Is Monopoly Fair?

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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]

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25 Responses to “Shift Calendar Template – FREE Download”

  1. Alvin says:

    Hi Chandoo,

    your recent postings include only Excel 2007 templates. Unfortunately the company I work at still runs Excel 2003. Is it possible to get your awesome files in other excel version as well?

    Thanks so much for your great excel stuff!

  2. Stelios Tserkezis says:

    Is it possible to do this for shifts with hours instead of days? To organise a three shift day?

    Thanks in advance,

    Stelios

  3. MASTHAN says:

    In my organization there are 45 employees i need split then into three shifts ex:A shift:14,B shift:14,C shift:14 and week off:3 kindly help me on this.

  4. Hui... says:

    @Masthan

    You need to understand what rules your company has for the various shifts / roster combinations

  5. Georges Lacombe says:

    Chandoo, I once did a shift control spreadsheet for my team. I put one person in each line, the columns were the days. I put a shift code in each cell indicating in which shift that person should work, or if the person were out that day. I have two codes for being out. One is for vacations and one is to compensate days worked in weekends. This way I was able to count how many persons I have in each shift, how many were on vacations and how many were out compensating (that's the term we use here) weekend worked hours.
    Later I included the possibility of a person be in two lines one for normal hours other for overtime. This is mainly used for planning purposes. If you would like I can send you an example. The only problem of this spreadsheet is that we don't have a person view, only this consolidated view.

    • Chuck Vaughan says:

      Hi George, I would like to have a copy of your spreadsheet if you can share it.
       
      Thanks in advance, Chuck   

  6. Idan says:

    Hi Chandoo,

    Where is the code located ? is it VBA ? If so , how do you hide it ? Or it is .NET ?

    Thx

  7. Hui... says:

    @Idan
    .
    No VBA or code, it is all done with Mirrors.
    Only Joking,
    .
    But there is no VBA or code,
    It is all done with Named Formulas and Lookups.
    Have alook at the cells in the calander area and Named Formulas in the Formulas, Name Manager Tab.

  8. Anand Sant says:

    How can i calculate between two or more different workbooks? Please, reply me as early as possible.

    • Hui... says:

      @Anand
      Open the workbooks you want to link to
      Start a formula = and click and change between workbooks as required.
      You can use the View, Switch window menu to change workbooks mid formula

      The format for using workbooks is
      =[Workbook.xlsm]Sheet1!$A$1
      or
      =SUM('[Book2.xls]Sheet1'!$A$1:$D$10)
      etc

  9. Shemi says:

    Hi Chandoo,
    I am working with a call centre wherein i ned to update at the month end 20 to 30 employees login hours which are defict to track it at the month end is very difficult is there any template which can be made to track that why on a particular day a guy who needs to be on calls was why not on calls.

  10. Denice Lognshaw says:

    Thank you so much Chandoo. This is really helping me. As usual, you rock.

  11. Mukesh Verma says:

    What's FortyTwoDays and Calendar in Name manager?

    Both are unused and FortyTwoDays doesn't make any sense.

  12. Dave says:

    I have a SQL db that contains records of events scheduled/completed on a particular date. Can this method ous building a calendar be used to display those events on the respective day?

  13. Jan Halliday says:

    Positively awesome!
    I'm attempting to help a friend create a schedule for adult classes - and of course its not"paid help".  Here is the scenario:
    20 classes, instructor, room#, student class size, start date, number of class days (need to subtract weekends)

    class
    instructor
    room
    students
    start
    #days

    PATH
    karen
    201
    21
    01/01/13
    11

    BILLING
    jane
    401
    15
    01/12/13
    13

    MEDISOFT
    mike
    301
    11
    01/25/13
    9

    he'd like to see these classes show up in different colors within the same month's calendar chart.  He can draw it, but I'd like to see it done automatically through data, and I just can't visualize it, but I KNOW this will work - can you help?
    Jan 🙂
     

  14. Chan Tean says:

    Dear chandoo,

    Try many way to download still can't access. Any way we want to try out 3 shifts with 3 guys in a group .eg Group A Morn, Group B Night and Group C Rest. And every each group must work on sunday to take turns. In fact we are security teams so that's why sunday is required to work. Pls guide and show how to put in the working calendar. Thank you in advance.

  15. Veronica Burggren says:

    I've been trying to copy and/or recreate this to use in a workbook I'm doing for the transportation department I'm working for. I need to have the calendar on the first sheet in my document (it has graph's from data on another sheet). I'm trying to use it to track (with the conditional formatting) accidents and injuries. I've redone the conditional formatting to do 4 different accident types (no injury, near miss, OSHA recordable injury and work loss injury), but when I enter the formula's you have in the calendar portion where it says "DateOfFirst-FirstWeekDay" I can't figure out how you did that. Are you able to help?

