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Server Time: 11/20/2008 9:48:20 PM PACIFIC |
 Flush Odds, Scott Bickley, 10. Dec 2003 16:22 | ||
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| I have read that the statistical probability of being dealt a flush is 4.xx%. Can someone show me the math on this one? Simple but stumped. | ||
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| Re: Flush Odds, SpaceAce, 10. Dec 2003 16:55 | ||
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| Do you mean your chances of getting a fourth flush card on the very next card? For instance, in Hold'Em, you get AsKs and the flop is xxx with two spades, what are your chances of getting a spade on the very next card? If so, the chances are 9 out of 47, or 38:9 (thirty-eight cards that will not make your hand and nine that will). That's around 4.85:1 (rounded), I think. Two figure it over both the turn AND river, it's 1 - (number that will NOT make your hand on the turn * number that will NOT make your hand on the river) / (total unseen cards on turn * total unseen cards on river) So, 1- (38*37) / (47*46) = about 35% (1.86:1 against) chance of making it if you stay for the turn and river. SpaceAce | ||
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| Re: Flush Odds, Scott Bickley, 10. Dec 2003 17:03 | ||
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| Thanks for the input, but I'm referring to the overall chances of having a flush dealt starting with zero cards. So knowing there are 13 per suit, what are my chances starting from ground zero of being dealt the flush. Can you help there? Your other explanation is also appreciated. Thanks, | ||
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| Re: Flush Odds, Aisthesis, 10. Dec 2003 19:56 | ||
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| For a 5- card hand it's fairly easy: The first card can be any suit, then the next ones all have to be the same, hence (12/51)*(11/50)*(10/49)*(9/48). For 7 cards it's a bit more complicated, since you have to take the total number of 7 card combinations, then see how many have 5 cards of one suit, how many have 6, and how many have 7. Since the practical relevance is not very high, I won't grind out the math, but that would be the basic idea. | ||
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| Re: Flush Odds, Chris W, 11. Dec 2003 18:11 | ||
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| The probability that you will be dealt a flush on the next hand is 3.05% assuming that you know nothing about your starting hand. There are three different cases where you will make a flush: 1. All seven cards are of the same suit: there are C(13,7) ways to select seven cards from one suit and four suits to choose from so there are C(13,7) x 4 = 6864 2. Six of the cards are the same suit: there are C(13,6) x 4 x 39 = 267696 ways to select six cards from one suit (and the seventh card is selected from one of the remaining 39 cards from the other suits). 3. five of the cards are the same suit: there are C(13,5) x 4 x C(39,2)= 3814668 ways to select five suited cards. So there are a total of 4089228 ways to make a flush out of a total of C(52,7) = 133784560 boards. Dividing that gives us 3.05%. Note that the third case includes some flushes where none of your whole cards contribute to your flush. If you're interested in the answer where you must use at least one card you need to subdivide case three to eliminate those flushes. | ||
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| Re: Flush Odds, Scott Bickley, 12. Dec 2003 19:54 | ||
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| Thanks, that was the explanation I was seeking. | ||
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| Re: Flush Odds, Mikewad, 14. Dec 2003 03:56 | ||
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| according to the mad genious himself (Mike Caro) the odds of being dealt a flush in 5 card draw is 367 to 1. But you will have to compensate for a joker not being in the deck so probably closer to 400 to 1. I dont try to figure out the mathamatical solutions No sense in reinventing the wheel. Good Luck | ||
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