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Odds Clarfication, mrbippy, 24. Aug 2003 17:55
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I have seen odds calculated several ways and was wondering how its really done.

Lets say I have 9 outs to a flush on the flop.

I have seen this represented as both 47/9 and 38/9

Which of these are correct?

Also how can I calculate the odds of one of my 9 cards falling on the flop and or the river. Can this be done without converting the fractions into percentages first?
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Re: Odds Clarfication, Paul Stine, 24. Aug 2003 21:00
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on 24. Aug 2003 17:55 mrbippy wrote:
> I have seen odds calculated several ways and was wondering how its really
> done.
>
> Lets say I have 9 outs to a flush on the flop.
>
> I have seen this represented as both 47/9 and 38/9
>
> Which of these are correct?
>
> Also how can I calculate the odds of one of my 9 cards falling on the flop and
> or the river. Can this be done without converting the fractions into percentages
> first?

Bippy,

First, try and think directly in terms of odds instead of fractions. 47 unseen cards - 9 outs = 38 misses. 38:9 is about 4.2:1. Note that this number is only accurate for the next card, if you have more than one card to come you need to do a different calculation...

A quick and dirty (a little inaccurate but fast) way to calculating your percent change of completing your draw is to multiply your outs (9) by 2% for each card yet to come (2). This says that with two cards to come your will complete your draw about 9*2*2% or 36% of the time. Since 33% is 2:1 against we know that 36% is close to about 1.8:1

Now, if your expected cost to continue times 1.8 is greater than the size of the pot, you are good to go (assuming you will win if you complete your draw: not always true.)

Paul Stine
College Station, TX
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Re: Odds Clarfication, George Rice, 25. Aug 2003 22:21
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The odds of one of your suit coming on the turn is 9/47 = .19149 = 1/ 5.222 = 38:9 against = 4.22:1 against. They all mean the same thing.

If you missed the turn, the odds of you making the flush on the river is 9/46 = .19565 = 1/5.111 = 37:9 against = 4.111:1 against. Again, they all mean the same thing.

The odds of flush cards coming both on the turn and river is 9*8/47*46 = .0333 = 1/30 = 29:1 against.

The overall odds of making your flush is 2(9*38 + 9*8/2)/47*46 = .34968 = 1/2.8588 = 1.8588:1 against.

The odds of only one of your flush coming is 2*9*38/47*46 = .31637 = 1/3.1608 = 2.1608:1 against. And yes, this is .0333 less than the chances of making the flush overall.




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