[jimwhitson]

Grover's algorithm does indeed look rather like magic, but even better is the geometrical proof - WP's description looks good at a quick skim. In my (fairly limited) experience, this sort of geometrical thinking is the best way to understand quantum algorithms intuitively.

[sev]

Although Grover's algorithm is extremely impressive...it's a probabilistic algorithm, which means that the result is not guaranteed, but very likely. And the likelihood can be increased by running the algorithm more than once.

[jessriedel]

The likelihood increases exponentially because each time you run the algorithm it's independent of the previous times. Even if it's only 75% sure, you only need to run it a few dozen times before it's more likely for there to be a hardware fault in your display giving you the wrong answer.