Matt and I finally figured it out after a few rounds.
Pretty funny. I figured it out after 2-3 rounds, but it might have taken longer if I'd stumbled across the site by accident.
Hmmm, maybe I should be card counter. Kind of a blunter version of the Flash Mindreader:
http://www.superlaugh.net/1/flashmindreader.htm
It even has an eerie "mind reading" sound effect which may be mistaken for the arrival of Kirk and Spock if said sound is inadvertenly played through 5.1 surround sound.