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Maverick511
10-15-2004, 10:33 PM
I know in holdem if you have four to the flush on the flop, you have a 19% chance to hit your flush on the turn and a 19.5% chance to hit it on the river. However if you are all in on the flop, you have a combined 35% chance to hit it from flop to river. Can anyone show me the math used to calculate the 35%??

Thanks
-=Maverick=-

BruceZ
10-15-2004, 11:08 PM
[ QUOTE ]
I know in holdem if you have four to the flush on the flop, you have a 19% chance to hit your flush on the turn and a 19.5% chance to hit it on the river. However if you are all in on the flop, you have a combined 35% chance to hit it from flop to river. Can anyone show me the math used to calculate the 35%??

Thanks
-=Maverick=-

[/ QUOTE ]

You already asked that, and got perfectly good answers (http://forumserver.twoplustwo.com/showthreaded.php?Cat=&amp;Board=probability&amp;Number=106 3497&amp;Forum=,All_Forums,&amp;Words=&amp;Searchpage=0&amp;Limit= 25&amp;Main=1063497&amp;Search=true&amp;where=&amp;Name=6964&amp;dater ange=&amp;newerval=&amp;newertype=&amp;olderval=&amp;oldertype=&amp;bo dyprev=#Post1063497) , so why ask again?

Mike Haven
10-16-2004, 08:42 AM
this is the way i do it, in simple English instead of by mathematical formulae, which are usually gobbledegook to me, i'm ashamed to have to admit

you know 5 cards

there are 47 unknown cards of which 9 are yours, so the fraction of the deck that fills your flush on the turn is 9/47ths

to find a percentage you multiply a fraction by 100, so (9/47) x 100 gives you the 19.15% chance of filling on the turn you mention

if you miss, you know 6 cards, and there are now 46 unknown cards, of which 9 are yours

the fraction is 9/46ths, or 19.57%

i think the step you are missing is that if you fail to flush on the turn you have to say that of the (100 - 19.15)% = 80.85% of time you fail you will then succeed on the river 19.57% of this time

19.57% of 80.85% is 80.85% x (19.57/100) = 15.82%

so you hit 19.15% + 15.82% of the whole time, which is 34.97% of the whole time

Vulpine
10-19-2004, 08:43 AM
The probability of making the flush by the river plus the probability of not making the flush by the river must add to 1. Its easier to calculate the probability of not making the flush on two trials because these are independent events.

The probability of not making a flush by the river is:

Probability of not making flush on turn * probability of not making flush on river

Which is:

(47 unseen cards  9 cards making a flush)*(46 unseen cards  9 cards making a flush)

Probability of making the flush by the river = 1  Probability of not making the flush by the river

Hence:

The probability of making the flush by river = 1  (38/47)*(37/46) = 34.967

This is a classic problem that was originally solved by both Blaise Pascal and Pierre de Fermat and set forth the modern theory of probability. See page 24 of the:

"American Mensa Guide To Casino Gambling: Winning Ways"
by Andrew Brisman, Sterling Publishing; (December 31, 1999)
ISBN: 080694837X