Simple Game 1
Worksheet 1
Enter the Prob of success for this simulation that you were assigned as your part of the class project? _________________
What is the expected value for the number of successes in 25 trials with this probability of success? ______________ (E = N P for simple binomial events like this one)
Load the STELLAã Model “simple prob event.STM” and enter the probability of success for your trial in the converter named “Prob level”.
In this simulation imagine that you are playing a game in which one point will win. You will play 25 games and keep track of how many you win. This type of experiment is sometimes called a Bernoulli Trial.
Enter 25 trials into the stock container named “Trials”.
Now run the trial and enter the results of the trial in the table below:
Repeat the simulation until you have done the experiment 20 times
Complete the information below the table and enter in the Class Data pool with the other simulations.
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Simulation Number |
1 |
2 |
3 |
4 |
5 |
6 |
7 |
8 |
9 |
10 |
11 |
12 |
13 |
14 |
15 |
16 |
17 |
18 |
19 |
20 |
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Number of wins |
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Count the number of times the number of wins was within ±1 of the expected value computed above. ___________________
Calculate the median value of the data _____________
Cross out the three highest scores, What is the highest score remaining?______________
Cross out the three lowest scores. What is the lowest score remaining? _____________
Here are some additional questions that you should try to answer using this simulation:
1) When one player is much better than the other they will sometimes give a handicap or spot of several points to the other player, or several losses to their own record. Suppose you are a much better player (let’s use .7 as your prob of success). Can you adjust the model to give a spot of 3 points to the opponent? Think about how you will “handicap” yourself by giving away five points in the model. Run your adjusted model for ten simulations of the 25 point game and average the number of wins in your simulations. Average = __________________
2) To make the 25 point game a “fair” game, you should have a mathematical expectation of 12.5 points. If you had a .7 probability of success, how many points do you think you should handicap yourself to make the 25 point game a “fair” game. Run several simulations and write a short paragraph to support your choice based on the results of some simulations.
3) Without performing another simulation, estimate the number of points handicap needed if the winning percentage was .9? Write your estimate here________. Now use the STELLAã model to evaluate this estimate. Describe what you did in the simulation and how it supports, or indicates a need to change, your suggested handicap.