Trading: Applying Game Theory to Monopoly

“Well well well…that’s the last property available for purchase, and I do believe that I will be purchasing it!”

My brother looks over at me with a menacing smile, knowing all too well that I was dying to get my hands on Illinois Avenue before he could.  It was my last chance at acquiring a “natural monopoly”.  Now I have to play ball.

“I guess it’s time to trade, bro.  Talk to me!”

And here we have it…the most dynamic, intricate, and (apparently) LEAST scientifically analyzed part of Monopoly:  TRADING!

The art of trading in Monopoly is ultimately what makes the game so seductive.  It draws upon our humanity — our creativity, our social skills, and our biases.  But in the end, no matter how you slice it and dice it, trading simply boils down to an exchange of assets.

So why not attempt to analyze it like any other part of the game?

First we will look at the dynamics behind trades made in a two-player game.  Unlike in games with more players, one-on-one monopoly battles are often decided with only one trade (or fewer).  From an analytic perspective, this makes it the perfect place to begin.

To be continued…

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Don’t Touch That Token!!

Most Monopoly players identify with a particular token more than the others: the car, the dog, the ship…the cat (seriously, wtf?! lol).

But whatever your favorite piece may be, this post is geared toward helping you move it WITHOUT having to count out each space on the way to its destination.  I always find it slightly amusing when I see an opponent slowly tap each space of the board as he/she counts up to the amount rolled on the dice…that is, until I realize how long playing with this person will be!  It’s yet another reason so many Monopoly games take longer than necessary.

Even for those of you who hate math, I promise that it is not very difficult to do. In fact, from an early age my brother and I have been able to utilize a critical aspect of the Monopoly board…

Every side has exactly 10 spaces! The railroads are exactly 5 spaces in, which works well to further break down the spaces in a systematic and geometrically pleasing way.

Let’s go through a few examples:

  • You are on GO and roll a 7.  I’m sure that many of you have all of the first rolls memorized, but this is how confident you should feel FROM ANY SPACE.  So here’s the way to do this quickly, using the geometry mentioned above:
    - The distance between GO (a corner space) and Reading Railroad (a middle space) is 5.
    - This leaves 2 left from the 7 that was rolled.  Visually, you find the space two ahead of    RR, which is…drum roll everyone…Chance!
  • You are on Free Parking and roll an 11.
    - You are on a corner space, and you have rolled a 10 or higher.  This means that you     find the next corner space (10 away) and visually find the space 1 ahead of it (11 – 10 = 1).  Pacific!

Here are some general guidelines to help optimize your thought process while determining the destination space for your token:

  1. Rolling a 2, 3, or 4
    These are best handled by simply counting the spaces ahead of your token, but by all means please do it in your head.  :)
  2. Rolling a 5
    If you’re on a corner space, then let’s call the next railroad the next “marker”.  Like a ruler, think of the corner spaces as the inch lines and the railroads as the half-inch lines.  Rolling a five will always push you past (or up to) the next marker on the board.  So, if you’re on a corner space, the next marker is a railroad…and vice versa.  If you’re in-between markers, then your destination will always be the same distance ahead of the next marker as you currently share with your nearest marker.

    Example:  Mediterranean is one ahead of GO, so rolling a five will move you to one ahead of Reading Railroad…Oriental.

  3. Rolling a 6, 7, 8, or 9
    Always be aware of your spot on the side of the board!  This, of course, is good advice for strategic reasons, but it is also important if you want to be able to move your token effortlessly.  More specifically, always know your distance from the next corner space…and remember that the railroad space is there to help you count!

    The reason I have waited until now to emphasize knowing the distance to the next corner is because it is crucial to determining your destination square when rolling a 6 through 9:
    - If your roll is equal to the distance to the next corner, then that’s your destination
    - If your roll is less than the distance to the next corner, then combine [1]  and [2] above to find your destination on the same side of the board.
    - If your roll is greater then the distance to the next corner, then visually count ahead of the next corner the difference between your roll and the current distance to the next corner.

  4. Rolling a 10
    This is handled just like the last note of [3].  Subtract the distance to the next corner and visually count the remainder spaces ahead of that corner.  Visually, I like to think of rolling a 10 as bending a string around the edge of the board.
    When a game is started, the string extends from GO to Jail.  All 10 slots that the string covers are on one side of the board.  But now imagine that string shifted over one.  Now there are 9 slots on the first side of the board and 1 on the second.  Then 2 and 8, 3 and 7, 4 and 6, 5 and 5, etc…  The distances always add up to 10, but try to visually picture what the distances look like:  envision the string’s length of 1, 2, 3, etc as your token moves from spot to spot.
  5. Rolling an 11 or 12
    This is handled just like a 10, except either 1 or 2 extra spaces need to be tacked on at the end.  Combine [1] and [4] for a more detailed explanation.

All in all, moving the tokens around a Monopoly board is not very difficult.  In fact, there are many times when I don’t even think about it at all.  We humans are very visual creatures, and pattern recognition is something that drives us.  After enough practice (and hopefully thanks to the confidence/guidelines that this post has given you), you can save your brain cells for more interesting tasks…like figuring out who to pay for that hotel you just landed on!  :-P

Remember to keep the visual of a string in mind as you look at the board, and try imagining it for all possible rolls.  What does a string that is two spaces long look like?  How about eight spaces long?  Soon, you will instinctively know where to move your token.  And in the cases that your vision is unclear, rely on the rules listed above to get it right.

