Gambler's Ruin Worksheet
Directions: Use the print feature on your browser to print out this
page. Then answer the questions from the Gambler's
Ruin page. Each of the questions on the
Gambler's Ruin page has a space for writing in the solutions.
- You are to compute the chance of success by simulating individual
gamblers and tallying results.
Tally the number of winners here:
Tally the number of losers here:
Tally the number of unfinished gamblers here:
Compute the approximate chance of success here:
- Using the same paramters as the first problem, simulate the gambling
process using 32, 64, 128, 256, 512 1024 gamblers and tabulate the chance
of success. Discuss how the relationship to the exact value as the number
of gamblers is increased.
- Using the same paramters as the first problem, simulate the gambling
process as the goal gets larger. That is, let the goal start at $10 and
gradually increase the goal. Discuss what happens.
- Using the same paramters as the first problem, simulate the gambling
process as the chance of winning a play of the game decreases. That is,
let the chance start at 0.4736 and gradually decrease the chance to about
0.2. Discuss what happens.
- You are to compute the chance of success by simulating 250 gamblers. This
is repeated 5 times and the results compared to the exact value.
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Simulation No/
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Chance of Success/
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Difference from Exact
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Compute the average approximate chance of success here:
Compute the difference from the exact chance of success here:
Discuss the results of the simulations.
- Repeat the previous exercise using 500 gamblers.
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Simulation No/
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Chance of Success/
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Difference from Exact
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Compute the average approximate chance of success here:
Compute the difference from the exact chance of success here:
Discuss the results of the simulations.
- Discuss the differences in the results from the previous two problems.
Make a conjecture as to what would happen if the number of gamblers was
increased to 1000, 2000, and so on.
- Discussion of the problem of unfinished gamblers.