/*
 * Monte Carlo simulation of the bingo game, as found in Pickham and
 *  Baccarat.  This assumes the games are honest, that is, number
 *  drawing is uncorrelated with everything else.
 *
 * Output consists of one line every 1<<20 games, giving
 *
 *	number of games played
 *	number of games won
 *	winnings
 *	for each of the seven possible payout amounts, in order highest
 *		to lowest, the percentage of games winning that amount
 *	total percentage of games won (the sum of the previous seven)
 *	expected profit per token staked, per game
 *
 * The last number, for example, is positive, meaning the player can
 *  expect to make "money" playing the game (in contrast to real casino
 *  games).
 */

#include <time.h>
#include <stdio.h>
#include <stdlib.h>

static int combosinit[][5]
 = { {  0,  1,  2,  3,  4 },
     {  5,  6,  7,  8,  9 },
     { 10, 11, 12, 13, 14 },
     { 15, 16, 17, 18, 19 },
     { 20, 21, 22, 23, 24 },
     {  0,  5, 10, 15, 20 },
     {  1,  6, 11, 16, 21 },
     {  2,  7, 12, 17, 22 },
     {  3,  8, 13, 18, 23 },
     {  4,  9, 14, 19, 24 },
     {  0,  6, 12, 18, 24 },
     {  4,  8, 12, 16, 20 } };
#define NCOMB (sizeof(combosinit)/sizeof(combosinit[0]))

typedef struct cell CELL;
typedef struct combo COMBO;

struct cell {
  int n;
  int filled;
  int ncombos;
  COMBO *combos[4];
  } ;

struct combo {
  int nfilled;
  CELL *cells[5];
  } ;

static CELL board[25];
static COMBO combos[NCOMB];
static unsigned int list[25];
static int nlist;

static void init(void)
{
 int i;
 int j;
 CELL *c;

 for (i=25-1;i>=0;i--)
  { c = &board[i];
    c->n = i;
    c->ncombos = 0;
  }
 for (i=NCOMB-1;i>=0;i--)
  { for (j=0;j<5;j++)
     { c = &board[combosinit[i][j]];
       c->combos[c->ncombos++] = &combos[i];
       combos[i].cells[j] = c;
     }
  }
}

static int drawnumber(int cell)
{
 CELL *b;
 COMBO *c;
 int i;

 b = &board[cell];
 if (b->filled) abort();
 b->filled = 1;
 for (i=b->ncombos-1;i>=0;i--)
  { c = b->combos[i];
    if (++c->nfilled >= 5) return(1);
  }
 return(0);
}

static int picklist(void)
{
 int x;
 int v;

 x = random() % nlist;
 v = list[x];
 nlist --;
 if (x != nlist) list[x] = list[nlist];
 return(v);
}

static int onegame(void)
{
 int i;

 for (i=25-1;i>=0;i--) board[i].filled = 0;
 for (i=NCOMB-1;i>=0;i--) combos[i].nfilled = 0;
 for (i=25-1;i>=0;i--) list[i] = i;
 list[12] = 24;
 nlist = 24;
 if (drawnumber(12)) abort();
 if (drawnumber(picklist())) abort();
 if (drawnumber(picklist())) abort();
 if (drawnumber(picklist())) abort();
 if (drawnumber(picklist())) return(400);
 if (drawnumber(picklist())) return(200);
 if (drawnumber(picklist())) return(100);
 if (drawnumber(picklist())) return(50);
 if (drawnumber(picklist())) return(25);
 if (drawnumber(picklist())) return(10);
 if (drawnumber(picklist())) return(5);
 return(0);
}

int main(void);
int main(void)
{
 long long int winnings;
 long long int games;
 long long int wongames;
 long long int wincounts[7];
 int v;

 init();
 srandom(time(0));
 games = 0;
 wongames = 0;
 winnings = 0;
 for (v=7-1;v>=0;v--) wincounts[v] = 0;
 while (1)
  { games ++;
    v = onegame();
    winnings += v;
    switch (v)
     { case 400: wincounts[0] ++; break;
       case 200: wincounts[1] ++; break;
       case 100: wincounts[2] ++; break;
       case  50: wincounts[3] ++; break;
       case  25: wincounts[4] ++; break;
       case  10: wincounts[5] ++; break;
       case   5: wincounts[6] ++; break;
     }
    if (v) wongames ++;
    if (! (games & 1048575)) printf("%llu %llu %llu [%g %g %g %g %g %g %g] %g %g\n",games,wongames,winnings,(wincounts[0]*100.0)/games,(wincounts[1]*100.0)/games,(wincounts[2]*100.0)/games,(wincounts[3]*100.0)/games,(wincounts[4]*100.0)/games,(wincounts[5]*100.0)/games,(wincounts[6]*100.0)/games,(wongames*100)/(double)games,(winnings-games)/(double)games);
  }
}