Author: Jason Williamson
Date: 16:34:04 04/25/01
Go up one level in this thread
On April 25, 2001 at 14:57:26, Dann Corbit wrote:
>On April 25, 2001 at 14:35:16, Uri Blass wrote:
>
>>On April 25, 2001 at 14:29:54, Dann Corbit wrote:
>>
>>>// stronger.cpp: Is your favorite player really stronger?
>>>// Programmed by Leen Ammeraal
>>>#include <iostream>
>>>#include <iomanip>
>>>#include <cmath>
>>>using namespace std;
>>>
>>>double binom(int n, int k)
>>>{ double x = 1;
>>> for (int j=0; j<k; ++j)
>>> x *= double(n - j) / (j + 1);
>>> return x;
>>>}
>>>
>>>int main()
>>>{ int n, nA, nB, nD;
>>> double p = 0.5;
>>> cout << "Player A may be stronger than player B "
>>> "or may have won by luck.\n";
>>> cout << "How many times has A won? ";
>>> cin >> nA;
>>> cout << "How many times has B won? ";
>>> cin >> nB;
>>> cout << "How many draws (preferably an even number)? ";
>>> cin >> nD;
>>> nA += nD/2;
>>> nB += nD/2;
>>> n = nA + nB;
>>> cout << "Our computation will be based on the score "
>>> << nA << " - " << nB << endl;
>>> double s = 0, t = 0;
>>>
>>> for (int i=0; i<=nB; ++i)
>>> { t = binom(n, i) * pow(p, i) * pow(1-p, n-i);
>>> // t is the probability of B obtaining i points.
>>> s += t;
>>> }
>>> // s is the probability of B obtaining nB points or less.
>>> // This is equal to the probability of A obtaining nA points
>>> // or more.
>>> cout << "If A and B had the same strength, the probability of A\n";
>>> cout << "obtaining this score (or better) would be equal to "
>>> << fixed << setprecision(1)
>>> << s * 100 << "%.\n";
>>> return 0;
>>>}
>>>/*
>>>E:\>stronger
>>>Player A may be stronger than player B or may have won by luck.
>>>How many times has A won? 5
>>>How many times has B won? 0
>>>How many draws (preferably an even number)? 0
>>>Our computation will be based on the score 5 - 0
>>>If A and B had the same strength, the probability of A
>>>obtaining this score (or better) would be equal to 3.1%.
>>>*/
>>
>>You are right if the probability to win is 50% but practically it is clear that
>>there is a positive probability for a draw so 3.1% is only an upper bound in
>>case of equal programs.
>>
>>I used the assumption that white has probability of 40% to win and black has
>>probability of 30% to win and got less than 0.5% probability to get 5-0 when 3
>>of the wins are with black.
>
>In any case, the error bar is err...
>_Rather Large_
>at this point
>
>Let's wait and see what happens when the dust settles. If it is Deep Junior
>24-0, then we will all have to do homage, I think.
Maybe Enrique has two deep fritzes going at the same time ;)
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