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Server Time: 10/15/2008 11:51:57 PM PACIFIC |
 Flush Draw Probability, CRCarson, 29. Nov 2003 03:52 | ||
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| My starting hand is suited. Say, Ad9d. What is the probability of making a flush with five cards to come, AND what is the mathematical formula for calculating it? Thanks. | ||
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| Re: Flush Draw Probability, MozMan, 29. Nov 2003 04:03 | ||
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| There are 11 cards out of 50 that are diamonds, so you are 50:11, or roughly a 5:1 dog to make your flush. -Moz "Hey! You made me ink!" | ||
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| Re: Flush Draw Probability, ADAM THE EXPERT, 29. Nov 2003 15:36 | ||
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| MOZMAN, I LIKE YOU, BUT BOY, ARE YOU WAY OFF!! | ||
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| Re: Flush Draw Probability, MozMan, 29. Nov 2003 21:24 | ||
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| Yup, I was thinking of the four flush... ugh... somtimes one fires off automatically without any real thought! :) -Moz "Hey! You made me ink!" | ||
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| Re: Flush Draw Probability, PairTheBoard, 29. Nov 2003 05:14 | ||
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| I'll take a stab at it. I think the answer is around 1 in 17 or so. Let's see if that's what I get. A standard formula used in a lot of these problems counts the number of ways you can choose k objects from N without replacement. We can use shorthand notation for this number as C(N,k). It is calculalted by: C(N,k) = N*(N-1)*...*(N-k+1)/k! where k!= k*(k-1)*...*2*1 You can calculate the probabilities of hitting exactly 3 of your suit, exactly 4 of your suit, and exactly 5 of your suit. Then add them together. For exactly 3 of your suit, the number of 5 card combinations, not counting order is C(50,5). This is the denominator. The numerator is the number of ways 3 of your suit can be chosen from 11, multiplied by the number of ways 2 cards not of your suit can be chosen from 39. Thus the probabilty is: C(11,3)*C(39,2) / C(50,5) = (11*10*9/3*2)*(39*38/2) / (50*49*48*47*46 /5*4*3*2) I think I'll just let you punch these into your calculator. Similarly, the probabiities for exactly 4 and exactly 5 of your suit is given by: C(11,4) * 39 / C(50,5) and C(11,5) / C(50,5) Calculate all three and add them together. | ||
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| Re: Flush Draw Probability, ADAM THE EXPERT, 29. Nov 2003 15:35 | ||
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| DEAR CRCARSON ASSUMING THAT YOU NEVER GO FOR A BACKDOOR FLUSH DRAW THE CHANCES OF MAKING A FLUSH, IS 4.61 PERCENT. HOWEVER, YOU CANNOT ASSUME THAT YOU WILL NEVER GO FOR A BACKDOOR FLUSH!! SOMETIMES, THE POT WILL BE SO BIG, THAT YOU HAVE TO "TAKE ONE OFF" OTHER TIMES, YOU WILL BE GIVEN A FREE CARD, AND NOW PICK UP A FLUSH DRAW (AND HAVE SUITABLE POT ODDS TO CALL) WITH THESE VARIABLES, IT'S IMPOSSIBLE TO TELL YOU THE EXACT ODDS, EVEN IF I WAS A MATH GENIUS LIKE MIKE OR MASON (WHICH ALL MY READERS KNOW: I'M NOT!!! AND NOT ASHAMED OF IT!!) FIGURE ANOTHER 1 PERCENT OR SO, DEPENDING ON THE GAME, HOW MANY FREE CARDS ARE GIVEN, POT SIZE, ET CETERA ENJOY!! A.T.E. | ||
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| Re: Flush Draw Probability, jajo, 10. Dec 2003 09:08 | ||
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| The easiest and most accurate way to calculate this is by using the combination formula. all possible 5-card combinations are: 50 C 5 = 2,118,760 combinations that contain three-flush: (11 C 3) * (39 C 2) = 165 * 741 = 122,265 cobinations that contain four-flush: (11 C 4) * (39 C 1) = 330 * 39 = 12,870 combinations that contain five-flush: 11 C 5 = 462 adding it all up: 122,265 + 12,870 + 462 = 135,597 135,597 / 2,118,760 = .0639 your chance of hitting a flush is therefore 6 percent. you can see mnay other odds calculations on my website: http://pokerstrategy.org/poker_stats/poker_stats.htm | ||
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