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1) Entertain the player.
2) Demonstrate calculator operation.
3) Teach and develop logic, language or math skills.
4) Demonstrate programming technique.
The serious users of calculators who say "I haven't got time for games" or "Games are too trivial for me to spend my time" are really only considering role number 1 above. If the calculator game only played the role of number 1 above, games would indeed be a waste of time for the serious problem solver. Role number 2 is quite useful for an expensive owner.
During a Thanksgiving gathering, you are asked to demonstrate your new HP-67. Will you impress your family and friends by showing how a program will solve a second order differential equation, or will a blackjack game better show what the calculator will do?
Some games are not really games in that they are excellent training exercises. If you can play ten games of Bagels with an average score of three guesses for a three digit number, then you don't need any training! If numbers are not very interesting to you, try some of the word games. Hangman is good and Word Bagels is always a fun challenge. Play any of these for a while and your thinking and reasoning powers will be sharpened considerably.
If the playing of games is not of interest to you, there is the most powerful use of games open for your benefit: Most GOOD games are written by highly skilled programmers. Not only do these users know their machines, but the know some pretty neat programming tricks. If you can understand the rules of the game, and usually the rules are simple enough to understand, you should be able to follow the program.
Why Games? People work because they have to. They play because they want to, and a game is an excellent meeting ground for two good minds: yours and the authors!