RFID will probably be your best bet for recognition of card values. Possibly, if you used a simple light sensor that recognizes color, you could use that to indicate which chip is which. Another simple method would be to use something like a coin hopper to 'make change' with chips, and rely on someone to insert those chips properly.
As for cards, you'll need to determine a way to recognize each card individually. Robotic Vision (Aka a webcam and some processing power) is the most obvious solution, but it isn't something the Arduino can handle. However it could handle locating cards to pick up, identifying chips, and reading what cards it drew. Cards are luckily quite regular in where they locate the value, which is handy.
We are not trying to dissuade you from doing this, but I think most of use are pretty serious in that this is not really in the scope of something to do with an Arduino. However, the complexity of this project is on the scale of something I'd expect from a graduate student.