Four to a flush on the community board: % chance he has a flush

[MorrowCosom]

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.

[MApoker]

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%.

[MorrowCosom]

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!"

[cyberfish]

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.

"he has got to have at least one diamond!"

So sometimes this might be a legit thought.

[MApoker]

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.