Monopoly

I have recently managed to convince my (now) wife to play Monopoly with me, which has caused her to realize she is much better than she thought. Even I was mildly surprised at her newfound skill. This has forced me to expand on my knowledge of the game with the hopes of improving my own skills and therefore chances of winning against my new and quite formidable opponent. Expanding my knowledge on this topic has been no easy task, given that previously in my lifetime I have read many books on Monopoly, own at least 10 official versions, created my own magnetic travel Monopoly, and even wrote a computer program (in Pascal of all languages) to simulate the game and keep track of the related statistics. This post tells of some of the things I have learned this time around.

The first hurdle of my learning process was to understand and come to terms with the changes that have been made to the game since the boards that I'm used to playing on were issued. This was somewhat difficult because the version I have recently purchased is entirely in Polish (as it was purchased here in Warsaw, Poland) and has some mistakes in the rules and cards. In fact the recent changes to the rules and those few mistakes created some intense confusion while playing with my wife and some of her family here in Poland. Luckily, I understood very little of what was said during this confusion, and therefore avoided the additional controversy present in many board game nights.

With the help of a great source (Monopoly-History.com) I was able to nail down that none of the recent rules changes are seriously game changing:

• You can't pay 10% income tax, only $200,
• You start the game with less small change, but more $100 bills (still $1500 total),
  
• Three of the Community Chest cards are slightly different:
  
  • Pay school fee of $50 instead of $150,
  • From sale of stock receive $50 instead of $45,
  • Collect $10 from every player instead of $50,
• Luxary tax is now $100 instead of $75, and
  
• The dark purples are now brown.
  

After learning Polish well enough to read the rules and cards, I also realized that the remaining differences between my Polish version and my older versions are most likely mistakes or translation errors:

• Some of the Chance and Community Chest cards are slightly different/messed up:
  
  • The "advance to nearest utility" card tells you to advance to "Elektrowni" (electric company), roll the dice, and pay owner the appropriate amount (instead of 10 times the amount thrown),
  • The "advance to the nearest railroad" cards simply tell you to go to the nearest railroad, creating confusion on whether or not to go forwards or backwards, then continues to tell you to roll the dice and pay owner the appropriate sum (which makes no sense at all, they must have just copied and pasted from the previously mentioned card, and
• The rules say to collect "2 miliony dolarów Monopoly", which means 2 million Monopoly dollars (they must have gotten confused with the Here-and-Now edition),

Since sorting out the above, fewer arguments developed, but I was still having a hard time winning consistently. Next I thought I would attempt to better understand the statistics and data engrained within Monopoly. Inspired by the Information is Beautiful blog to attempt to create a few of my own visualizations, I thought an "all encompassing" Monopoly visualization would be the way to go:

  

While making this image I learned more about Monopoly than I was expecting, and now that I have it, I have found it to be a useful reference when confronted with difficult mid-game choices. All at once, it shows:

• The chances of receiving money, paying money, or being relocated if you draw a chance or community chest card,
  
• The monetary return on investment you will gain for each visitor that lands on one of your spaces, if that space is fully upgraded at the time (shown in terms of the cost of the local buildings: for example if someone lands on your fully upgraded Tennessee Avenue they will pay you $950, which is worth almost 10 houses on Tennessee at $100 per house, or almost 2 full hotels), and
  
• The theoretical chances of landing on each space within the first 22 rolls of a game (normalized such that Reading Railroad is not faded at all and Mediterranean Avenue is minimally faded). Jail was not used for normalization even though it is by far the most landed on space because it would overpower all the other data, eliminating most of the distinction between the other spaces.
  

As a side note, while working towards this visualization, I came up with a cool video that shows what happens to the probabilities of landing on each space for each of the first 8 rolls of any Monopoly game. I like to think of this as a representation of the quantum probabilities of every monopoly game, or a weighted combination of all the possible Everett Universes encompassing the entire board with time:

Also, a huge thanks to Brad Frost Web for starting me off with a Monopoly photoshop template.

Please contact me (or comment below) for more information, how I did my calculations, the raw data that went into this visualization, or any number of (slightly uglier, excel based) graphs and charts that provide insight into additional interesting Monopoly data.