probability of over-cards

[Paul Thomson]

Hi Guys -

Sorry for the elementary question, I'm bad at probability.

What is the probability of over-cards landing on the flop in hold'em.

For example, if the Hero holds 88.

What is the probability of one over card on the flop? two over cards? and 3 over-card?

More advanced...what if the Villain holds A2? of AJ?

Thx in advance. I can probably figure out how to calculate in the future if u show the math.

[Paul Thomson]

bump...can anyone help me with the first part?

what is the probably of two over cards and 3 overcards landing on the flop if the Hero holds 88?

thx again.

[rufus]

There are 50 unknown cards, so the number of possible flops is
50 choose 3 = (50*49*48)/(3*2*1)
If you're holding 88o there are 24 overcards (A-9 * 4) so there are
(24 choose 0) * (26 choose 3) = 1 * (26*25*24)/(3*2*1)
ways to have no overcards
(24 choose 1) * (26 choose 2) = 24/1 * (26*25)/(2*1)
ways to have one overcard
(24 choose 2) * (25 choose 1) = (24*23)/(2*1) * 26/1
ways to have two overcards
(24 choose 3) * (25 choose 0) = (24*23*22)/(3*2*1) * 1
ways to have three overcards.

So you can take the fractions to figure out your probabilities.

[Paul Thomson]

rufus...you the man. thx

[Adrian20XX]

http://www.math.sfu.ca/~alspach/comp34/

Regards ...