#1
|
|||
|
|||
Beginners question
How can you calculate the chance of flopping a flushdraw using combinations? Thank you. |
#2
|
|||
|
|||
Re: Beginners question
I'd say the easiest way is to type something like: Take p = C(n,k) / n! ^ exp(k), where n is the number of suits, k is the expected value, and divide p by C(x, f), where x is the number of cards in a standard deck and f is the number of cards in a standard flop. The sheer idiocy of what you type will then induce Mike Haven, Lorinda, BruceZ, or Irchans to calculate the correct chance for you. PP |
#3
|
|||
|
|||
Re: Beginners question
Carlos, I always find it difficult to explain probability, but I will give it a try. C(m,n) is the number of ways that you can pick n items from a list of length m if the order that you pick them is unimportant. To figure out the probability of flopping a flush draw, you need to calculate the number of possible flops and the number of flops with flush draws. Then (prob flushdraw) = (number flushdraws) / (number flops) The number of possible flops is C(52-2, 3) if you hold 2 cards. If you hold two suited cards, there are C(13-2,2) ways to choose 2 cards in your suit from the remaining 11 cards. There will also be one other, non-suited card in the flop. There are 13*3 possible non-suited cards. (number flushdraw) = C(11,2)* 13*3 (number flops) = C(50,3) (prob flushdraw) = C(11,3) * 13*3/ C(50,3) = 0.328316 I will attach a url with some basic poker probability. Lastly, it is very easy to make mistakes in reasoning when doing probability, so it is best to check answers before posting them. I will foolishly skip the verification step in this post do to lack of time. Hopefully, at least the reasoning is readable even if there is an error. |
#4
|
|||
|
|||
lol [img]/images/smile.gif[/img] *NM*
|
#5
|
|||
|
|||
Re: Beginners question
Okay, sorry about that...here's the real answer. I'm assuming that your question is: If I hold 2 suited cards, what is the chance that exactly 2 cards of the same suit will come on the flop? So, pre-flop 50 cards are unknown to you, 11 of which are in the desired suit (leaving 39 in the other 3 suits). The number of possible flops is: C(50,3) The number of flops with 2 of your suit and one other is: C(11,2) * C(39,1) So, your chance of flopping a flush draw is C(11,2)*C(39,1) / C(50,3) or roughly 11%. If this seems fishy, you can always double check it with the good ol' probability tree... Chance of your suit then your suit then other: (11/50)*(10/49)*(39/48) Chance of your suit then other suit then yours: (11/50)*(39/49)*(10/48) Chance of other suit then two of yours: (39/50)*(11/49)*(10/48) Add them all together and you get: (3*11*10*39) / (50*49*48) This is what C(11,2)*C(39,1) / C(50,3) reduces to when you...er...reduce it. Hope that helps, PP |
#6
|
|||
|
|||
Re: Beginners question
Hey Irchans, I was too slow adding my real answer -- you beat me to it [img]/images/wink.gif[/img]. I like your explanation, but I think you might have made a small typo in the line: (prob flushdraw) = C(11,3) * 13*3/ C(50,3) = 0.328316 It should be C(11,2), not C(11,3). Make that change, and our two posts will agree. PP |
#7
|
|||
|
|||
Re: Beginners question
I knew I would make a mistake! Thanks for the catch Pseudo. C(11,2) * 13*3/ C(50,3) = 0.109439 |
#8
|
|||
|
|||
Thanks all! *NM*
|
|
|