This is a case of a Drunkard's walk, and as such the deviation from expectation value is proportional to sqrt(N). With 30 steps, you have a 96% confidence interval of 37% deviation from expectation, 10^4 realizations will give you a 96% confidence interval of 2%. I wrote some code to lump results and stuck it on the end of BrowserUk's; for the results the first column should correspond closely to the weights vector. The following is for 10 ships and 10^5 reps

#! perl -slw
use strict;
use List::Util qw[ sum ];

our $SHIPS ||= 10;
our $REPS ||= 1e5;

sub pick {
    my( $weights, $total ) = @_;
    my $rand = rand $total;
    ( $rand -= $weights->[ $_ ] ) < 0 
        and return $_ for 0 .. $#$weights;
}

sub pickAll{
    my @weights = @_;
    my $total = sum @weights;
    my @order;
    for( 0 .. $#_ ) {
        my $pick = pick( \@weights, $total );
        push @order, $pick;
        $total -= $weights[ $pick ];
        $weights[ $pick ] = 0;
    }
    return @order;
}

my @weights = map rand( 16 ), 1 .. $SHIPS;
my $total = sum @weights;
$weights[$_] /= $total for 0 .. $SHIPS-1;

print "$_ : $weights[ $_ ]" for 0 .. $#weights;

print "\n";

my @results;
for (1 .. $SHIPS) {
    push @results, [0 x $SHIPS]; # $results[ship][pick location]
}
for (1 .. $REPS) {
    my @realization = pickAll( @weights );
    for (0 .. $SHIPS-1) {
        ++$results[$realization[$_]][$_];
    }
}
for (@results) {
    for (@{$_}) {
        $_ /= $REPS;
    }
}
print sprintf "%.4f " x $SHIPS, @{$_} for @results;

C:\test>WeightedPick.pl -SHIPS=10 -REPS=100000

0 : 0.156588763610903
1 : 0.0946606629807576
2 : 0.0327748134913928
3 : 0.100654289094377
4 : 0.162546174460996
5 : 0.135885704628311
6 : 0.135469229097757
7 : 0.0780801081629204
8 : 0.0401747990052874
9 : 0.0631654554672976


0.1574 0.1495 0.1394 0.1308 0.1174 0.1041 0.0857 0.0629 0.0386 0.0143 
0.0938 0.0970 0.1014 0.1043 0.1110 0.1138 0.1147 0.1123 0.0974 0.0543 
0.0330 0.0373 0.0398 0.0467 0.0533 0.0651 0.0830 0.1115 0.1781 0.3523 
0.0993 0.1032 0.1067 0.1089 0.1115 0.1134 0.1129 0.1085 0.0882 0.0474 
0.1632 0.1523 0.1434 0.1296 0.1176 0.1005 0.0845 0.0602 0.0359 0.0129 
0.1350 0.1332 0.1295 0.1261 0.1177 0.1107 0.0981 0.0784 0.0507 0.0205 
0.1364 0.1330 0.1297 0.1257 0.1176 0.1098 0.0952 0.0792 0.0517 0.0216 
0.0782 0.0822 0.0864 0.0927 0.1012 0.1078 0.1191 0.1279 0.1230 0.0815 
0.0408 0.0451 0.0507 0.0552 0.0635 0.0740 0.0922 0.1232 0.1863 0.2690 
0.0629 0.0672 0.0732 0.0800 0.0892 0.1007 0.1147 0.1360 0.1500 0.1262
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