Effective odds

[countrynole]

Ok, I started reading Sklansky's book "The Theory of Poker," and I got to the chapter about effective odds. The example that he uses is getting a four-flush off the flop in hold 'em. He then says that the odds of completing the flush within the next two cards is 1.75 to 1; and if you dont get it on fourth street then the odds are about 4 to 1. My question is, how did he calculate the odds of getting that card on fourth street?

P.S. I don't really need an explanation, just an equation would be fine.

Thanks

[bigpooch]

Without knowing any of your opponents' cards nor their
probability distribution, we can use the following
approximation: there are 47 unseen cards, 9 of which give
you a flush which is almost 1/5th of them so it is about
4:1 against turning your flush. It is just a crude
estimate.

[shutupndeal]

how about <and my math stinks as well> if we take the exact amount of cards that we know will give us the flush "9" and divide the remaining cards by that number so we will have a representation of all remaining cards divided by the helping cards to our flush like so
36/9 which results in a 4-1 shot to me, then you would divide that by 2 since you have 2 chances to make the flush with the 2 remaining draws Ok? Now, I can guarantee you that somehow and someway that Mason and David's math is somehow right but Ill be damned if I can see how they came up with it myself! lol [img]/images/graemlins/shocked.gif[/img] [img]/images/graemlins/shocked.gif[/img] [img]/images/graemlins/shocked.gif[/img] [img]/images/graemlins/shocked.gif[/img] [img]/images/graemlins/shocked.gif[/img] [img]/images/graemlins/shocked.gif[/img]

[BruceZ]

The probability of completing a flush draw in 2 cards is 35% or 1.86-1. David was just being approximate in that section. The 35% figure is well known (e.g. see appendix in HEP or HEPFAP). Here is a link to 3 correct methods for doing this problem. Taking "half the 4-1 odds" for 1 card to get 2-1 is an approximation which happens to be quite close. Note that this is not the same as doubling the probability or doubling the outs, which would be a much worse approximation because it double counts the times we get a flush card on both the turn and the river.

[shutupndeal]

Thanx so much for that Bruce, I get real leary answering even these simple Probability-Statistical problems as I have forgotten most of it, I used to be pretty decent at them and was one of those kids that got looked at sideways because I actually liked "MOST" Math in school. You see to me numbers was kinda like "straightforward," once you understood the way to do the equation they were all pretty much the same and so as long as you made sure you knew your rules you were Ok. It wasnt like that in other subjects for me where I actually had to think ya know? lol

Anyway, thanx again Bruce, I am gonne look into that 35% thing now cuz to be honest while it doesnt make sense to me yet I think I rememer that figure somewhere waaay back in like a stud book and Im kinda interested to see if Im right and whether or not it does translate to Holdem correctly.

Hey Bruce, ya think you could answer my question about Mike Pretriv's odds book somewhere here in the "probability" section, I posted it on the 8th I believe so it cant be too hard to find and now that I know who the resident genius is (you, of course aside from our wonderful hosts that is)) please dont be offended if I tap that resource between your ears once in a while Ok? [img]/images/graemlins/cool.gif[/img]

[BruceZ]

Hey Bruce, ya think you could answer my question about Mike Pretriv's odds book somewhere here in the "probability" section

I already did answer it at the bottom of this post in response to your other question.


You see to me numbers was kinda like "straightforward," once you understood the way to do the equation they were all pretty much the same and so as long as you made sure you knew your rules you were Ok. It wasnt like that in other subjects for me where I actually had to think ya know?

Probability is one area where you can easily justify the wrong answer, so for many problems it is necessary to think and understand the fundamentals, rather than just plugging into equations. You want to know principles rather than equations. You can do many problems very easily using just a few principles, but you have to understand them very well. The 3 methods for doing the flush draw problem require understanding the principles of independence, and mutually exclusive events. This post should help explain how those principles relate to this problem.


Anyway, thanx again Bruce, I am gonne look into that 35% thing now cuz to be honest while it doesnt make sense to me yet I think I rememer that figure somewhere waaay back in like a stud book and Im kinda interested to see if Im right and whether or not it does translate to Holdem correctly.

It would be the same for stud if you have a 4-flush on 5th street, but only if you don't take any of the other player's cards into account.