Monopoly Simulation

If you are like me, you want to win in everything you do. Nothing is worth losing for, and any statistical advantage you can utilize is worth it.
One day, I was playing Monopoly and the idea that certain properties might be landed on intrigued me. I decided to make a simulator that could move around the Monopoly board more times than anyone could do themselves. The idea was fairly simple: just take a piece and roll two dice, then move the piece around the board and record the number of times each property was landed on. None of the financial aspects of the game needed to be included, but the Chance and Community Chest cards certainly needed to.
The following results were produced by the php script I wrote here: monopoly.zip.
It’s fairly well commented, and to increase or decrease the amount of turns taken by the script, the while loop needs to be adjusted. It should run on any php server, but I ran it on Apache 2.2.14 with PHP 5.3.1 on Linux, for reference. Inside the zip is the results page of a 100,000 turn game in a text file as well as a spreadsheet with all the card information from the game.
So let’s look at the results. First, the color groups:
Magenta: 11,625 landings - 11.6%
Purple: 1443 landings - 1.4%
Red: 10,434 landings - 10.4%
Railroads: 12,201 - 12.2%
Orange: 7173 - 7.2%
Blue: 7279 - 7.3%
Cyan: 5264 - 5.3%
Yellow: 3673 - 3.7%
Green: 3338 - 3.3%
Utility: 3342 - 3.3%

From this, it looks like Magenta, Red and the Railroads are the most landed on. This would suggest that the Railroads might be worth owning, if you own 3 or 4. For each color group, not owning all nullifies the meager rent you can collect without a monopoly, though. Now let’s examine the individual properties’ landings:

GO: 10,206 - 10.2%
Mediterranean: 522 - .5%
Community Chest [all]: 4411 - 4.4%
Baltic: 921 - .9%
Income Tax: 1372 - 1.4%
Reading Railroad: 7783 - 7.8%
Oriental: 1603 - 1.6%
Chance [all, only non-directing cards]: 2900 - 2.9%
Vermont: 1816 - 1.8%
Connecticut: 1845 - 1.8%
Jail: 12,938 - 12.9%
St. Charles Place: 8007 - 8%
Electric Company: 1997 - 2%
States: 1658 - 1.7%
Virginia: 1960 - 2%
Pennsylvania Railroad: 2321 - 2.3%
St. James: 2354 - 2.4%
Tennessee: 2480 - 2.5%
New York: 2339 - 2.3%
Free Parking: 1914 - 1.9%
Kentucky: 1777 - 1.8%
Indiana: 1287 - 1.3%
Illinois: 7370 - 7.4%
B&O Railroad: 1295 - 1.3%
Atlantic: 1225 - 1.2%
Ventnor: 1274 - 1.3%
Water Works: 1345 - 1.4%
Marvin Gardens: 1174 - 1.2%
Pacific: 1306 - 1.3%
North Carolina: 1171 - 1.2%
Pennsylvania Ave: 861 - .9%
Short Line Railroad: 802 - .8%
Park Place: 555 - .6%
Luxury Tax: 487 - .5%
Boardwalk: 6724 - 6.7%

Knowing the odds for each space allows us to know the actual worth of a property. For example, Park Place amounts to only .6% of all the landed upon spaces. It might not be landed on once in a typical game, but owning Park Place along with Boardwalk, which holds almost 7% of all landed on spaces, allows a player to double the normal rent without houses and take in significant cash with houses and hotels on the Blue spaces. St. Charles Place, holding 8% of all landings, makes States Ave and Virginia Ave worth owning alongside.

So there we have it: certain spaces are more likely to be landed on than others. Should this factor into your strategy? I know it will mine.

Short Link: http://cms07.org/?p=5

Posted by at 12:46 am on November 7th, 2011. 3 comments... »
Categories: Uncategorized.

3 comments.

  1. I’m interested in writing a computer simulation of a boardgame, and was just starting to do some reading on it when I found this blog post.

    I notice the link to your code isn’t working (it just redirects me to this page). Did you take it down?

    Posted by Andrew on January 26th, 2012.

  2. I apologize. I moved servers, and forgot to check links.

    I must say, though, that the code is probably not the best. For starters, PHP is not a very fast language (compared to C). I’m not sure if the simplistic handling of Chance and Community Chest cards is the best way, but it was the best I had at the time.

    Best of luck.

    Posted by admin on January 26th, 2012.

  3. Thanks! I downloaded the code, and hopefully I’ll get a chance to look at it tomorrow.

    Posted by Andrew on January 29th, 2012.

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