If it were just that then taking the tests three times at once would have a similar effect. Instead, it's mostly that you're measuring a quantity that's varying over time, and more samples gives you more chances for one of them to be at a time when the quantity is high.
The math is more intuitive if you say it decreases the failure rate. i.e. if you try something with a 10% success rate 3 times, your odds are 1 - (0.9 ^ 3) = 27.1% chance of success.