rand() doesn't follow Gaussian Distribution & Central Limit Theorem - c

Question

I've created a program that use rand() to generate repeated number in C.
However the repeated number doesn't follow Central Limit Theorem
Can anyone solve this rand() bug problem or is there an alternative other than using rand() C library to generate better random number?
Here's the screen shot:
#include <stdio.h>
#include <string.h>
#include <stdlib.h>
#include <time.h>
#include <windows.h>
#define TOTAL_THROW 10000000
typedef enum _COINTOSS {
UNDEFINED = 0,
HEAD = 1,
TAIL = 2
} COINTOSS;
COINTOSS toss_coin () {
int x = rand() % 2;
if (x == 0) return HEAD;
else if (x == 1) return TAIL;
}
void main () {
int x, i, j, v1 = 0, v2 = 200, total = 0;
int head_range[25] = {0};
int tail_range[25] = {0};
int no_range = 0;
int count = 0;
int repeated = 0;
COINTOSS previos_toss = UNDEFINED;
COINTOSS current_toss;
srand(time(NULL));
for (i=0; i<TOTAL_THROW; i++) {
current_toss = toss_coin(); // current toss
if (previos_toss == current_toss) {
count++;
} else {
if (current_toss == HEAD) head_range[count] += 1;
else if (current_toss == TAIL) tail_range[count] += 1;
previos_toss = current_toss;
count = 0;
}
}
for (i=24; i>=0; i--) {
printf("+%d = %d\n", i+1, head_range[i]);
}
puts("________________\n");
for (i=0; i<25; i++) {
printf("-%d = %d\n", i+1, tail_range[i]);
}
printf("\nTOTAL_THROW: %d\n", TOTAL_THROW);
printf("\nPress [ENTER] to exit. . .");
getchar();
}

Answer 1

Your problem is using modulus to get your random number into the required range, which uses the lower bits (it's a classic gotcha):
int x = rand() % 2;
The lower bits of rand() (a linear congruential generator (LCG)) are not as random as the high bits. This applies to all LCG's regardless of library or language.
For a range of [0..N), you should do something like this (which uses the high bits):
int r = rand() / ( RAND_MAX / N + 1 );