Author: Dann Corbit
Date: 11:57:26 04/25/01
Go up one level in this thread
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.
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