Retroactive Hypnosis. We're all actually making choices that are completely unrelated to the end result, but when we click the last time the screen sends us a subliminal message: THIS IS THE CARD YOU CHOSE... and because our original choice has been erased from our minds we all think, that's right, Blimey, it's magic!

Damned if I know how it works. A friend sent me the Mind-reading Crystal Ball a while back and that did the same thing.