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 Omaha/8 Discussions of Omaha High-Low Split (Eight or Better) Poker.

 11-25-2008, 11:06 PM #1 journeyman     Join Date: Sep 2006 Posts: 215 Odds of flopping a straight flush? So I flopped a straight flush (with a J9 in the hole) tonight on Cake. Got to talking with a guy at the table about what the odds were. I threw out "one in a million). So, question is, what are the odds of flopping a straight flush in PLO8?
11-26-2008, 01:11 AM   #2
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Location: Los Angeles, California
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Re: Odds of flopping a straight flush?

Quote:
 Originally Posted by cantac So I flopped a straight flush (with a J9 in the hole) tonight on Cake. Got to talking with a guy at the table about what the odds were. I threw out "one in a million). So, question is, what are the odds of flopping a straight flush in PLO8?
Depends. If you hold J, 9, A, 3, you flop a straight flush with
K, Q, T,
Q, T, 8, or
T, 8, 7.

There's one way to flop each of the above, and knowing the four cards in your hand but no others, there are 48*47*46/6 = 17296 possible flops.

Thus you have 3 ways out of 17296 to flop a straight flush with those particular cards. The odds against it are 17293 to 3, or 17293/3 to 1 or about
5764 to 1 against it.

"One in six thousand" is a close approximation.

For T, 9, A, 3 the odds against it would not be as great (17292 to 4).
For Q, 9, A, 3, the odds against it would be greater (17294 to 2).
For K, 9, A, 3, the odds against it would be greatest (17295 to 1).

Buzz

 11-26-2008, 04:31 AM #3 Soldier of Minbet     Join Date: Apr 2008 Location: DOMUS CLAMANTIUM Posts: 9,197 Re: Odds of flopping a straight flush? Hope you got paid by the Ace high flush or the board paired and you got paid bigger and/or you had a good low with it if one came!
 11-26-2008, 08:40 AM #4 centurion   Join Date: Nov 2008 Posts: 193 Re: Odds of flopping a straight flush? I've flopped a straight flush a couple of times before. One time in a sit'n'go this guy flopped a straight flush and then hit runner runner for a 7 CARD STRAIGHT FLUSH! now tell me the odds of that happening.
 11-26-2008, 08:45 AM #5 Soldier of Minbet     Join Date: Apr 2008 Location: DOMUS CLAMANTIUM Posts: 9,197 Re: Odds of flopping a straight flush? I flopped a royal flush on Full Tilt playing \$1/\$2 O8 a while back. I had AQJ2 raised it up pre, called in 3 spots, flop came AKT. I led flop turn and river (best line!!!) and two people called me down
11-26-2008, 09:49 AM   #6
Carpal \'Tunnel

Join Date: Sep 2002
Location: Los Angeles, California
Posts: 15,114
Re: Odds of flopping a straight flush?

Quote:
 Originally Posted by - ka-boomed - I've flopped a straight flush a couple of times before. One time in a sit'n'go this guy flopped a straight flush and then hit runner runner for a 7 CARD STRAIGHT FLUSH! now tell me the odds of that happening.
Depends. If you hold J, 9, A, 3, the probability of flopping a straight flush and then extending that to a seven card straight straight flush is

3/17296*3/990=1/1902560, or approximately two million to one against. (actually 1,902,559 to 1 against)

Enough!

Buzz

 06-29-2012, 11:22 PM #7 stranger   Join Date: Jun 2012 Posts: 1 Re: Odds of flopping a straight flush? In order to flop (or turn or river) a straight flush in Omaha, you must have at least two cards that are no more than three ranks apart. For example, you'll never make a straight flush with Ac 6c 9s Kh. Assuming that you have a hand with straight flush possibilities, the toughest to "convert" would be a hand with a 3-gapper and no other potential, such as As 3c 4h 8h. There's only one way to flop a straight flush with such a hand, and there are (48 x 47 x 46) = 17,296 possible flops. The "easiest" hand with which you can flop a straight flush is one containing two suited connectors, such as 4d 5d Jc Tc. That kind of hand can flop a straight flush in eight different ways: Ad 2d 3d, 2d 3d 6d, 3d 6d 7d, 6d 7d 8d, 7c 8c 9c, 8c 9c Qc, 9c Qc Kc, or Qc Kc Ac. So the odds of flopping a straight flush in Omaha, assuming you have any such possibility, are between 2,161 to 1 and 17,295 to 1. Here's another weird one: About six years ago, in my Wednesday night home game, a player was dealt all four aces in Omaha. (He folded preflop, but not before he showed his hand to his neighbor, so we have two witnesses to the miracle.) The odds against that were 270,724 to 1! Earlier this year, in the same home game, the same player got four aces AGAIN! We play a lot of poker, but it's dealer's choice, so we probably don't deal more than 50 hands of Omaha per night, and lots of Wednesdays we can't get enough players together for a game. Safe to say that player, who doesn't play online or in casinos and missed about 18 months of the home game after his daughter was born, wasn't dealt even 10,000 Omaha hands in the intervening six years! Last edited by Big Ox; 06-29-2012 at 11:28 PM. Reason: math error
06-30-2012, 04:48 AM   #8
Carpal \'Tunnel

Join Date: Sep 2002
Location: Los Angeles, California
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slight correction

Quote:
 Originally Posted by Big Ox In order to flop (or turn or river) a straight flush in Omaha, you must have at least two cards that are no more than three ranks apart. For example, you'll never make a straight flush with Ac 6c 9s Kh. Assuming that you have a hand with straight flush possibilities, the toughest to "convert" would be a hand with a 3-gapper and no other potential, such as As 3c 4h 8h. There's only one way to flop a straight flush with such a hand, and there are (48 x 47 x 46) = 17,296 possible flops.
Yes, there are 17,296 possible flops, but 48*47*46 doesn't get there.

You need 48*47*46/1/2/3 to convert from permutations to combinations.

Buzz

 06-30-2012, 05:12 AM #9 old hand     Join Date: Nov 2011 Location: Australia/Micro stakes Stars tab Posts: 1,743 I went runner runner royal flush a few weeks back playing NLHE, silly russian should have stopped trying to steals my blinds by shoving every hand. Cash btw. Was such beautiful justice.

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