View Full Version : what is the probability of any 3 cards on flop?

08-10-2005, 01:42 PM
what is the formula for determining the probability of any three cards on the flop?

08-10-2005, 02:05 PM

Do you mean 3 cards suited? 3 of a kind (e.g., 3 Aces on the flop)? If so, then for suited it woould depend on if you have any of the suited or Aces in the hole.

But general forumla for all 3 desired cards showing up is
P(x) = (# ways an event can occur/total # of events)^3.

08-10-2005, 02:24 PM
what is the formula for determining the probability of any three cards on the flop?

[/ QUOTE ]


but I think you mean something else.

08-10-2005, 04:54 PM
You are liable to get some sarcastic answers here, which you do deserve for wording this question so ambiguously.

If what you mean is the odds of flopping 3 specific cards, given that you have no information about opponents' hole cards, the formula is as follows:

P = (3/50)*(2/49)*(1/48)

08-10-2005, 05:00 PM
yeah that's correct. my formula assumed replacement (i need to get some coffee before posting in the probability forum).

08-10-2005, 05:01 PM
just random cards on a flop

08-10-2005, 05:02 PM
Are they specific cards?
Not sure exactly you mean. If it helps there are 19,600 flops if order dosen't matter.

08-10-2005, 07:11 PM
Well there has to be a formula for the probablitlity of dealing three cards, ie, 52 cards one out, 51 cards one out 50 cards one out. I don't know how to express it in terms of a formula but I am sure it has something to do with powers and whatnot.

Sorry if this was ridiculously hard.

08-10-2005, 07:13 PM
If you mean three specific cards, like K /images/graemlins/diamond.gif 9 /images/graemlins/spade.gif 3 /images/graemlins/diamond.gif, the answer is 1/22,100. This is also the probability of two flops in a row being identical except for order. If you are looking at one of the hands, then the odds go to zero for flops that contain one or more of the cards in that hand, and up to 1/19,600 for all other flops.

Normally you want to compute the probability of ranges of hand. Say you're holding two spades and want to know the probability of flopping a flush. You can pick 3 from the 11 remaining spades in 165 ways, so the chance is 165/19,600.

08-10-2005, 08:34 PM
Your wording just didn't make sense. There are 19,600 flops if order dosen't matter. This is
C(50,3). Or 50*49*48 / 3*2*1. Is that what you wanted to know?

08-11-2005, 03:16 AM
i think what he wanted to know was that the probability of any flop coming out is 1/19600...

so about 0.005% for each flop...