the odds for no collision are easily calculated:

> perl -e ' $x=1; $x*=(1e7-$_)/1e7 for 1..3723; print $x '
0.499919268547978
[download]

So the odds of a collision is already bigger than 50% after 3723 draws!¹

Actually there are already combinatorial formulas that avoids the loop completely.

For the interested readers:

• Birthday problem ²
• Conditional probability

¹) and bigger than 99% after 9600 draws!

²) which many of us should have encountered at school already ... :-/