MDM4U Games - choosing player A or player B

The last few classes have been used to consolidate the concepts we have been working with thus far. Students were asked to ensure they had a definition in their notes for: probability, bar graph, histogram, probability distribution, random variable, discrete random variable, continuous random variable, and probability histogram. I did hand out a worksheet to practice probability and measures of central tendencies. 

Today we played several short dice games (I created these off the top of my head looking for some that have an equal probability of occurring and others that do not). Students were paired up and played each of the following games recording who won each game. 

Game #1:

• Roll the pair of dice. (2 standard dice)
• If sum is Even, Player A gets 1 point
• If sum is Odd, player B gets 1 point
• Play the game 10 times

Game #2:

• Roll the pair of dice. (2 standard dice)
• If the product is Prime, Player A gets 5 points
• If the product is not prime, Player B gets 1 point
• Play the game 10 times

Game #3:

• Roll the pair of dice (1 6-sided dice; 1 12-sided dice)
• If the sum is even, Player A gets 1 point
• If the sum is greater than 7, Player B gets 1 point
• Play the game 10 times

Game #4:

• Roll a set of dice (1 6-sided dice; 1 30-sided dice)
• If one number is even, Player A gets 1 point
• If one number is odd, Player B gets 1 point
• If both numbers are even, both players get 1 point
• If both numbers are odd, both players lose 1 point
• Play the game 10 times

Game #5:

• Roll the pair of dice (1 6-sided dice; 1 12-sided dice)
• If one number is prime, player A gets 2 points
• If the sum is less than 6, player B gets 3 points
• Play the game 10 times

Game #6:

• Roll the set of dice (2 standard dice)
• If the sum is odd, Player A gets 1 point
• If the sum is greater than 10, Player B gets 1 point
• If the sum is less than 5, both players lose 2 points
• Play the game 10 times

Game #7:

• Roll the set of dice (2 standard dice)
• If the product is less than 10, Player A gets 4 points
• If the product is greater than 18, Player B gets 4 points
• If the product is between 10 and 18, each player loses 2 points.
• Play the game 10 times

We gathered the data as a class to see if Player A or Player B had an advantage in each of the games. Based on our results, only game 6 had a clear advantage for player A - all other games were pretty even.

Students were then asked to determine the probability of each player getting points in each game. An interesting outcome was in game #2 where the probability of player A getting points is MUCH less than player B but our class results when playing the games showed that each player won the same number of times. 

This lead nicely to the start of a discussion of fair games and realizing that it is about more than just the probability of an outcome but what the point values are in a game. 

Our next class will be used to define a fair game and look at the mathematics behind determining if a game is fair or not.