My first LEGO Mindstorms project was an automated card dealer, created during the summer before starting undergraduate studies at UBC in 2002.
The dealer consists of 3 components: a fixed base on four rubber casters, a rotating unit, and a card dispensing tower. To deal, a flywheel at the bottom of the card stack pushed the lowest card against a gate so that as soon as the gate opens, the card would fly out. For the gate, the robot used a standard 10-point technic axle. By slowly rotating this ridged axle, the slot size through which the card could escape would vary until the lowest card on the card stack was dispensed. A sensor would detect this and force the gate to close. Here’s an illustration of the upper unit:
This construction works very well with standard fare plastic cards, in which case the robot never deals out more than one card at once. The middle unit is illustrated below.
The middle unit rotates in relation to the lower unit, pictured below. Holes in the bottom unit provide feedback for the touch sensor in the rotator unit so that it can stop at any of eight positions. For this reason, eight is the largest number of players that can be dealt to.
As far as the design of the base component, the credit is fully Dave Baum’s. It is illustrated very succinctly in his wonderful book, Definitive Guide to LEGO Mindstorms, as part of a robot arm.