... there's also the quite real possiblity of 4 never being returned from rand!

In that case, the pseudo random number generator would be broken (taking 'never' literally). In theory, it might occasionally take a 'long time' for any certain number to occur, but that's unlikely in practice.

Actually, presuming a statistically equal distribution of values returned by the PRNG, the probability to get a certain (integer) number is expected to be 1/N (N being 32 in this case).  So, even on the last turn, when all but one of the 32 values are already taken, the chance to get the final remaining number is 1/32 (or 32 attempts, on average); when there are still two numbers left, the chance is 2/32 (16 attempts), etc.

Doing some simple simulation statistics confirms this quite well (although slightly modified in implementation, the central algorithm is functionally the same as that of the OP): 

#!/usr/bin/perl

use strict;
use warnings;

my $n = 1e4;  # number of runs for the statistics
my $N = 32;
my @sum;
my @max = (0)x($N+1);

for (1..$n) {
    my @have_num = ();
    
    for my $i (1..$N) {
        my $attempts = 0;
        while(1) {
            my $rand = int(rand($N));
            #print ".";
            $attempts++;
            unless ($have_num[$rand]) {
                #print " $i: $rand\n";
                $have_num[$rand] = 1;
                last;
            }
        }
        $sum[$i] += $attempts;
        $max[$i]  = $attempts if $attempts > $max[$i];
    }
}

for my $i (1..$N) {
    my $avg = $sum[$i]/$n;
    my $bar = "*" x int($avg+0.5);
    printf "%2d: %6.3f [%6.3f] %s max=%d\n",
            $i,  $avg, $N/($N-$i+1), $bar, $max[$i];
}

__END__

 1:  1.000 [ 1.000] * max=1
 2:  1.033 [ 1.032] * max=4
 3:  1.065 [ 1.067] * max=4
 4:  1.104 [ 1.103] * max=5
 5:  1.142 [ 1.143] * max=7
 6:  1.186 [ 1.185] * max=7
 7:  1.230 [ 1.231] * max=8
 8:  1.283 [ 1.280] * max=8
 9:  1.334 [ 1.333] * max=8
10:  1.392 [ 1.391] * max=10
11:  1.453 [ 1.455] * max=10
12:  1.521 [ 1.524] ** max=11
13:  1.601 [ 1.600] ** max=13
14:  1.684 [ 1.684] ** max=13
15:  1.779 [ 1.778] ** max=14
16:  1.882 [ 1.882] ** max=16
17:  1.999 [ 2.000] ** max=19
18:  2.137 [ 2.133] ** max=17
19:  2.283 [ 2.286] ** max=23
20:  2.462 [ 2.462] ** max=20
21:  2.674 [ 2.667] *** max=26
22:  2.904 [ 2.909] *** max=29
23:  3.198 [ 3.200] *** max=31
24:  3.551 [ 3.556] **** max=37
25:  3.996 [ 4.000] **** max=48
26:  4.554 [ 4.571] ***** max=47
27:  5.331 [ 5.333] ***** max=55
28:  6.400 [ 6.400] ****** max=79
29:  8.026 [ 8.000] ******** max=95
30: 10.597 [10.667] *********** max=140
31: 15.983 [16.000] **************** max=211
32: 32.092 [32.000] ******************************** max=343

[download]

The second column is the number of attempts, averaged over 10000 runs in this case (a single run doing what the OP's code did). The values in brackets are the corresponding expected values. "max=" is the worst case number of attempts that ever occurred.

In reply to Re^2: How much random is rand()? by almut
in thread How much random is rand()? by gmoque

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