Project I MC method

Project I MC method - Project I Monte Carlo...

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Unformatted text preview: Project I Monte Carlo Simulation for the Monopoly Game Description: Imagine you and one of your friends are playing a monopoly game following a greatly simplified rule. The game will be on an 11 by 11 area, just like a normal monopoly game. At the beginning, each player possesses $10,000 (game dollar of course). Two stones, each of which represents a player, are placed at the beginning place. The game starts by taking turns to throw one dice. The stone moves in one direction (clock ­wise) with the number of grids as given by the dice. A player wins the game is the other player’s cash becomes negative. The game rules are given as follows: 1. If that land is not owned by anybody, the player can buy the land with $200 if he/she has enough money. Note: the starting point cannot be bought by anybody. 2. If that land is pre ­owned by the player him/herself, the player will build one story of house with $200 if he/she has enough money to do so. 3. If that land is pre ­owned by the other player, the current player has to pay the rent according to the following formula: M rent = $100 × 5 , where M is the level of the house. 4. Whenever one player passes the starting point, this player will receive a bonus of $200. € Question: Write a Monte Carlo simulation code to answer the following questions. 1. How much advantage does the first player have over the second player? 2. If the second player has $20,000 while the first player has $10,000 when game starts, who has more advantage and by how much? 3. How much more money should the second player have so that the game is fair? Here the “advantage” means that one player has higher probability to win the game than the other. For example, if probability for the first player to win is 55%. We say the first player has an advantage by 55% vs. 45%. Requirement: Submit your code, along with a report of your simulation results and your answers to the three questions. Note: The solution may not be unique since they are decided from a Monte Carlo simulation. But you solution should be close enough. (From my test runs, 100,000 Monte Carlo runs seem to be necessary. They took me at least 15 seconds in Matlab on my MacBook Pro Laptop. If you are concerned with efficiency, you can try to use C or other language for your project. ) ...
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This note was uploaded on 01/20/2012 for the course CS 3414 taught by Professor Cs3414 during the Fall '01 term at Virginia Tech.

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