Author: Eric Campos
Date: 19:31:04 07/25/03
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On July 25, 2003 at 14:31:58, Tom Kerrigan wrote: >On July 25, 2003 at 07:14:19, George Tsavdaris wrote: > >>On July 24, 2003 at 23:46:50, Tom Kerrigan wrote: >> >>>Given a round robin tournament with 13 participants of equal strength, 5 of >>>which are The King: >>> >>>There's a 14% chance The King would take the top 3 spots. >> >>I don't know for sure***, but i think you are wrong. >> >>Because if the participants have equal strength we can do the following: >> >>If N is the number of all possible classifications of the programs >>then N = 13!/5! as we have five "The King". > >As Ricardo Gibert pointed out, this doesn't take into account the possibility of >draws. I imagine the program I wrote is reasonably accurate. > >-Tom When talking about the probability of a certain program coming in 1st or 2nd place, I don't think the possibility of draws comes into play. I understand that the possibility of "ties" in the ranking does come into play, but that's a different story. I have to agree with George's math. As a check, the prob(1st and 2nd and 3rd) is 5/13 * 4/12 * 3/11, which gives the same result of 3.50%. This ignores the fact that programs can tie in the rankings, e.g. CM could tie another program for 3rd / 4th place, but we haven't defined how to treat this case anyway. When I check your 11.4% expected 1st place outcome for other programs, something doesn't add up. 11.4% * 8 = 91.2%, which leaves CM only an 8.8% chance of clinching 1st. The probability of getting 1st, 2nd and 3rd must be less than this, but your simulation shows 14%. Perhaps I just misunderstand what you meant with your 11.4% number. The probability of a non-King program winning is still 1/13 (7.69%). Consider ties: -------------- The probability of sole possession of 1st place is lower than 7.69%. The probability of 1st place or sharing 1st place is greater than 7.69%. So the answer depends on how you want to define 1st place. One last thought: If all of the programs had equal capability, the odds of The King getting 1st, 2nd, and 3rd is exactly equal to the odds of it capturing the last three places! - Eric
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