And don’t forget to have a fun, innocent chuckle inside as you watch a friend count out the spaces next time he/she rolls the dice.

Posted in The Basics | Tagged , , , , , , , | 3 Comments

Monopoly Quiz of the Week

Here’s the scenario:  

You are playing against two opponents and have all properties split up among the three of you, but none of you have a complete color group / monopoly and must therefore trade.  You each have about 1100 (give or take a few bucks) in cash and are all coincidentally sitting on “GO”.

After a lot of arguing, negotiating, and compromising, a most interesting choice has been reached.  Each player will end up with one of the following color groups:  magenta, red, or yellow.  It just so happens that all other properties are mortgaged, but these are not.

Assuming that you are able to convince your opponents to settle for any of the three aforementioned monopolies, which should you choose and why?  What factors are the most sensitive to this decision?

I look forward to your answers, and good luck!

** Now imagine the same scenario, except that the magenta properties are substituted with the light blues. How does this impact your decision and why?

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Monopoly Simulator Updated!

** Update – As of 11/3/12, the simulator will now validate all entered position information, in an effort to avoid invalid or corrupted sample games / win percentages.

Well, it’s taken a bit longer to post an update than I had originally planned, but I guess that’s what happens when the storm of the century turns everything upside down for a week!

Head on over to http://pandora.dyndns.biz/monopoly/simulator.html to check out some of the radical and exciting changes made. My personal favorite is the added functionality for getting a sample game and literally watching it play out in “Auto Action” mode.

An brand new tutorial / sample usage video can be found here:

As always, please hit me up with any bugs, limitations, or shortcomings that you would like to see fixed. Here are some of the next steps I’m planning on taking:

1. I will be making the entire position setup reversible, which is certainly a lot less frustrating than having to start from scratch after a mouse slip.
2. I’ll be implementing a server-side method of storing previously-tried positions, which will help go back-and-forth when analyzing slightly different starting positions.
3. I will continue to perfect the timing of actions taken on the board, as well as expanding the simulator’s building strategy to handle multiple monopolies.

Without further ado, enjoy!! Keep an eye out for a new video tutorial / trailer.

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Monopoly Simulator Online!

After several weeks of Java, Javascript, and PHP coding, I am proud to present the beta release of the Monopoly Nerd’s online simulator!

Here is a brief video tutorial on how to use the tool. Keep in mind that it is still far from a finished product, but the numbers seem quite reliable.

As always, I welcome your comments, questions, and suggestions.

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Do You Know the REAL Rules of Monopoly?

I thought that I would make today’s post a little more interactive than usual, so I encourage all of you to make your comments below.  They may not show up right away, but I will do my best to approve them as quickly as possible.  Once I get enough comments and replies, I will re-post the questions along with the official answers.

Now…onto today’s challenge!  So you think you know how to play Monopoly, huh?  We’ll see.  :)

Below are 10 questions that hit upon specific (or general) rules of the game.  Feel free to comment with your answers to any or all of them.  Good luck:

  1. How much money does a player receive when landing on GO?
  2. How much money does a player receive when landing on Free Parking?
  3. How much rent is paid to the owner when landing on Boardwalk, assuming it is unmortgaged but the owner’s Park Place is mortgaged?
  4. Situation:  You roll a seven, land on the chance space near Free Parking, and pick up the “Advance to Nearest Utility” card.  How much money do you owe the owner of Water Works, assuming that it is unmortgaged and he/she also owns Electric Company?
  5. How much does it cost to unmortgage New York Avenue?
  6. What is the highest payment possible for the owner of three railroads?
  7. Which came first…the Monopoly square spaces or the street names in Atlantic City?
  8. Is it possible to receive money from another player via trade if you do not possess any properties?
  9. If you are able to spend — via mortgage and cash — up to 1100 to build houses on the yellow properties (currently without houses or hotels and assuming no housing shortage), what is the maximum number of houses that can stand on Marvin Gardens after spending your money?
  10. You are grinning ear to ear after building hotels on the orange properties at what seems to have been the perfect time.  After doing so, the remaining twelve houses in the bank were quickly scrounged up by your desperate opponents, who could each only build one or two houses around the rest of the board.  You roll the dice, land on Luxury Tax, and owe the bank $75 (or $100 if you play the new Monopoly).  In an effort to build your hotels, you mortgaged every other property you own and have only $20 cash in hand.  Assuming that trading with your jealous opponents is off the table, how do you pay the bank?

Good luck to all who participate! 

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It’s NOT Just a Game of Luck!

It's NOT Just a Game of Luck!

This photo highlights the importance of board position when making a critical trade. Using my recently-completed Monopoly simulator, I’ve been able to precisely quantify the jump in win% when owning the light blues (versus oranges) and building when your opponent is on Mediterranean (the MOST DANGEROUS place for him/her to roll from) versus Connecticut (the SAFEST place).

The numbers along the bottom represent how much cash each player has before building, and the assumption is that both players build as aggressively as possible at the end of each of their turns…until one of them goes bankrupt.

All other property is mortgaged, to eliminate unwanted noise or variance.

My favorite is when starting with $1000 each. As the person ending up with the light blues, your probability of winning jumps from a miserable 32.51% to a favorable 57.7% just by timing it when your opponent is in solid striking distance!

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