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Server Time: 3/15/2010 5:07:19 PM PACIFIC |
 Rolled up at 7 Card Stud, therazz, 22. Oct 2002 09:25 | ||
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| What are the odds of two players being rolled up during the same 7 Card Stud hand? | ||
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| Re: Rolled up at 7 Card Stud, Mano, 23. Oct 2002 10:47 | ||
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| on 22. Oct 2002 09:25 therazz wrote: > What are the odds of two players being rolled up during the same 7 Card Stud > hand? By my calculations in a 7 handed game the odds are about 8668:1 against 2 or more rolled up hands. I can go into details if you care about how I calculated it. | ||
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| Re: Rolled up at 7 Card Stud, therazz, 24. Oct 2002 12:00 | ||
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| tyvm Mano, for your calculation. I thought it would be more than that. If it's not too much trouble, how did you calculate this? Thanks. | ||
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| Re: Rolled up at 7 Card Stud, Mano, 24. Oct 2002 14:27 | ||
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| OK. First of all compute the probability of 3 random cards all being the same rank. There are 4 ways to have trips in any rank, 13 different ranks, so there are 52 different ways of being dealt 3 of a kind. There are C(52,3) = 22100 different 3 card combinations in an ordinary deck (52*51*50 different ways to get dealt 3 cards divided by 6 different orders for every 3 card combo). So the probability that a random hand is rolled up is 52/22100 = .00235. Lets call this probability P. Let Q = the probability that you are NOT dealt three of a kind, which is = 1-P or about .9976. The probability that noone is dealt 3 of a kind is Q^7 The probability that only the first player is dealt 3 of a kind is P*Q^6 . Likewise for the probability that only the second, third and subsequent players. So the probability that either zero or 1 players are dealt 3 of a kind is Q^7 + 7*P*Q^6 = .999884645 . Call this probability S. Now, the probability that at least 2 people are dealt 3 of a kind is 1 - P(zero or one person dealt 3 of a kind) = 1 - S. To go to odds you take (1 - probability)/probability = (1 - (1 - S))/(1-S) = S/(1-S) which rounds up to 8668 : 1 against. Clear as mud, aye. Well hope this helps. | ||
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| Re: Rolled up at 7 Card Stud, therazz, 25. Oct 2002 22:33 | ||
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| Thank you so very much for all your trouble and effort Mano. I've played many hands of Stud in my life and never came accross this until last week. I was rolled up with 5's and lost to a friend of mine who was rolled up with 6's. I didn't beleive him :-( | ||
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| Re: Rolled up at 7 Card Stud, george epstein, 27. Oct 2002 13:50 | ||
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| Without resorting to combinations and permutations, I get a somewhat different answer: 25,707 to 1 against two players being rolled up on third street>>> Odds of getting 3-of-a-kind on third street are 424 to 1 against you. (3/51 x 2/50 -- that's 1/425 chances or 1/424 odds). There are 7 remaining players; so odds of a 2nd player getting 3-of-a-kind are 7/424. Odds of both events in same deal: 1/424 x 7/424 = 1/25,707. george | ||
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| Re: Rolled up at 7 Card Stud, Mano, 29. Oct 2002 02:08 | ||
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| on 27. Oct 2002 13:50 george epstein wrote: > Without resorting to combinations and permutations, I get a somewhat different answer: > 25,707 to 1 against two players being rolled up on third street>>> > Odds of getting 3-of-a-kind on third street are 424 to 1 against you. (3/51 x 2/50 -- > that's 1/425 chances or 1/424 odds). > There are 7 remaining players; so odds of a 2nd player getting 3-of-a-kind are 7/424. > Odds of both events in same deal: 1/424 x 7/424 = 1/25,707. > george > Checked my numbers and they seem OK - please let me know if you see any errors in my math or logic. Not sure, but I think the difference in our calculations may be that I was figuring the odds at least 2 players having 3 of a kind, and you are calculating the odds of yourself and one other player having 3 of a kind. There are C(7,2) = 21 unique subgroups of 2 players that can be made from a group of 7 players, which would explain the approximately factor of three difference in our answers. Again, I am no expert (been a long time since I took a probability class), so if you see any flaws in my reasoning please let me know. | ||
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| Re: Rolled up at 7 Card Stud, LuckyOne, 28. Nov 2002 16:41 | ||
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| I don't think I like the answer, because the way you calculated, the more people in the hand the LESS chance there is of being rolled up! I think manos calculations SOUND more impressive, but it doesn't fit with my intuitive idea that a thing that has a 1/400 chance matched with another thing with 1/400 is about 1/16,000 for heads up Smile and say Hi at the tables to LuckyOne, LuckyWon, LuckyToo, ScoopHL or LuckyGal | ||
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| Re: Rolled up at 7 Card Stud, LuckyOne, 28. Nov 2002 16:34 | ||
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| well, it is about 400 to one that one player is rolled up, and in all the hilo , and stud hi I have played, live and online, it has only happened to me twice. Once i was the winner and once the loser, but the loser was at fifteen thirty, lol, and the winner was 1488, so you can guess that I am way behind rollup versus rollup. Seriously, if two people play heads up I think it is about 400 times 400 , and every additional person makes it one chance in four hundred more likely. That is not exact, but I think it is relatively close enough for you to at least visualize the odds, and I almost guarantee, that someone who really gets into these things will let me know exactly how wrong I was ;-) I am sure the numbers get skewed when you take three of one rank out of the deck, lol, so the answer isn't exact by a long shot! Smile and say Hi at the tables to LuckyOne, LuckyWon, LuckyToo, ScoopHL or LuckyGal | ||
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