Easy Hold 'em Question

[FletchJr.]

Ok here's the situation,
I got KJs and I flop the flush.
There's another player in the pot and i figure he's got the Ace but he's not suited. What's the chances of him hitting the a 4th flush card on me.

I think it's like this
flop 3 cards seen, 2 in my hand. that's 5 flush cards seen. out of the 13, but then there's 1 i assume the opponent has. That means 6 cards out of 17 which leaves 7.
7/45(52-2(my hand)-2(his hand)-3(flop))
equals .1555555
river
7/44
equals .159090909
so I think I should add those two together.
done.
.31464646
But how do I find my chances I mean like 3.123 to 1,

So that's what i know, or think i know. But I'm sure it's easy to do, if someone could show me once. I shouldn't have a problem with any other math problems.(Hold'em anyways)
Thanks, Also I'd like to figure out exact percents, nothing close, exact figures rounded to like the 100th's.

[pudley4]

The easiest way is to figure out the chance that he doesn't hit the flush, then subtract from 1 to find the chance he does.

7 total cards known, 45 remaining. 6 flush cards known, 7 remaining.

Probability of not hitting on the turn= 38/45.
Probability of not hitting on the river= 37/44.

Multiply these together to get 1406/1980.
Subtract from 1 to get 574/1980=.28989.... So he has a 28.9898% chance of hitting the flush by the river.

To figure out the odds, it's 1406 to 574 against him hitting=2.449 to 1 against.

[pudley4]

The other way to figure it out is to figure out the chance of hitting on the turn, then adding the chance of hitting on the river (what you tried to do in your example).

You got the chance of hitting on the turn (7/45)=.1555555

The chance of hitting on the river is the chance he didn't hit on the turn (38/45) multiplied by the chance he did hit on the river (7/44) = .134343434...

Add the two together to get .2898989...

[Zoe's Echo]

Pudley4,

I was just wondering if the Ax's odds of hitting the flush are .28989 - isn't the Ax a 3.449 to 1 dog here??

574 wins versus 1980 possible outcomes

Good Luck!

[FletchJr.]

Perfect after a few reads, It became clear as glass. Hey also thanks for the fast post /forums/images/icons/smile.gif It is simple as i thought it would be, but extremely important.

[Lin Sherman]

True odds are the ratio of losing outcomes to winning outcomes. So the true odds are (1980-574):574 = 1406:574 = 2.449:1

Lin

[FletchJr.]

Just as pudley4 posted:
The easiest way is to figure out the chance that he doesn't hit the flush, then subtract from 1 to find the chance he does.
The brackets are my added information so it is easier to understand)

"7 total cards known,(2 flush cards you hold, ace flush card the opponent holds, the other non flush card the opponent holds and the flop) 45 remaining (52 - 7 known). 6 flush cards known ( 3 on flop, 2 in your hand, and two 1 in opponents hand), 7 remaining.

Probability of not hitting on the turn= 38/45. (45 - 7 flush cards left)
Probability of not hitting on the river= 37/44. (44 - 7 flush cards left)

Multiply these together to get 1406/1980. (this is the chance of him not getting the flush)
(subtract from one gives you the opposite, so obviously the chance of him getting the flush)Subtract from 1 to get 574/1980=.28989.... So he has a 28.9898% chance of hitting the flush by the river.

To figure out the odds, it's 1406 to 574 (chances of him not getting the flush compared to him getting the flush) against him hitting=2.449 to 1 against.

Yet again thanks for the perfect post pud