Little math problem(s) February 2019

02202019, 02:14 AM
Post: #5




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(1p)) 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(1p) + 6(1p)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(N1+k,k) * (1p)^k, k = 0 to N1) Code: Bestof Whole Tournament, expected better player winning 

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