最近好像有關於遊戲抽獎機率問題的爭議。
雖然知道隨機有時是不準的，但我仍想用 C++ (僅梅克森旋轉演算法)親自嘗試。
以下為測試用程式碼。
#include<bits/stdc++.h>
using namespace std;
//隨機樹使用參數為時間(毫秒)
unsigned seed = chrono::steady_clock::now().time_since_epoch().count();
mt19937_64 rng(seed);
//平均分布
uniform_int_distribution<int> dis(1,100);
long long RandomNumber(){
return dis(rng);
}
void TestRamdon(int K){
int mx=0,mn=100000000;
for(int i=0;i<100000;++i){
int ct=0;
for(int j=0;j<K;++j){
int tp=RandomNumber();
// 1~100 理論隨機 <=10 機率為 0.1(10%)
if(tp<=10){
ct++;
}
}
mx=max(ct,mx);
mn=min(ct,mn);
}
long double maxRate=1.0*mx/K;
long double minRate=1.0*mn/K;
cout<<"Max Rate In 10^5 Times "<<K<<" Times Random : "<<maxRate<<"\n";
cout<<"Min Rate In 10^5 Times "<<K<<" Times Random : "<<minRate<<"\n";
cout<<endl;
}
int main(){
// test if random K times is enough to get reality rate
const int K=400;
const int TestTime=10;
for(int i=0;i<TestTime;++i){
TestRamdon(K);
}
}經過我實測，在理論機率為 10% 時，測試 400 次最悽慘的機率約莫落在 0.04(4%) ，而最佳機率則約為 0.17(17%)
測試結果 K=400
Max Rate In 10^5 Times 400 Times Random : 0.17
Min Rate In 10^5 Times 400 Times Random : 0.0375
Max Rate In 10^5 Times 400 Times Random : 0.1775
Min Rate In 10^5 Times 400 Times Random : 0.0425
Max Rate In 10^5 Times 400 Times Random : 0.17
Min Rate In 10^5 Times 400 Times Random : 0.04
Max Rate In 10^5 Times 400 Times Random : 0.1675
Min Rate In 10^5 Times 400 Times Random : 0.0325
Max Rate In 10^5 Times 400 Times Random : 0.165
Min Rate In 10^5 Times 400 Times Random : 0.0375
Max Rate In 10^5 Times 400 Times Random : 0.17
Min Rate In 10^5 Times 400 Times Random : 0.0375
Max Rate In 10^5 Times 400 Times Random : 0.17
Min Rate In 10^5 Times 400 Times Random : 0.0425
Max Rate In 10^5 Times 400 Times Random : 0.17
Min Rate In 10^5 Times 400 Times Random : 0.045
Max Rate In 10^5 Times 400 Times Random : 0.165
Min Rate In 10^5 Times 400 Times Random : 0.0425
Max Rate In 10^5 Times 400 Times Random : 0.17
Min Rate In 10^5 Times 400 Times Random : 0.0375而到底應該要幾次以上才會到 min=0.09(9%) 呢？歡迎各位親自嘗試。以下是關於我有測試的次數
K=10
Max Rate In 10^5 Times 10 Times Random : 0.6
Min Rate In 10^5 Times 10 Times Random : 0
Max Rate In 10^5 Times 10 Times Random : 0.7
Min Rate In 10^5 Times 10 Times Random : 0
Max Rate In 10^5 Times 10 Times Random : 0.7
Min Rate In 10^5 Times 10 Times Random : 0
Max Rate In 10^5 Times 10 Times Random : 0.7
Min Rate In 10^5 Times 10 Times Random : 0
Max Rate In 10^5 Times 10 Times Random : 0.7
Min Rate In 10^5 Times 10 Times Random : 0
Max Rate In 10^5 Times 10 Times Random : 0.6
Min Rate In 10^5 Times 10 Times Random : 0
Max Rate In 10^5 Times 10 Times Random : 0.7
Min Rate In 10^5 Times 10 Times Random : 0
Max Rate In 10^5 Times 10 Times Random : 0.8
Min Rate In 10^5 Times 10 Times Random : 0
Max Rate In 10^5 Times 10 Times Random : 0.7
Min Rate In 10^5 Times 10 Times Random : 0
Max Rate In 10^5 Times 10 Times Random : 0.6
Min Rate In 10^5 Times 10 Times Random : 0K=100
Max Rate In 10^5 Times 100 Times Random : 0.25
Min Rate In 10^5 Times 100 Times Random : 0
Max Rate In 10^5 Times 100 Times Random : 0.25
Min Rate In 10^5 Times 100 Times Random : 0
Max Rate In 10^5 Times 100 Times Random : 0.25
Min Rate In 10^5 Times 100 Times Random : 0
Max Rate In 10^5 Times 100 Times Random : 0.26
Min Rate In 10^5 Times 100 Times Random : 0
Max Rate In 10^5 Times 100 Times Random : 0.25
Min Rate In 10^5 Times 100 Times Random : 0
Max Rate In 10^5 Times 100 Times Random : 0.25
Min Rate In 10^5 Times 100 Times Random : 0
Max Rate In 10^5 Times 100 Times Random : 0.25
Min Rate In 10^5 Times 100 Times Random : 0
Max Rate In 10^5 Times 100 Times Random : 0.25
Min Rate In 10^5 Times 100 Times Random : 0
Max Rate In 10^5 Times 100 Times Random : 0.25
Min Rate In 10^5 Times 100 Times Random : 0
Max Rate In 10^5 Times 100 Times Random : 0.25
Min Rate In 10^5 Times 100 Times Random : 0K=1000
Max Rate In 10^5 Times 1000 Times Random : 0.148
Min Rate In 10^5 Times 1000 Times Random : 0.061
Max Rate In 10^5 Times 1000 Times Random : 0.143
Min Rate In 10^5 Times 1000 Times Random : 0.061
Max Rate In 10^5 Times 1000 Times Random : 0.143
Min Rate In 10^5 Times 1000 Times Random : 0.063
Max Rate In 10^5 Times 1000 Times Random : 0.147
Min Rate In 10^5 Times 1000 Times Random : 0.063
Max Rate In 10^5 Times 1000 Times Random : 0.143
Min Rate In 10^5 Times 1000 Times Random : 0.063
Max Rate In 10^5 Times 1000 Times Random : 0.144
Min Rate In 10^5 Times 1000 Times Random : 0.061
Max Rate In 10^5 Times 1000 Times Random : 0.146
Min Rate In 10^5 Times 1000 Times Random : 0.055
Max Rate In 10^5 Times 1000 Times Random : 0.144
Min Rate In 10^5 Times 1000 Times Random : 0.061
Max Rate In 10^5 Times 1000 Times Random : 0.145
Min Rate In 10^5 Times 1000 Times Random : 0.061
Max Rate In 10^5 Times 1000 Times Random : 0.142
Min Rate In 10^5 Times 1000 Times Random : 0.061但是剛剛測測試次數皆為 10^5，若換成 10^6 呢？
Max Rate In 10^6 Times 400 Times Random : 0.1775
Min Rate In 10^6 Times 400 Times Random : 0.03變成 0.03(3%)！
不得不說，跟我想的好像不一樣。希望大家自己測試，筆者因為電腦不夠好(i5 古早版本)只能做到這了。