Probability of facing a diamond card on the flop

[SunKidDance]

Hi,
an easy question, but i can't figure it out myself at the moment [img]/images/graemlins/confused.gif[/img] :

What is the probability of facing at least one opponent on the flop with a exactly one diamond card, if there are three opponents and you do not hold a diamond card yourself?

Thanks,

SKD

[Buzz]

Hi SunKidDance - Do you mean "What is the probability at least one of three opponents holds at least one diamond?

The answer depends on what the flop cards are.

If the flop has three diamonds, and you have two non-diamonds, then there are
• ten missing diamonds and
• thirty seven missing other cards.

In that case, your three opponents have six cards between themselves. The probability at least one of those six cards is a diamond is most easily found by finding the probability none of them is a diamond, and then subtracting from 1.

1-C(37,6)/C(45/6) =
1-2324784/8145060 =
1-0.28542258 = 0.71457742

So if there are three diamonds on the flop, then it's about 7 to 3 that at least one of your three opponents has at least one diamond.

I'm not sure if that's what you wanted or not.

Buzz

[SunKidDance]

Hi Buzz,

that's exactly what I wanted to know.
Thanks a lot!

SKD