Re: On the mathematics of three way ties

[osumo3@native.usc.edu (Olaf Meeuwissen)]

|> --- Begin redistributed message ---
|>
|> Date: Tue, 3 Aug 93 12:30:26 PDT
|> From: olaf@rcf.usc.edu (Olaf Meeuwissen)
|> Subject: Re: On the mathematics of three way ties
|> 
|> Oops, Martin is right. I did make a goof. I wrote:
|> 
|> |> The probability  that the basho is decided  after the n-th bout is given
|> |> by:
|> |>
|> |>  p(n) = 1/2 ^ n  for n > 1 (since two wins in a row are needed)
|> |>
|> |> where "^" denotes exponentiation.
|> 
|> where I should have written:
|> 
|> The probability that rikishi X decides the basho  in the n-th bout is given
|> by:
|> 
|> 	p(X,n) = p(n) = 1/2 ^ n	for n > 1 (two straight wins are needed)
|> 
|> where "^" denotes exponentiation.
|> 
|> This, summed over all rikishi and all  n, does yield  1, although not  in a
|> very straightforward manner.  I did check this in my previous post (see the
|> "NOTE").
|> 
|> Further,  it  may  be  interesting to note, that by  introducing S for  the
|> summation part, sum{ p(3i) }, I never have to actually do the summation and
|> arrive  at  equations  equivalent to  those  Martin  mentioned.   Also  the
|> summation is a standard one that you can look up in any math table book, so
|> it not as  hard as it looks, besides  it being freshman math level to begin
|> with (well, it is where come from ...).
|> 
|> Martin, thanks for pointing out the slip of the keyboard :-)
|> 
|>     ____
|>    / __ \ /\          ___  Olaf Meeuwissen           (e-mail: olaf@usc.edu)
|>   / / / // /____     / __\ Dept. of Chemistry, Univ. of Southern California
|>  / / / // // __ \  _/ /    ------------------------------------------------
|> / /_/ // // /_/ / /  _/    These days  are precious,  and I'd  rather spend
|> \____//_/ \_____\ / /      them goofing around than studying.
|>                  /_/                                              -- Calvin
|>
|> --- End of redistributed message ---

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