tgolly
Joined: Sep 15, 2010
• Posts: 4
October 13th, 2010 at 1:39:41 PM permalink
My question is while playing 9 handed hold-em what are the odds that two people flop a flush?

If it is 118:1 to flop a flush for one player, say myself in the hand, then I think the odds for two people to do it must be much higher. If I flopped one then it is that much harder for the second person to do it since I have 2 of his outs.

Thanks

Tom Golly
crazyiam
Joined: Feb 5, 2010
• Posts: 44
October 13th, 2010 at 1:43:59 PM permalink
Quote: tgolly

My question is while playing 9 handed hold-em what are the odds that two people flop a flush?

If it is 118:1 to flop a flush for one player, say myself in the hand, then I think the odds for two people to do it must be much higher. If I flopped one then it is that much harder for the second person to do it since I have 2 of his outs.

Thanks

Tom Golly

Are you asking given that you have a flush what are the odds someone else does? Or do you want to know the odds to two people having a flush on a given flop?

These are very difference questions.
Ayecarumba
Joined: Nov 17, 2009
• Posts: 6512
October 13th, 2010 at 6:14:06 PM permalink
Quote: tgolly

My question is while playing 9 handed hold-em what are the odds that two people flop a flush?

If it is 118:1 to flop a flush for one player, say myself in the hand, then I think the odds for two people to do it must be much higher. If I flopped one then it is that much harder for the second person to do it since I have 2 of his outs.

Thanks

Tom Golly

From the Wizard's, "Poker Probabilities" page on the WoO site, there are 5,108 ways to make a flush with five cards, out of 1,302,540 possible hands, or 1 in 255. The odds of another player having two cards of the same suit in the hole is 1276/1302539 or, 1 in 1021. I'm no expert, but I suspect that since the two hands are dependent on each other, the actual numbers may be somewhat different.
Simplicity is the ultimate sophistication - Leonardo da Vinci
mkl654321
Joined: Aug 8, 2010
• Posts: 3412
October 13th, 2010 at 11:38:41 PM permalink
Quote: Ayecarumba

From the Wizard's, "Poker Probabilities" page on the WoO site, there are 5,108 ways to make a flush with five cards, out of 1,302,540 possible hands, or 1 in 255. The odds of another player having two cards of the same suit in the hole is 1276/1302539 or, 1 in 1021. I'm no expert, but I suspect that since the two hands are dependent on each other, the actual numbers may be somewhat different.

It's real simple. Two conditions have to come true: one, Player A flops a flush, and two, Player B also has two cards of the same suit. Now, there are 8 cards left out of 47, so Player B has an (8/47)*(7/46) chance of getting two of those cards. Multiply the resultant fraction by 1/255, and you're done.
The fact that a believer is happier than a skeptic is no more to the point than the fact that a drunken man is happier than a sober one. The happiness of credulity is a cheap and dangerous quality.---George Bernard Shaw
tgolly
Joined: Sep 15, 2010
• Posts: 4
October 14th, 2010 at 1:18:10 PM permalink
I am asking what are the odds of two people flopping a flush at the same time. Or as you put it "the odds to two people having a flush on a given flop."
tgolly
Joined: Sep 15, 2010
• Posts: 4
October 14th, 2010 at 1:24:05 PM permalink
Ok so I did the math and the answer I get is 1.015. Does that mean the chances of the event occurring are 1%?

Thanks again.
Doc
Joined: Feb 27, 2010
• Posts: 6889
October 14th, 2010 at 1:59:42 PM permalink
Quote: tgolly

Ok so I did the math and the answer I get is 1.015. Does that mean the chances of the event occurring are 1%?

Looks like a calculation error. I have not tried to verify that the fractions you were given are correct, but even if they are, you are quite a few places off with the decimal point in your answer. Did you use a slide rule? (Sorry, just a geezer joke there.)
tgolly
Joined: Sep 15, 2010
• Posts: 4
October 15th, 2010 at 2:43:25 AM permalink
I want to know that odds of two people having a flush on a given flop.

Thanks :-))
Kelmo
Joined: Aug 15, 2010
• Posts: 85
October 15th, 2010 at 8:28:42 AM permalink
Quote: tgolly

I want to know that odds of two people having a flush on a given flop.

Thanks :-))

If I was to hazzard a guess, I would say there is about a 27.73% chance of getting one or more flush after the flop on a nine player game, if you include straight-flushes as well.

The question of what percentage of this would be exactly two, I did not look at this, as it is easier to determine what the chances are of no players making a flush in a nine player game and taking the remaining percentage as the answer. not to say that it would be too hard to figure out.
DorothyGale
Joined: Nov 23, 2009
• Posts: 639
October 15th, 2010 at 9:04:03 AM permalink
A computer simulation of 100,000,000 hands gives an answer of p = 0.001632 (about 1-in-613). In computing this ... exactly two people of the 9 flop a flush, and this is a flush, not a straight flush or a royal flush.

The results for 2 or MORE people flopping a flush on the same hand is ... p = 0.001689 (about 1-in-592).

I did some combinatorial computations that show this is reasonable, so I trust this result. This is a very tough combinatorial problem. I see how to do it to get the exact answer, but the sheep and pigs are waiting for breakfast ...

Note ... this does NOT answer the question "suppose I flop a flush, what is the probability that one of the other 8 players also flopped a flush?" That is a different question.

--Dorothy
"Who would have thought a good little girl like you could destroy my beautiful wickedness!"