Trading: Assessing Your Position

Some board games — like chess or checkers — have an easily defined game state despite their complex nature.  If you need to save the game for another time, you simply remember or write down whose turn it is as well as where each piece stands on a 64-square board.

Another term for “game state” that is often used in chess is “position”.  But unlike the former term, “position” encompasses the underlying intricacies of the game.  Indeed, whereas an amateur chess player may look at a certain game state and see a “boring position”, a master could very well see something beautiful.  Whether it’s because of a five-move deep mating combination or a subtle endgame maneuver, the beauty of a chess position is in the mind of the beholder.

In Monopoly, assessing your position as well as the position in a game is critical to coming out on top of a trade.  Here are some of the variables and considerations that come into play when assessing a typical Monopoly (two-player) position:

  1. Does either player currently own a monopoly (aka color group)?

    This is (far and away) the most important component of any Monopoly game.  With the exception of the first color group (Mediterranean and Baltic Avenues), being the sole owner of a monopoly in a two-player game has virtually a 100% likelihood of leading to victory.

    NEVER give up your status of sole monopoly holder in a game, and do ANYTHING you can to convince your opponent to give up his/her status of sole monopoly holder.  I don’t care if your opponent offers you three additional monopolies for “just one” in return:  NEVER agree.  The additional utility of a second/third color group is a small fraction of that obtained from a player’s first.**

    [** This is mainly because you will normally start building on a second monopoly only once you have reached at least three houses on each property (the critical level) of your first monopoly AND you have spare cash in hand.  But if you find yourself in this wonderful scenario, then you are probably already crushing your opponent as it is.]

    NOTE:  ALL ITEMS BELOW ASSUME NEITHER PLAYER HAS A MONOPOLY.

  2. Does either your opponent or you still have a chance to complete a color group “naturally” (aka by simply landing on the needed property and purchasing it)?

    This rule is strongly linked to rule #1 for obvious reasons.  In short, NEVER trade with your opponent if you are the only one capable of completing a color group naturally.  On the flip side, ALWAYS try to trade with your opponent if he/she is the only one capable of obtaining a natural monopoly.

    BE ALERT!  Always pay attention to which properties belong to whom.

    NOTE:  ALL ITEMS BELOW ASSUME NO CHANCE AT NATURAL MONOPOLIES.

  3. According to the monopoly simulator, only a fraction of two-player games reach the point where trading is required for a player to own a monopoly / color group.  But these are often the epic battles that make Monopoly so enjoyable in the first place.  In other words, this is why we play the game!  So now what?

    Now we assess our position.

  4. Does our opponent have any biases or holes in his/her game that an be exploited?

    Just like poker, Monopoly is a game whose short-term outcomes are mostly determined by luck.  As human beings, our natural inclination toward pattern recognition and “learning from our mistakes” often gets us into trouble when it comes to games of chance.

    For example, after winning a game with Boardwalk and Park Place because all three of our opponents landed on us in succession, we may focus too much on the powerful rent prices that the dark blues provided us and not enough on how lucky we were to have been landed on so often.  [ie. three in a row is at least 20-to-1 against happening even in the best-case scenarios]

    In general, the approximate priority list of color groups in a two-player game is as follows:  oranges, reds/magentas, yellows, light blues / dark blues, dark greens, dark purples.  While cash/liquidity and other factors often trump the above list, it is certainly a reliable way to check for biases.  If someone really loves the dark greens or really hates the reds, by all means take advantage of that!  Maybe your opponent got destroyed once upon a time when he/she held the orange color group and is willing to give them up cheaply.  It doesn’t get any better than that!  :)

  5. Ok, so we’re not playing a “sucker”…now we need start analyzing the board position.What is each player’s approximate liquidity?

    I define liquidity in Monopoly as the sum of cash, houses/hotels (at selling price), and properties (at mortgage price).  In other words, liquidity is a measure of how much cash you can come up with alone if absolutely necessary.

    The rules of Monopoly state that a player need not disclose how much cash he/she has during the game, as long as all bills are visible (or part of a stack that is visible).  Therefore it is very important to keep track of any significant gains/losses that your opponent has encountered up to this point.  Has he/she been lucky with advanced to Go cards or the bank error card?  Has he/she been sent to jail a lot and has therefore not received $200 for passing go often?

    If you are not sure, then you can always ask your opponent for a cash count as a prerequisite of any deal happening, but remember that he/she can simply refuse and wait you out.  In that case, here are a few ways to get a decent idea of where he/she stands:

    - If you are unable to remember thinking to yourself at some point, “Wow, my opponent keeps getting lucky,” then chances are that you can use your financial position as a base for figuring out your opponent’s.  Take a quick glance at his/her properties as well as your own (which by mandate of the rules of Monopoly must always be visible to all players).  Estimate the difference in property value (purchase price) between you and your opponent and subtract/add that from your cash total to estimate his/hers.
    –  Mortgaged properties often point to an opponent with little cash.
    –  Mention that you’re interested in the light blues (by far the best monopoly for someone with low liquidity) and see whether he/she puts up a fight.  If he/she does, then you can be pretty sure that your opponent is tight on cash.

More to follow in my next post…

Posted in Advanced Monopoly Strategies, Statistics and Analysis, Trading | Tagged , , , , , , , , , | Leave a comment

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 , , , , , , , | 4 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?

Posted in Quizzes and Challenges | Tagged , , , , | 11 Comments

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! 

Posted in Quizzes and Challenges | Tagged , , , , , , , | 8 Comments