Racing Game with One Die

What is Racing Game with One Die?

This applet allows the user to simulate a race where the results are based on the roll of a die. The user can determine which player moves forward for a given roll, and can then experiment with the race by determining which player will win more often based on the rules that they specify. The rolling of a die is one example of probability. Each roll of the die gives you a one in six chance that a certain number will appear. Probability is just the expected value of what the outcome should be. If you run the applet a hundred times you will see that the probability you came up with (known as the experimental probability) will be close but not always exactly what you would expect (known as the theoretical probability).

Probability began in the middle of the seventeenth century by a man named Pascal. One day a man proposed a question about gambling. His question was "If I play a game that I have eight chances to roll a six and I fail the first three times, how much of my bet should I get back?" The game involved chance just as most games do now, such as Monopoly and card games. Las Vegas is a city that is dominated by people that have invested in this field of mathematics. Today, probability has found its way into the fields of science, medicine, and statistics.

Related Resources

• Activity Advanced Monty Hall
• Activity Crazy Choices Game
• Activity Experimental Probability
• Activity Generalized Monty Hall
• Activity Racing Game with Two Dice
• Activity Simple Monty Hall
• Activity Two Colors Applet
• Discussion about Equally Likely (Fair) Choice
• Discussion about Probability of Simultaneous Events
• Discussion about Probability vs. Statistics
• Discussion about Random Number Generators
• Worksheet Racing Game (One Die) Suggestions
• Worksheet Racing Game (One Die) Suggestions (doc)
• Worksheet Racing Game Field

How Do I Use This Activity?

This activity allows the user to play a game in which two players move towards the finish line based on the roll of a six-sided die.

A more complicated version of this game, Racing Game with Two Dice, is available, too.

Controls and Output

• Independent Run Panel

  • Clicking the Roll Die button simulates rolling the dice and making a move in the game. Only the lucky player, as determined in the Configuration Panel (see below), moves each time.

    

  • Clicking the Restart button starts the race over again.
  • Sliding the Race Segments slider bar increases or decreases the length of the race (number of steps to the finish line).
  • The graphic of the race track shows each players current position:
• Configuration Panel

  • You can determine the "lucky player" by clicking the radio buttons to choose which player gets to move for each roll value. So, if you say that red moves on 1, 2, and 3, each time one of those values is rolled on the die, the red car moves ahead one space.

    

  • Notice that this panel gives you the option of collecting cumulavtive stats. If you choose yes, then the statistics in the multiple run panel (see below) will include every run that you do. If you choose no, then the statistics will only include the most recent race.
• Multiple Run Panel
  • This panel allows you to simulate many races without having to run each one individually. To do this, you must enter the number of runs that you wish to complete and click on the Race! button.
  • After you run a number of races, you will see that this panel displays the number of races each car has won, the percent of the races that each car has won, and a pie chart showing graphically the percentage of races each car has won.
  • Use the Clear Stats button to remove cumulative stats and start over with the statistics collection.

Description

This activity allows the user to play a game in which two players move towards the finish line based on the roll of a six-sided die. This activity would work well in mixed ability groups of two or three for about twenty minutes if you use the exploration questions and ten to fifteen minutes otherwise.

Place in Mathematics Curriculum

This activity can be used to:

• introduce the notions of chance and probability
• allow students to experiment with probability and the notion of a fair game
• motivate the notion of conditional probability
• motivate the notion of random numbers

Be Prepared to

• give implicit directions on what they are to do. For example "Today we are going to play the racing game. We are going to try to determine the likelihood of the cars winning if they advance when certain numbers are rolled. I want you to figure out how often the red car wins when he advances on one number, two numbers,..., all six numbers on the die..."
• answer the question "What is the cumulative stats button for?"
• discuss experimental probability and theoretical probability.

Related Resources

• Activity Advanced Monty Hall
• Activity Crazy Choices Game
• Activity Experimental Probability
• Activity Generalized Monty Hall
• Activity Racing Game with Two Dice
• Activity Simple Monty Hall
• Activity Two Colors Applet
• Discussion about Equally Likely (Fair) Choice
• Discussion about Probability of Simultaneous Events
• Discussion about Probability vs. Statistics
• Discussion about Random Number Generators
• Lesson on Conditional Probability and Probability of Simultaneous Events
• Lesson on Ideas that Lead to Probability
• Lesson on Introduction to the Concept of Probability
• Lesson on Tree Diagrams and Probability
• Worksheet Racing Game (One Die) Suggestions
• Worksheet Racing Game (One Die) Suggestions (doc)
• Worksheet Racing Game Field