Probability Evaluation 11/12 th Grade Statistics Fair Games Random Number Generator Probable Outcomes Resources Why Fair Games? Probable Outcome Examples Fair Game Examples

Fair Games A fair game is a game or situation in which each person is equally likely to “win”. For a single player, this means the expected payout of the game is 0. For multiple players, each player has the same expected payout. For determining expected value/payout check out this video: lity/random-variables- topic/random_variables_prob_dist/v/expecte d-value--e-x lity/random-variables- topic/random_variables_prob_dist/v/expecte d-value--e-x

Why Fair Games? When thinking about games for entertainment purposes, fair games are important because no player wishes to play at a disadvantage. In gambling, unfair games could lead to a loss of money, so determining the fairness of a game is important in deciding whether or not to play. There are a few ways that unfair games can be made fair through random number generators.

Fair Game Examples Some fair games include chess and Stratego, where the amount of complexity makes the chances equally likely. The lottery is both fair and unfair. Each person has the same chance to win, but for each person the lottery is unfair because they are expected to lose. All casino games are unfair: “The house always wins”. Monopoly, LIFE, and most card games are fair games due to random chance.

Random Number Generators Random Number Generators can make games fair or assist in making them fair. Common random number generators include flipping a coin and rolling dice. For larger situations such as the lottery, an actual machine which generates random numbers is used. This can be found easily on a computer or calculator.

Probable Outcomes Similar to expected value, probable outcome is the expected result from a course or several courses of action. Probable outcome is usually associated with objective terms instead of mathematical terms. They are determined by assigning probabilities to payoff values and determining expected value as normal. People make decisions based on probable outcome all the time without realizing it.

Probable Outcome Examples An everyday probable outcome determination can be as simple as this: “I don’t think we should go to the beach because it is going to rain.” More complex would be like this: “How long will my new computer last?” Common complex probable outcome instances include the stock exchange, betting on races and other events, and insurance companies. An example and explanation of a complex probable outcome situation: variables-topic/random_variables_prob_dist/v/term-life-insurance-and- death-probability variables-topic/random_variables_prob_dist/v/term-life-insurance-and- death-probability

Resources Image slide 1: Bank.html Image slide 3: Image slide 4: Definitions from: Video linked in slide 2: variables-topic/random_variables_prob_dist/v/expected-value--e-x Video linked in slide 7: variables-topic/random_variables_prob_dist/v/term-life-insurance-and-death- probability