Odds of two people flopping a flush.

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.

Someone please reply with the answer.

Thanks

Tom Golly
tgolly@centurylink.net

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.

Someone please reply with the answer.

Thanks

Tom Golly
tgolly@centurylink.net

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.

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.

Someone please reply with the answer.

Thanks

Tom Golly
tgolly@centurylink.net

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.

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.

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."

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.

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.)

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

Thanks :-))

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.

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

Quote: Kelmo

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.

I misunderstood this question and was looking at it conditional to a flop. Obviously, as there is only a 5.18% chance of having a three card suited flop and any possible flushes.

Quote: DorothyGale

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. ...

My combinatorial result, 0.001655, is close to yours, but higher because I counted straight flushes and royals as flushes. Assuming the flop is three suited cards, here are my probabilties of having 0 to 5 flushes (including straight flushes and royals) for nine players:
0 0.69004
1 0.27676
2 0.03197
3 0.00121
4 0.00001
5 0.00000

Quote: ChesterDog

My combinatorial result, 0.001655, is close to yours, but higher because I counted straight flushes and royals as flushes.

This was exactly why I did the simulation for the flush (only) question. Getting over the "royal/straight" flush issue is very tough combinatorially.

I re-ran 100M rounds with the royals/straight flushes counted as flushes, to verify our results against each other. My simulation gave 165407 dual flushes in 100M rounds, for a simulated probability of 0.001654. I'd say we're close enough ...

Running time for the simulation was just under 3 minutes, was written in C, and used Cactus Kev's super awesome poker library with the addition of the fast_eval routine for 5 card poker hands.

--Dorothy