Trade-Offs
Deterministic algorithms have a space/time trade-offs. In the same way, Monte Carlo and Las Vegas algorithms have a trade-offs of speed and accuracy. Las Vegas algorithms are always accurate, but in some cases might be very slow or not stop at all. Monte Carlo algorithms are always fast, but they never give a definitive answer.
These categories are generally interchangeable: by a sacrifice of speed (repeating the process until the answer is correct) a Monte Carlo algorithm may become an infallible Las Vegas algorithm. By a sacrifice of accuracy (breaking off after a certain time) a Las Vegas algorithm may become Monte Carlo algorithm.