Video poker probability question

#include <stdio.h>
#include <stdlib.h>
#include <time.h>
main() {
  srand(time(NULL));
  int currentCount = 0;
  int ctr, p, n;
  int x[5000] = {};
  int t = 0;
  int success = 0;

  for (n = 1; n <= 1000000; n++) {  
    currentCount = 0;
    for (ctr = 0; ctr < 5000; ctr++)
      x[ctr] = 0;
    for (ctr = 0; ctr < 25000000; ctr++) {
      p = rand()%40391;
      if (p == 0 && x[ctr%5000] == 1) 
        currentCount = currentCount; // dummy
      else
      if (p == 0 && x[ctr%5000] == 0) {
        currentCount++;
        x[ctr%5000] = 1;
      }
      else
      if (p > 0 && x[ctr%5000] == 1) {
        currentCount--;
        x[ctr%5000] = 0;
      }
      else
      if (p > 0 && x[ctr%5000] == 0) {
        currentCount = currentCount; // dummy
      }
      else
        exit(1); // should never occur

      if (currentCount >= 6) {
        success++;
        break;
      }
    }    
    printf("%6d, %6d, %1.6f\n", n, success, (double)success/n);
    fflush(stdout);
  }
}

int idx = ctr%5000;
if (p)
{
   if(x[idx]) { x[idx] = 0; currentCount--; }
}
else
{
   if(!x[idx]) { x[idx]=1; currentCount++; }
}

int *xp = x + ctr%5000;
if((*xp == 0) == (p == 0)) { *xp = !p; currentCount += p ? -1 : 1; }

#!/usr/bin/perl

$p = 1/40000;

my ($total,$wins) = (0,0);
while(1)
{
   $total++;
   my $strikes = [];

   printf("%10d: %10f\n", $total, $wins/$total) unless $total % 100000;

   for (1 .. 25000000)
   {
      next unless rand() <= $p;
      push(@$strikes, $_);
      shift(@$strikes) if($_ - $strikes->[0] > 5000);     
      ($wins++,last) if (@$strikes >= 6);
   }
}

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

struct sb { int x[6], start, end; };

void shift(struct sb *b) { b->start = b->start == 5 ? 0 : b->start+1; }
int first(struct sb *b) { return b->x[b->start]; }

void push(struct sb *b, int v)
{
    b->x[b->end]=v;
    b->end = b->end == 5 ? 0 : b->end+1;
}

int sz(struct sb *b)
{
    int s = b->end - b->start;
    return s < 0 ? s+5 : s;
}

main()
{

    struct sb strikes;
    int total = 0, wins = 0, hand = 0;
    clock_t start = clock();
    float elapsed = 0;

    srandom(time(0));

    while(1)
    {
        strikes.start = strikes.end = 0;
        for(hand = 0; hand < 25000000; hand++)
        {
          if(random()%40000) { continue; }
          push(&strikes, hand);
          if(hand - first(&strikes) > 5000) { shift(&strikes); }
          if(sz(&strikes) >= 6)
          {
              wins++;
              break;
          }
        }
        total++;

        elapsed = ((float) clock() - start)/CLOCKS_PER_SEC;
        printf("%6d, %10.6f, time: total %10.6f, avg: %10.6f\n", total, (float) wins/total, elapsed, elapsed/total);
    }
}

    96,   0.000000,          0, time: total  21.230000, avg:   0.221145
    97,   0.000000,          0, time: total  21.590000, avg:   0.222577
    98,   0.000000,          0, time: total  21.830000, avg:   0.222755
    99,   0.000000,          0, time: total  22.059999, avg:   0.225102
   100,   0.000000,          0, time: total  22.290001, avg:   0.222900

real    0m22.318s
user    0m22.280s
sys     0m0.020s

> require (expm)
Loading required package: expm
Loading required package: Matrix
Loading required package: lattice

Attaching package: ‘expm’

The following object is masked from ‘package:Matrix’:

