time you win.


You probably need about 7 players for three bets each preflop, and passive play postflop, to give you enough to justify drawing to only a back door flush.


Good luck,

Bob T.

Thank you Bob and Mike for taking the time to respond and explain the nitty gritty of calculating pot odds. Obviously my procedure is flawed, so I'll make the necessary adjustments. Your responses have been very helpful, and also show that it's going to take a lot of practice to be proficient at the calculating aspect of hold 'em. Thanks again!

This is the third or fourth time I've seen someone post a specific question -- and in their post casually make reference to being able to win with a hand that won't win.


This seems like a big deal to me. How can you being trying to learn pot odds and the correct times to draw to a backdoor flush when you aren't thinking of what hands will win the game.


The question: "What cards will win this hand for me?" should be one of the MOST important things you answer. Then deal with the more intricate natures of the game.


Point in referece from icarus' post:


" flop is 9h 7s 2d. For the sake of argument, you know with 100% certainty that someone is holding a set of 9's. Thus, the only way you can possibly win (besides runner runner A's or K's, which is so unlikely it shouldn't be considered?) "


** Runner runner AA or KK will give the 9's a full house **


Know what cards you want!

I think the best way to look at it is to assume that after the flop it will cost you one bet on the flop, and if you hit on the flop it'll cost you another bet on the turn to draw to your backdoor flush. So you'll be spending 1 small bet 37/47 times when you don't hit and 3 small bets 10/47 times when you do catch a draw on the turn.


So the total amount of small bets you'll be spending is (37/47)*(1) + (10/47)*(3) = 1.4 small bets.


We know that you have a 24-1 shot to make a backdoor flush by the river, so there will need to be 24(1.4) about 34 small bets in the pot at the end of the hand to make this a break even call.


To put it in perspective, if 6 players called 3 bets preflop (18 small bets), then all 6 called one flop bet (6 small bets) and four players called one turn bet (8 big bets) there would be 32 big bets in the pot, and you'd have to get two big bets on the river to make this play break even.


It would be a rare sitution where it would be correct to call for ONLY a backdoor flush.


Rube

Thank you for pointing out my mistake mkpoker. You make a very good point. I'll be sure to watch out for this little trap the next time I consider drawing!

thanks for checking my figures, bob


yes, your correction is right, of course


i missed out the fact that you have to play the 4.7 turns 5.1 times to ensure a flush, on average


so i should have said if you don't turn a fourflush you have lost 3.7 x 1sb = 3.7sb x 5.1 times = 18.87sb


then total loss is 18.87 + 12.3 = 31.17sb before you hit your backdoor flush ( this differs from your 31.25 only because of my rounding off figures)


i agree, now, it is difficult to see too many realistic situations where it's worth chasing only a backdoor flush


mike

Further to this, odds of hitting the flush are discounted by two draws as this will make the boat for pocket 9's. Its tough to make it profitable as it is but if you absolutely know someone is on a set, a backdoor flush is a big loser!!

odds are slightly better since we 'know' that one bettor has 99 not of our suit in his hole...