View Full Version : Calculating Probability of Flush

06-17-2003, 12:15 PM
Can someone tell me the probability of getting a flush in hold 'em if you have suited hole cards and no other cards have been seen. How is this calculated?

06-17-2003, 12:29 PM
Most do this with combination probability but i don't think you are pascal and will be able to work out his combination triangle at a poker table, so i'll show you the pretty basic way.

You want 3 cards of your suit over a possible 5 cards.

P(SSSNN) S standing for suited and N for not. Not that can be re writen as P(NNSSS) (just showing the different orders these cards can come out).

Which is: 10 different ways.

Then to work out probabilities you take the amount of cards left that you want divide the total amount of cards.

Imagine eye colour, assuming we only have blue, green and brown and they all come out an equal amount, the probability the next new born kid has blue eyes is 1/3. 1 in every 3 kids born.

Ok, back to flush.

50 cards left in the deck, 11 of your suit.

Going with the order of: S S S N N you get:

11/50 * 10/49 * 9/48 * 39/47 * 38/46

then times this result by 10 (the amount of different orders it can happen, and you get:

0.057, also known as 5.7% also known as 1 in 17 times.

I think that is pretty accurate, i'm pretty sure someone will do combination probability next and get a minorily different answer to mine.

The probabilities you are concerned with when going for the flush are:

1 in 8 times you'll get your flush draw on the flop.
About 1 in 4 times you'll complete your flush on the next card.
1 in 2.5 times you'll complete your flush by the river

06-18-2003, 05:32 AM
JayP's formula is correct for figuring out the probability that 3 of the 5 board cards will be in your suit. (5.77%) You might also want to add in the probability that 4 or 5 of the board cards will be in your suit.

P(4 of 5) = 11/50 * 10/49 * 9/48 * 8/47 * 39/46 * 5
= c[11, 4]* 39 /c[50, 5]
= 0.61%

P(5 of 5) = 11/50 * 10/49 * 9/48 * 8/47 * 7/46
= c[11, 5]/c[50, 5]
= 0.02%

So the chance of making a flush in your suit starting with two suited cards preflop is

5.77% + 0.61% + 0.02% = 6.40% = 1 / 15.6