    expm

> 
> p <- 1/40000
> q <- 1-p
> 
> A <- matrix(c(q,p,0,0,0,0,0,
+ (1/5000)*q,(4999/5000)*q + (1/5000)*p,(4999/5000)*p,0,0,0,0,
+ 0,0.00039999,0.99957502,0.00002499,0,0,0,
+ 0,0,0.000599985,0.99937503,0.000024985,0,0,
+ 0,0,0,0.00079998,0.99917504,0.00002498,0,
+ 0,0,0,0,0.000999975,0.99897505,0.000024975,
+ 0,0,0,0,0,0,1), byrow=T, nrow=7,
+ dimnames = list(c(0:5,"6+"),c(0:5,"6+ royals")))
> A
             0          1           2          3           4          5
0  0.999975000 0.00002500 0.000000000 0.00000000 0.000000000 0.00000000
1  0.000199995 0.99977501 0.000024995 0.00000000 0.000000000 0.00000000
2  0.000000000 0.00039999 0.999575020 0.00002499 0.000000000 0.00000000
3  0.000000000 0.00000000 0.000599985 0.99937503 0.000024985 0.00000000
4  0.000000000 0.00000000 0.000000000 0.00079998 0.999175040 0.00002498
5  0.000000000 0.00000000 0.000000000 0.00000000 0.000999975 0.99897505
6+ 0.000000000 0.00000000 0.000000000 0.00000000 0.000000000 0.00000000
    6+ royals
0  0.0000e+00
1  0.0000e+00
2  0.0000e+00
3  0.0000e+00
4  0.0000e+00
5  2.4975e-05
6+ 1.0000e+00
> system.time(B <-A%^%(25000000-5000))
   user  system elapsed 
      0       0       0 
> B
           0         1           2            3            4            5
0  0.8823753 0.1102997 0.006892508 0.0002870711 8.958995e-06 2.183479e-07
1  0.8823751 0.1102996 0.006892507 0.0002870710 8.958994e-06 2.183479e-07
2  0.8823734 0.1102994 0.006892493 0.0002870704 8.958976e-06 2.183475e-07
3  0.8823455 0.1102959 0.006892275 0.0002870613 8.958692e-06 2.183405e-07
4  0.8816746 0.1102121 0.006887035 0.0002868431 8.951881e-06 2.181745e-07
5  0.8601908 0.1075265 0.006719218 0.0002798536 8.733750e-06 2.128583e-07
6+ 0.0000000 0.0000000 0.000000000 0.0000000000 0.000000e+00 0.000000e+00
      6+ royals
0  0.0001362516
1  0.0001364697
2  0.0001384332
3  0.0001700795
4  0.0009302446
5  0.0252746144
6+ 1.0000000000
> v0<-c(0.88249552366128,0.110314698325118,6.89346204814203E-03,2.87119872301923E-04,8.96733669524682E-06,2.24009670889038E-07,4.66231783332393E-09)
> C <- v0%*%B
> C
             0         1           2           3            4            5
[1,] 0.8823753 0.1102996 0.006892508 0.000287071 8.958995e-06 2.183479e-07
        6+ royals
[1,] 0.0001363178
> C[1,7]
   6+ royals 
0.0001363178 
> 1/C[1,7]
6+ royals 
 7335.798 

Loading required package: expm

Loading required package: Matrix


Attaching package: 'expm'


The following object is masked from 'package:Matrix':

    expm


             0          1           2          3           4          5
0  0.999975000 0.00002500 0.000000000 0.00000000 0.000000000 0.00000000
1  0.000199995 0.99977501 0.000024995 0.00000000 0.000000000 0.00000000
2  0.000000000 0.00039999 0.999575020 0.00002499 0.000000000 0.00000000
3  0.000000000 0.00000000 0.000599985 0.99937503 0.000024985 0.00000000
4  0.000000000 0.00000000 0.000000000 0.00079998 0.999175040 0.00002498
5  0.000000000 0.00000000 0.000000000 0.00000000 0.000999975 0.99897505
6+ 0.000000000 0.00000000 0.000000000 0.00000000 0.000000000 0.00000000
    6+ royals
0  0.0000e+00
1  0.0000e+00
2  0.0000e+00
3  0.0000e+00
4  0.0000e+00
5  2.4975e-05
6+ 1.0000e+00
           0         1           2            3            4            5
0  0.8823753 0.1102997 0.006892508 0.0002870711 8.958995e-06 2.183479e-07
1  0.8823751 0.1102996 0.006892507 0.0002870710 8.958994e-06 2.183479e-07
2  0.8823734 0.1102994 0.006892493 0.0002870704 8.958976e-06 2.183475e-07
3  0.8823455 0.1102959 0.006892275 0.0002870613 8.958692e-06 2.183405e-07
4  0.8816746 0.1102121 0.006887035 0.0002868431 8.951881e-06 2.181745e-07
5  0.8601908 0.1075265 0.006719218 0.0002798536 8.733750e-06 2.128583e-07
6+ 0.0000000 0.0000000 0.000000000 0.0000000000 0.000000e+00 0.000000e+00
      6+ royals
0  0.0001362516
1  0.0001364697
2  0.0001384332
3  0.0001700795
4  0.0009302446
5  0.0252746144
6+ 1.0000000000
             0         1           2           3            4            5
[1,] 0.8823753 0.1102996 0.006892508 0.000287071 8.958995e-06 2.183479e-07
        6+ royals
[1,] 0.0001363178
   6+ royals 
0.0001363178 
6+ royals 
 7335.798 
>