Poker Rarity - What are the odds???

mark424 · #1 10-13-2006, 01:34 PM

Last night at a home game, I held 9s 10s. The flop came out 3s 6s 9s. This is a $50 buy-in .25/.50 blind, NL Hold'em game. I let out from the small blind for $5 into about a $5 pot. I got 2 callers. The turn was a red card, so I led out $15. Both players called. The river was another red card. I bet $15 again and both players behind me went all in. Well, I only had $10 left, so I called figuring one of them had me. Well, BOTH of them had me. UTG had Ks 8s, and the button had Js Qs (No this was not a new deck that wasn't shuffled properly, this deck has been used for weeks). I know the odds of 1 player flopping a flush are somewhere around 1 in 120. What are the odds of THREE players all flopping a flush on the same hand?

Bantam222 · #2 10-13-2006, 01:58 PM

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Last night at a home game, I held 9s 10s. The flop came out 3s 6s 9s .

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I would think the odds would be good with this deck...

mark424 · #3 10-13-2006, 02:31 PM

Thanks smart-ass. Ok, I don't remember EXACTLY which spades flopped out, but the hole cards were correct, and 3 spades DID flop out. So again, I ask my question (to non smart-asses only)...what are the odds of 3 people flopping a flush?

Caballa · #4 10-13-2006, 02:54 PM

[ QUOTE ]
Thanks smart-ass. Ok, I don't remember EXACTLY which spades flopped out, but the hole cards were correct, and 3 spades DID flop out. So again, I ask my question (to non smart-asses only)...what are the odds of 3 people flopping a flush?

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100%

kaboshedx · #5 10-13-2006, 03:06 PM

[ QUOTE ]
Thanks smart-ass. Ok, I don't remember EXACTLY which spades flopped out, but the hole cards were correct, and 3 spades DID flop out. So again, I ask my question (to non smart-asses only)...what are the odds of 3 people flopping a flush?

[/ QUOTE ]

why dont you stop talking for a while.

wiggs73 · #6 10-13-2006, 03:19 PM

1 in eleventy billion

alphatmw · #7 10-13-2006, 05:19 PM

whats funnier here? how bad OP apparently is at poker or the fact that he really wants a response but no one's giving it to him?

mark424 · #8 10-13-2006, 05:51 PM

I think the funniest thing is you nerds posting on message boards for half your life and not having any friends. I also think it's hilarious that a [censored] thinks he can tell how good or bad someone is at poker by reading their only post on this message board in the last 6 months.

Grizwold · #9 10-13-2006, 06:48 PM

Whoah whoah relax. Take a chill pill everyone. Welcome to these forums. You will find an incredible amount of info here, and participating is even more fun and productive. However I do not think you will get very far calling people names and getting so angry when people point out some mistakes. That is one of the purposes of these forums, and if you can't deal with that then maybe you had better just be a lurker.

Anyway, mark still does have a legitimate math question and I will try to provide some input despite the fact that I am no math genius and I don't have a final answer. This is the first time I attempt to answer one of those long drawn out math problems, so please fix any erros. It seems your question is what are the odds of 3 opponents all holding cards of the same suit, and flopping 3 cards of that same suit. So this is a combination question, I starting thinking of what are the odds of each player getting 2/13 spades, then 2/11 spades, then 2/9 spades, and then 3/6 spades flop. And then multiply those figures together? But I thought about it a little more, and really the same scenario is that between 3 players and the flop, what are the odds that all 9 cards are of the same suit. So 13_C_9? And then divide that by 52_C_9 to get the final answer? This is where I get a lil foggy as you can see lol. But I'll give it my best shot hoping someone can help me learn...

13_C_9 = 13! / (9!*(13-9)!)
= (13*12*11*10)/(4*3*2)
=(13*11*5)
=715 possible combinations of 9 spades out of the first 9 cards being seen/dealt. (I'll assume 3-handed game only, though idk if that matters?)

52_C_9 = 52!/(9!*(52-9)!)
=52!/(9!*43!)
=(52*51*50*49*48*47*46*45*44)/(9*8*7*6*5*4*3*2)
=(52*17*10*7*47*23*5*11)
=3,679,075,400 possible 9 card combinations out of 52 cards in the first 9 cards being dealt/seen.

So...
715/3,679,075,400 = .00000019

So about 0.00002% chance?

Bantam222 · #10 10-14-2006, 03:30 AM

Why are there so many of these kinds of questions? This is fairly basic math as far as I can see...Plus your question is vauge. Do you want to know the odds of 3 specific people flopping the flush? or the the odds of 3 people of the 10 flopping a flush? are we assuming everyone is seething flop?