Is Monopoly Fair?

Posted on February 25th, 2007 in Learn Excel , simulation , wonder why - 15 comments

Ever since we have purchased the Monopoly board game, it has become a weekend ritual for us. Almost every Friday/Saturday night Jo would pull out the board, currency, wooden dice, small houses and deed cards and spread them.

We are in for a surprise after playing the game for few weeks. As kids we thought the game is a GAME, ie random to high extent but fun. But as we develop an eye for the detail, the game does come out to be rather unfair. How else can you explain that one of us is paying rents through their noses to the other one owning reds and oranges and how else can you explain that the one who purchased properties next to GO seldom gets a visitor, including themselves. We started questioning, is monopoly fair? And thats where I set out to find it myself.

For starters, The monopoly board has 40 cells, and every player starts at GO. The moves are decided by sum of the faces on a 2 dice throw. If you get a double you get to throw again.

I have tried to simulate the game using excel. I have observed all the rules like community chest / chance cards, Jail and go to jail. But I have not observed doubles rule for I thought it had little impact on the outcome. I wanted to see if the expected probabilities of each cell (which is 1/40 or 2.5%) are close to the actual probabilities.

When I ran the simulation for 10000 dice throws for 4 players, the absolute difference between expected probabilities of each cell, color group are more or less near to the actual probabilities as you can see in the below charts. (click on them for bigger versions)

The maximum deviation is to the tune of 6% for individual cells and 1.93% for a color group (for there will be cancellations in color groups, as one cell gets more visitors the other would get less)

But that is not we experience when we play the game. We end up landing in Jail or a chance an awful lot of times more than we expect to land there. Thats because, no one ever plays a 10000 throw per person game, not in day to day versions. Its more like 200-400 throws. So when I ran the same experiment for 200 turns for 4 players, the results were more interesting as you can see them below.

As you can see the deviation in the actual probability and expected probability is huge. Some times 60% more for individual cells and 20% for color groups. This I guess explains the reason behind the Monopoly game strategies like buy anything in Orange and Red groups etc.

Obviously one fault of this experiment is if you run it again the actual probabilities are going to change in favor of something else. But almost always far from the expected results.

Write to me just in case you want to play around with my monopoly board game simulation excel sheet, I can mail it. The file is rather huge for upload.

Related links: Monopoly Wiki, Monopoly Fun Facts & Strategies, Similar Monopoly Simulations [1, 2]

Written by Chandoo
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15 Responses to “Is Monopoly Fair?”

  1. I just recently found your site
    please send me a copy of the excel monopoly simulation sheet

  2. Chandoo says:

    @michael bells, thanks for visiting PHD. I am sorry, but unfortunately I donot have the excel sheet with me now, I have moved to America recently and the stuff was on my old comp in India. May be when I go back I can get you this sheet, not sure when that happens. Will drop another comment if I ever come across the excel.

  3. Kevin Stone says:

    You stated that "You Can't : Refer to other sheets in conditional formating. You can only refer to the sheet where conditional formating is being applied."

    There is a way to do this using "Named Ranges."

    On sheet 1, Define the Name of Cell A1 as "Upper", and Cell A2 as "Lower." Enter 120 in A1, and 80 in A2.

    On sheet 2, enter a bunch of numbers, including some over 120 and some under 80. Highlight the numbers and go to Conditional Formatting. For Condition 1 choose "greater than" and enter "=Upper" (without the quotes); for Condition 2 choose "less than" and enter "=Lower".

    You get the idea here. Now you can have multiple sheets that look to your values on sheet 1 for Cond Formatting!

  4. Chandoo says:

    @Kevin Stone .. thanks for the comments, welcome to PHD.
    Thats a nifty trick you suggested for conditional formatting across worksheets, will keep in mind and use it.

  5. [...] That is why whenever I get sometime I experiment with simulating games to know them better [read Why Monopoly board game is not as random as it appears]. So, out of curiosity I have created an excel sheet that can generate bingo / housie (housey) [...]

  6. [...] I have used this logic to simulate monopoly board game and prove that it is not really that random. [...]

  7. Greg says:

    Why is this even about monopoly? All you showed is that a particular string of events might not occur with the most probable incidence of each event. You can demonstrate that by rolling a single die once: You certainly don't get each number 1/6 of the time.

    Let's list your argument:

    Here is the expected incidence
    Here is what actually happened
    It is different, and will probably be different every time

    I still don't think you've said anything.

    Also, you have graphs saying "actual probabilities". They aren't actual probabilities. The actual probabilities are the expected values of incidence. That's what makes them probabilities!

  8. adam says:

    Hi. Nice post, i'll certainly be playing for the first time in a while tonight! One thing though, not sure I understand your "deviation from expected" graphs.
    surely the sum total of %'s shouls be zero. I dont see how every single square on the board had a higher than expected deviation from the expected...?

  9. Chandoo says:

    @Adam... thanks.. you are right, the deviations should be zero. What I have plotted are "absolute of deviations from expected values" thus all of them are positive.

  10. Chandoo says:

    @Greg: I agree, that is exactly what I said. "simulated monopoly". This is more of an experiment to see whether each square on monopoly board has same probability of having you landed there. As with any experiment (or test) you should always take the results in that light only. When you change the pre-conditions (or repeat the experiment) the results may vary. In this case, they may not vary that much.

    Just to keep it real, I have made sure that the dice throws are reasonable.

  11. [...] have used excel to simulate monopoly board game, just so I can play it better than my [...]

  12. ashvindx says:

    very interesting insights!

    The core of monopoly remains to teach you about finance! the strategy to win is definitely to take from a single colour and build as many houses in a single location - instead of buying everywhere.

  13. Krishna says:

    Great analysis Chandoo.

    Can you share the link to me?


  14. Jordy says:

    Hi this is great

    could you send me a copy?

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