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 05-21-2012, 04:20 AM #1 centurion   Join Date: Apr 2011 Posts: 150 Four to a flush on the community board: % chance he has a flush We are playing No-Limit Hold'em, and the river puts 4 diamonds on the community board. My opponent and I are heads ups and I have no diamonds. Not considering dead cards, what is the percent chance he was dealt a diamond? This is also read independent just for the sake of simplicity. Thanks for the help.
 05-21-2012, 04:54 AM #2 adept     Join Date: Jun 2005 Location: Playin' It Smart Posts: 749 Re: Four to a flush on the community board: % chance he has a flush There's 45 unseen cards, and 36 non-diamonds among them. The chance he has no diamonds is (36/45)*(35/44) = 1260/1980 = 63.6%. So the chance he has at least one diamond is 1 - .636 = 36.4%.
 05-21-2012, 05:19 AM #3 centurion   Join Date: Apr 2011 Posts: 150 Re: Four to a flush on the community board: % chance he has a flush Thanks man, I knew it was not as scary a situation as it appears to most people. I got like 40% (I am a math idiot), but this is even better. Almost every one seems to think, "he has got to have at least one diamond!"
05-21-2012, 06:47 AM   #4
journeyman

Join Date: Sep 2004
Posts: 360
Re: Four to a flush on the community board: % chance he has a flush

Quote:
 Originally Posted by MorrowCosom This is also read independent just for the sake of simplicity.
This is an important assumption in your question. Reads are very important in real-life scenarios.

A possible scenario:
He bets the river. You raise his bet. He moves all-in. It's not gonna be close to 36.4% I guess.

Quote:
 "he has got to have at least one diamond!"
So sometimes this might be a legit thought.

05-21-2012, 12:08 PM   #5

Join Date: Jun 2005
Location: Playin' It Smart
Posts: 749
Re: Four to a flush on the community board: % chance he has a flush

Quote:
 Originally Posted by MorrowCosom Almost every one seems to think, "he has got to have at least one diamond!"
If he's been betting with a bunch a diamonds on the board, that should increase your subjective estimation of the probability he has diamonds, since he's apparently not worried about you having a flush.

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