Assuming the game is played without cheating, in the three-card monte, can a logical approach increase the player's chance of beating the house?
At first glance it would seem to be unlikely but a recent article in the BBC news indicates that in the somewhat similar two person game rock-paper-scissors, knowledge and application of a simple set of natural human habits can have a pretty drastic impact on the odds.
Assuming you know where the card started can you make a logical choice, that will identify the most likely current position (regardless of distractions)?