Question

我正在尝试编写一个简单的蒙特卡罗模拟程序。确切地说，我想分析战斗结果，这取决于进攻和防守上不同的军队规模 - 这与此类似：http://en.wikipedia.org/wiki/Risk_(game)#Dice_probabilities

现在......风险II同时规则提供了不同的挑战：不同的军队规模意味着不同的骰子颜色（这意味着数字的分布函数不同）简而言之，你的军队规模越小，越多可能你会得到1分，而你的军队规模越大，你就越有可能获得更多的掷骰数。

由于对所有可能条件使用if语句是最好的愚蠢，我将所有可能的滚动结果列表为5x12数组。（所有骰子都有12个边，5个强度不同，所以得到5x12）

我想为每个进攻/防守组合进行10000次模拟，但是一旦我意识到这将意味着超过900万次计算，我决定将其缩短为每组合100次。

以下是代码;一旦我运行它，它给了我访问冲突错误。我不知道我在哪里犯了错误。如果您有任何建议可以提供，我也会很感激。提前致谢。

/* Risk II Combat Result Table 

For starter, we shall consider one-direction attack in RISK II
and generate the combat table for use.

Machine: Pentium Dual Core E6600 
Ram: 6G
OS: Windows 7
Compiler: Visual Studio 2010

Jimmy Smith, 24-March-2012

*/

#include <cstdio>
#include <cstdlib>
#include <cmath>

#include <iostream>
#include <algorithm>
using namespace std;

/* Initializing: 

    Range legend:

White  = 1 ~ 6
Yellow = 7 ~ 12
Orange = 13 ~ 20
Red    = 21 ~ 30
Black  = 31 ~

First row of Dice array corresponds to white dice, and so on. 

*/

int Dice[5][12] = { {1, 1, 1, 1, 2, 2, 2, 3, 3, 4, 5, 6}, 
                    {1, 1, 2, 2, 2, 2, 3, 3, 4, 4, 5, 6}, 
                    {1, 2, 2, 3, 3, 3, 4, 4, 4, 5, 5, 6}, 
                    {1, 2, 3, 3, 4, 4, 5, 5, 5, 5, 6, 6}, 
                    {1, 2, 3, 4, 4, 5, 5, 5, 6, 6, 6, 6} };

int Roll_Index [30]= {0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 2, 2, 2, 3, 3, 3, 3, 3, 3, 3, 3, 3, 4};


int main() {

float Table[30][30];

for (int i = 0; i < 30; i ++)
    for (int j = 0; j < 30; j ++)
        Table [i][j] = 0.0;

int Result[100];

for (int i = 0; i < 100; i++) Result[i] = 0;    

float prob = 0.0;

int Atk = 0;
int Def = 0;    //Number of attackers and defenders


int A_Ind = 0;
int D_Ind = 0;  //Dice side index

int A_Roll_Index = 0;   
int D_Roll_Index = 0; //Roll index on both sides

int A_Dice = 0;
int D_Dice = 0; //Roll result

int Damage = 0;

int Sum = 0; //Internal sum

FILE* fp;


//Time for hard core Monte-Carlo shit! 100 simulation for each situation

for (Atk = 0; Atk<30; Atk++) {

    for (Def = 0; Def < 30; Def++) {

        for (int i = 0; i < 100; i++) {

            int Attacker = Atk +1;
            int Defender = Def +1;

            while((Attacker>0)&&(Defender>0)) {

                A_Ind = (int)(rand()*12);
                D_Ind = (int)(rand()*12); //The die is cast!

                A_Roll_Index = Roll_Index[Attacker-1];
                D_Roll_Index = Roll_Index[Defender-1];

                A_Dice = Dice[A_Roll_Index][A_Ind];
                D_Dice = Dice[D_Roll_Index][D_Ind];

                Damage = min(A_Roll_Index, D_Roll_Index) + 1;

                if (A_Dice >= D_Dice) {
                    Defender -= Damage;
                    if (Defender == 0)  Result[i] = 1;
                }
                else {
                    Attacker -= Damage;
                    if (Attacker == 0)  Result[i] = 0;
                }
            }
        }

    for (int i = 0; i < 100; i++)   Sum+=Result[i];

    prob = (float)(Sum/100);

    Table[Atk][Def] = prob;

    }
}
/* open new file for output and write a title */

fp = fopen( "Combat.dat", "w+");

if( NULL == fp ) {
    printf( "cannot open file\n" );
    return( 0 );
}

for (Atk = 0; Atk < 30; Atk++){
    for (Def = 0; Def < 30; Def++)
        fprintf(fp, "%16.8f", Table[Atk][Def]);
    fprintf (fp, "\n");
}
fclose( fp );

return(EXIT_SUCCESS);

}

Answer 1

您的代码

A_Ind = (int)(rand()*12);
D_Ind = (int)(rand()*12);

表示您似乎认为rand()返回[0,1]范围内的数字，但实际情况并非如此。相反，int返回[0, RAND_MAX]范围内的整数，因此您需要以下内容：

A_Ind = rand() * 12.0 / RAND_MAX;

如果您的模拟必须在统计上是准确的，那么使用<random>库中的随机数生成器可能会更好：

#include <random>

typedef std::mt19937 rng_type;
std::uniform_int_distribution<std::size_t> udist(0, 11);

rng_type rng;

// ...

// seed rng first:
rng.seed(some_seed_value);

// roll dice
std_size_t A_Ind = udist(rng), D_Ind = udist(rng);

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