Little math problem(s) February 2019
02-20-2019, 02:14 AM
Post: #5
 Albert Chan Senior Member Posts: 627 Joined: Jul 2018
RE: Little math problem(s) February 2019
For best of N match puzzle, think binary, 0=lost, 1=win
let probability of better player winning be p, for whole tournament be T

Best of 1: 1 ==> T = p

Best of 2: 011 101 11 ==> T = p^2 *(1 + 2(1-p))

Best of 3: 00111 01011 01101 0111 10011 10101 1011 11001 1101 111
sort by length of games: 1x3 + 3x4 + 6x5, total 1+3+6 = 10 cases
==> T = p^3 * (1 + 3(1-p) + 6(1-p)²)

Best of 4: ... got coefficient of 1,4,10,20. My guess is the trend continues.
==> Best of N: T = p^N * sum(nCr(N-1+k,k) * (1-p)^k, k = 0 to N-1)

Code:
Best-of     Whole Tournament, expected better player winning 1      p =  60%    65%    70% 2         64.8%  71.8%  78.4% 3         68.3%  76.5%  83.7% 4         71.0%  80.0%  87.4% 5         73.3%  82.8%  90.1%  <-- T>90% for p=70%, best-of-5 6         75.3%  85.1%  92.2% 7         77.1%  87.1%  93.8% 8         78.6%  88.7%  95.0% 9         80.1%  90.1%  96.0%  <-- T>90% for p=65%, best-of-9 21        90.3%  97.6%  99.6%  <-- T>90% for p=60%, best-of-21
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 Messages In This Thread Little math problem(s) February 2019 - pier4r - 02-07-2019, 12:14 PM RE: Little math problem(s) February 2019 - pier4r - 02-11-2019, 10:10 AM RE: Little math problem(s) February 2019 - pier4r - 02-13-2019, 12:31 PM RE: Little math problem(s) February 2019 - pier4r - 02-19-2019, 07:40 PM RE: Little math problem(s) February 2019 - Albert Chan - 02-20-2019 02:14 AM RE: Little math problem(s) February 2019 - pier4r - 02-20-2019, 05:26 PM RE: Little math problem(s) February 2019 - Albert Chan - 02-20-2019, 06:39 PM RE: Little math problem(s) February 2019 - pier4r - 02-20-2019, 09:44 PM RE: Little math problem(s) February 2019 - Albert Chan - 02-20-2019, 10:55 PM RE: Little math problem(s) February 2019 - Albert Chan - 02-21-2019, 02:28 AM RE: Little math problem(s) February 2019 - lrdheat - 02-21-2019, 03:58 AM RE: Little math problem(s) February 2019 - lrdheat - 02-21-2019, 04:42 AM RE: Little math problem(s) February 2019 - ijabbott - 02-21-2019, 07:53 AM RE: Little math problem(s) February 2019 - Albert Chan - 02-21-2019, 10:59 AM RE: Little math problem(s) February 2019 - Albert Chan - 02-22-2019, 02:51 PM RE: Little math problem(s) February 2019 - lrdheat - 02-21-2019, 02:09 PM RE: Little math problem(s) February 2019 - pier4r - 02-23-2019, 01:15 PM RE: Little math problem(s) February 2019 - pier4r - 02-23-2019, 01:23 PM RE: Little math problem(s) February 2019 - Albert Chan - 02-23-2019, 04:23 PM RE: Little math problem(s) February 2019 - pier4r - 02-23-2019, 08:15 PM RE: Little math problem(s) February 2019 - Albert Chan - 02-23-2019, 10:01 PM It's easy to use LaTeX in your posts - Thomas Klemm - 02-23-2019, 04:06 PM RE: Little math problem(s) February 2019 - pier4r - 02-23-2019, 08:09 PM RE: Little math problem(s) February 2019 - pier4r - 02-23-2019, 11:55 PM

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