Ana (and son) explain a great card trick!

Ana Darcy Méndez is very, very good at math. She had to be, to navigate a vessel 25 light years from Thomo to Earth! Her son Julio is even better. Both were fascinated by this marvelous card trick:

http://www.wimp.com/mathcard/

Notice that the person performing it begs someone for an explanation. We can offer that gentleman an explanation, since Ana and Julio, her son, spent the better part of an hour playing with it. Ana said it's basically a simple matter of "odds and evens," made more confus...