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Several games can be based on this applet. Possible math goals of each game are indicated in parenthesis.
Game 1(idea of varying payoffs and its relationship with game fairness): Enter the probability of 0.1 for Player 1, and the probability of 0.3 for Player 2. Enter the payoff of 5 (points) for Player 1, and the payoff of 3 for Player 2. Run the program for many times (1000 or more) and observe which player wins more. Why does it happen?
Game 2(expected value): Without changing the probabilities, change payoffs in such a way that the game is fair. Do it in several different ways. Run the program many times to see if it is fair indeed.
Game 3(expected value; theoretical and experimental ways of finding expected value): Reset the payoffs and the probabilities in your own way. What average payoff per game do you expect for each player? This number is called expected value. Use Question #1 and Question #2 forms below the applet to have the computer check your expected payoffs. Run the program many (1000 or more) times to see if the average payoff per game gets close to your prediction. 
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