\datethis
@*Intro. This little program makes empirical tests by which I can
check the accuracy of the {\mc SETSET} program. (See that program
for explanations.)

@d m 12 /* size of each hand */
@d n 100000000 /* number of random trials */

@c
#include <stdio.h>
#include "gb_flip.h" /* use the Stanford GraphBase random number routines */
char deck[81];
char occ[81];
char z[3][3]={{0,2,1},{2,1,0},{1,0,2}}; /* $x+y+z\equiv0$ (mod 3) */
char third[81][128];

main()
{
  register int j,k,t;
  int reps,count;
  @<Initialize@>;
  while (1) {
    count=0;
    for (reps=0;reps<n;reps++) {
      @<Shuffle the deck@>;
      @<Increase |count| if there are no SETs@>;
    }
    printf("%d/%d\n",count,n);
  }
}

@ @d pack(a,b,c,d) (((a)*3+(b))*3+(c))*3+(d)

@<Initialize@>=
gb_init_rand(0);
for (k=0;k<81;k++) deck[k]=k;
for (k=81-m;k<81;k++) occ[k]=1;
{
  int a,b,c,d,e,f,g,h;
  for (a=0;a<3;a++) for (b=0;b<3;b++) for (c=0;c<3;c++) for (d=0;d<3;d++)
   for (e=0;e<3;e++) for (f=0;f<3;f++) for (g=0;g<3;g++) for (h=0;h<3;h++)
    third[pack(a,b,c,d)][pack(e,f,g,h)]= pack(z[a][e],z[b][f],z[c][g],z[d][h]);
}

@ @<Increase |count| if there are no SETs@>=
for (j=81-m;j<80;j++) for (k=j+1;k<81;k++)
  if (occ[third[deck[j]][deck[k]]]) goto set_found;
count++;
set_found:@;

@ @<Shuffle the deck@>=
for (j=81;j>81-m;j--) {
  t=deck[j-1];
  occ[t]=0;
  k=gb_unif_rand(j);
  deck[j-1]=deck[k];
  occ[deck[k]]=1;
  deck[k]=t;
}

@*Index.