question about calc'ing odds with 3 to a flush...

[waterman]

this is my first post on this site, so i hope i'm not being redundant by asking this question, as i don't know if it's been asked before, but here goes anyways.

what i'm wondering is if when calculating my odds, and i've got 3 to a flush on the flop, should i be including the 10 remaining suited cards to my outs, or is that something more for when i've got 4 to a flush? i'm guessing that they should be included, as they'd obviously help my hand, but i'm wondering what methods other people might use. any help would be greatly appreciated.

an example is if i had A K , and the flop came Q 5 2 , my outs in that situation would be 3 A's, 3 K's, and any would help as well, wouldn't it?

sorry if this seems like a "newbie" question, but i've been playing for about a year and have just recently begun using out odds in live games, so that's why i'm asking.

again, any help is greatly appreciated.

[Skribbles]

I'll give this a shot.... but I'm bad at math so someone will prolly correct me.



You'd need 1 of 10 cards on the turn and 1 of 9 on the river, so....


10 out of 47 cards for the turn is 4.7:1 and 9 out of 46 on the river is 4.6:1.

So hitting them both would be 21:1 or about 4.5% of the time.


Before you take this to heart let someone confirm this.



Edit: This is for the flush only.

[TheSalche]

quick 'scrubby' calcuation
chance of hitting a heart on the turn: 25%
chance of hitting a heart on the river: 25%
chance of both being hearts = about 6.25%

round down cause there are already hearts out there and you have about 5% ... the exact percentage isnt quite important ... but i believe that you CAN count runner runner flush as "1 out"

[xDiamond_CutteRx]

Chance of runner-runner flush: (10/47)(9/46) = 4.1%

Holding AK on that board, you will make a pair of aces or kings roughly 24% of the time... if you add the runner-runner possibility, you will probably make some type of hand (pair, back-door straight or back-door flush) about 28% of the time with this hand.

Chance of Ace or King: 1 - ((1-6/47)(1-6/46)) = 24.1%
Chance of runner-runner flush: (10/47)(9/46) = 4.1%
Chance of runner-runner straight (4/47)(4/46) = 0.7%

But, these are not independent events, since if you make an ace or king you cannot make the straight or flush. I think you would have to use a stochastic formula for calculating your true probability, and there's no way I'm going into that. So we'll estimate making a pair or better about 26% of the time.

[waterman]

excellent, thanks a lot guys. i figured that i'd be better off just calc'ing the odds for making a pair after the flop comes, and if a heart happens to hit the board on the turn, then i could add the flush into the math.

[snoogins47]

excellent, thanks a lot guys. i figured that i'd be better off just calc'ing the odds for making a pair after the flop comes, and if a heart happens to hit the board on the turn, then i could add the flush into the math.

If you throw a backdoor flush draw into the equation by adding "about one out" that'd probably be fine.

[Silhouette]

I never knew you could count runner runner as an out. That's brilliant.

[Sean_in_NJ]

I never knew you could count runner runner as an out. That's brilliant.

Odds of a runner runner flush are ~22:1, which is the about the same odds as a single card coming on the turn.

[Adamm]

BTW, nice job diamond. The math was good, but using the word "stochastic" was just showing off.