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…

About krusta80

I am a lover of mathematics, statistics, and games! Monopoly is the perfect storm of all of these, so I naturally I love Monopoly. :)
This entry was posted in Advanced Monopoly Strategies, Statistics and Analysis, Trading and tagged , , , , , , , , , . Bookmark the permalink.

3 Responses to Trading: Assessing Your Position

  1. Monopoly Mike says:

    Quick question. As rolling position is so important is it within the rules to offer cash either as an option or to the winning roller to start the game to take over their initial rolling position? And if so, is this worth $100-$200 to insure the best starting position?

    Thanks.

    • krusta80 says:

      Hey Mike! Thanks for the question.

      According to the rules, only items of material value may be included as part of a trade. It is illegal to promise anything as abstract as board position or immunity to future debts.

      That said, your question regarding a starting position’s worth is certainly interesting to ponder. First off, I assume by the word “starting” you are literally referring to the first roll of the game? If so, my guess is that it is probably NOT worth $100 (and therefore certainly not $200) to “buy” first roll, since there are still so many possible twists and turns left in the game. Although I have run simulations to show the adverse effect that late position has on naturally obtaining monopolies, very few games will ever be determined by properties landed on alone (especially ones involving more than three players).

      Maybe — just maybe — going from 5th or 6th to 1st is worth $100 however. Things really get tough for players five and six in my experience, but even then, giving up over 6% of your starting bankroll (let alone over 12%) with 100% likelihood to obtain a difficult-to-measure edge with a much more questionable likelihood seems unsound to me.

      For instance, let’s say that I proposition you to place a side bet (unrelated to monopoly) with me involving the flipping of a coin. Specifically, the game involves two players. The first player flips a fair coin once. If it comes up heads, he/she wins $1500 dollars. If not, the second player has a shot at getting heads for $1500, etc. In other words, the first person to flip heads wins…

      Clearly the first player has an advantage, since he/she has the first crack at winning the money:

      P(player 1 wins) = P(H) + P(TTH) + P(TTTTH) + … = 1/2 + 1/8 + 1/32 + … = 2/3
      E[V] = 2/3 * 1500 = $1000

      P(player 2 wins) = P(TH) + P(TTTH) + P(TTTTTH) + … = 1/3
      E[V] = 1/3 * 1500 = $500

      Even in this exaggerated example, going first is “only” worth $500. Now let’s change the game by making the winner the first player to roll a 6 (or really any number from 1 through 6) on a fair six-sided die:

      P(player 1 wins) = 1/6 + 25/216 + 625/7776 + … = 6/11
      E[V] = 6/11 * 1500 ~= $818

      P(player 2 wins) = 5/36 + 125/1296 + … = 5/11
      E[V] = 5/11 * 1500 ~= $682

      In this variant of the game, going first is worth about $136.

      The idea to note here is that as the probability of winning a game on the next roll decreases, so does the long-term monetary value of “buying the next roll”.

      • Monopoly Mike says:

        Krusta 80,

        Thank you for your thoughtful response! You answered my question and more!

        Best,

        Monopoly Mike

Leave a Reply

Fill in your details below or click an icon to log in:

WordPress.com Logo

You are commenting using your WordPress.com account. Log Out / Change )

Twitter picture

You are commenting using your Twitter account. Log Out / Change )

Facebook photo

You are commenting using your Facebook account. Log Out / Change )

Google+ photo

You are commenting using your Google+ account. Log Out / Change )

Connecting to %s