One of the greatest challenges I've seen game designers come up with is getting an immediate and clear bit of feedback for probability mechanics.
While sites like AnyDice make this relatively simple, I haven't been satisfied with them.
Simply input your desired modifier (for the person doing the original roll) and target for the roll; and it'll get to work.
It creates a thousand random dice tests, and feeds you the exact results of five random tests (to show that it's working).
It then creates an overview of the outcome sets (wins, ties, and failures).
It's not "truly" random, but PHP seems to reseed every "rand()" call, so it should work fine.
The source is available on my blog.