/* Numerical solution to simple Baseball Markov chain model */

/* Written by Carey Williamson, January 2019 */

#include <stdio.h>
#include <math.h>

/* Transition rates for Markov chain model */
#define LAMBDA1 0.20   /* transition rate to get first out */
#define LAMBDA2 0.25   /* transition rate to get second out */
#define LAMBDA3 0.25   /* transition rate to get third out */
#define LAMBDA4 0.50   /* transition rate for TV commercial */

#define DEBUG 1   /* verbose debugging */

int main ()
  {
    float p0, p1, p2, p3;
    float denom, ratio;

    denom = 1.0 / LAMBDA1;
    denom += 1.0 / LAMBDA2;
    denom += 1.0 / LAMBDA3;
    denom += 1.0 / LAMBDA4;
#ifdef DEBUG
    printf("denom value is %f\n", denom);
#endif

    p0 = 1.0 / (LAMBDA1 * denom);
#ifdef DEBUG
    printf("p0 is %f\n", p0);
#endif

    ratio = LAMBDA1 / LAMBDA2;
    p1 = ratio * p0;
#ifdef DEBUG
    printf("p1 is %f times p0, so p1 = %f\n", ratio, p1);
#endif

    ratio = LAMBDA1 / LAMBDA3;
    p2 = ratio * p0;
#ifdef DEBUG
    printf("p2 is %f times p0, so p2 = %f\n", ratio, p2);
#endif

    ratio = LAMBDA1 / LAMBDA4;
    p3 = ratio * p0;
#ifdef DEBUG
    printf("p3 is %f times p0, so p3 = %f\n", ratio, p3);
#endif

    printf("\n");
    printf("Analytical Markov Chain Model of Baseball\n");
    printf("\n");
    printf("  Prob(nobody out): p0 = %f\n", p0);
    printf("  Prob(one out):    p1 = %f\n", p1);
    printf("  Prob(two out):    p2 = %f\n", p2);
    printf("  Prob(three out):  p3 = %f\n", p3);
    printf("\n");
    printf("Sanity check: p0 + p1 + p2 + p3 = %f\n",
	   p0 + p1 + p2 + p3);
    printf("\n");
  }