Horse racing board game (Monte Carlo method analysis)

race.c

// Horse racing board game (Monte Carlo method analysis)
//   $ cc -O3 -fopenmp -o race race.c
//   $ ./race
// Ref: https://possiblywrong.wordpress.com/2022/07/07/analysis-of-horse-racing-board-game/
// This is free and unencumbered software released into the public domain.
#include <stdio.h>
#include <stdint.h>

#define BAR \
    "########################################################################"

static int
r2d6(uint64_t *s)
{
    uint32_t r;
    do r = (*s = *s*0x3243f6a8885a308d + 1) >> 32;
    while (r > (UINT32_C(0xffffffff) - 4));  // eliminate bias
    return "CDDEEEFFFFGGGGGHHHHHHIIIIIJJJJKKKLLM"[r%36] - 'A';
}

static uint64_t
hash(int32_t i)
{
    uint64_t h = i;
    h += 1111111111111111111; h ^= h >> 33;
    h *= 1111111111111111111; h ^= h >> 33;
    return h;
}

int
main(void)
{
    static int curve[] = {
    #if 0
        2,3,4,5,6,7,6,5,4,3,2
    #else
        3,6,8,11,14,17,14,11,8,6,3
    #endif
    };
    int32_t n = 1L<<24, hist[11] = {0};

    #pragma omp parallel for reduction(+:hist)
    for (int32_t i = 0; i < n; i++) {
        int horse[11] = {0};
        for (uint64_t s = hash(i);;) {
            int r = r2d6(&s);
            if (++horse[r-2] == curve[r-2]) {
                hist[r-2]++;
                break;
            }
        }
    }

    int maxi = 0;
    for (int i = 1; i < 11; i++) {
        maxi = hist[i] > hist[maxi] ? i : maxi;
    }
    for (int i = 0; i < 11; i++) {
        int len = hist[i] * (sizeof(BAR) - 1.0) / hist[maxi] + 0.5;
        printf("%.*s\n", len, BAR);
    }
}