  16. Pipin Fantom says:

    I would like to use Excel to solve the following problem for a community work. I want to create a Driver schedule for a given month from a pool of volunteers for a community service. Each of these volunteers can drive only on specific days in a week. I would like to populate the driving schedule for each weekday with primary, secondary and tertiary drivers in a random fashion so that I do not overburden one person. I would greatly any help you can provide.

  17. Ravichandra says:

    Hi chandoo,
    Thanks for your valuable effort for create this template and let me know how to add multiple employees in the the Roaster.

  18. Savitha says:

    Hi Chandoo,

    This article on shift roaster is very helpful. Could you please let me know how i can use the same for n number of resources who work 24/7, considering their leaves and holidays?

    Thanks,
    Savitha

  19. Balu says:

    Hi Chandoo,

    This article on shift roaster is very helpful to all. Could you please let me know how i can use the same if I want to add for some more shifts, since the color is not getting change if I add more shifts like 4,5 etc.,

    Thanks,
    Murali

  20. Sarah says:

    How can I change the date to 2017 under Shift Data worksheet.

  21. Cad says:

    solution 1:
    mydata=B2:C16
    stoplist=E2:E8

    =LET(RNG,A2:A16,SMR,C2:C16, F,(RNG=E2)+(RNG=E3)+(RNG=E4)+(RNG=E5)+(RNG=E6)+(RNG=E7)+(RNG=E8),SUM(SMR)-SUM(SMR*F))

    =LET(RNG,A2:A16,SMR,C2:C16,RH,N(B2:B16=B2), F,(RNG=E2)+(RNG=E3)+(RNG=E4)+(RNG=E5)+(RNG=E6)+(RNG=E7)+(RNG=E8),TOT,SUM(SMR)-SUM(SMR*RH*F),SUM(SMR*RH)-SUM(SMR* RH*F))

    ALTERNATE SOLUTION
    =SUM(C2:C16)-SUM(FILTER(C2:C16,ISNUMBER(BYROW(A2:A16,LAMBDA(a,TOROW(SEARCH(a,E2:E8),2))))))

    =SUM((B2:B16=B2)*(C2:C16))-SUM((ISNUMBER(BYROW(A2:A16,LAMBDA(a,TOROW(SEARCH(a,E2:E8),2))))*(B2:B16=B2)*(C2:C16)))

  22. Cad says:

    let
    Source = Excel.CurrentWorkbook(){[Name="Table1"]}[Content],
    #"Replaced Value" = Table.ReplaceValue(Source,null,";",Replacer.ReplaceValue,{"Column1"}),
    #"Transposed Table" = Table.Transpose(#"Replaced Value"),
    #"Removed Other Columns" = Table.SelectColumns(#"Transposed Table",{"Column1", "Column2", "Column3", "Column4", "Column5", "Column6", "Column7", "Column8", "Column9", "Column10", "Column11", "Column12", "Column13", "Column14", "Column15", "Column16", "Column17", "Column18", "Column19", "Column20", "Column21", "Column22", "Column23", "Column24", "Column25", "Column26", "Column27", "Column28", "Column29", "Column30", "Column31", "Column32", "Column33", "Column34", "Column35", "Column36", "Column37", "Column38", "Column39", "Column40", "Column41", "Column42", "Column43", "Column44", "Column45", "Column46", "Column47", "Column48", "Column49", "Column50", "Column51", "Column52", "Column53", "Column54", "Column55", "Column56", "Column57", "Column58", "Column59", "Column60", "Column61", "Column62", "Column63", "Column64", "Column65", "Column66", "Column67", "Column68", "Column69", "Column70", "Column71", "Column72", "Column73", "Column74", "Column75", "Column76", "Column77", "Column78", "Column79", "Column80", "Column81", "Column82", "Column83", "Column84", "Column85", "Column86", "Column87"}),
    #"Merged Columns" = Table.CombineColumns(#"Removed Other Columns",{"Column1", "Column2", "Column3", "Column4", "Column5", "Column6", "Column7", "Column8", "Column9", "Column10", "Column11", "Column12", "Column13", "Column14", "Column15", "Column16", "Column17", "Column18", "Column19", "Column20", "Column21", "Column22", "Column23", "Column24", "Column25", "Column26", "Column27", "Column28", "Column29", "Column30", "Column31", "Column32", "Column33", "Column34", "Column35", "Column36", "Column37", "Column38", "Column39", "Column40", "Column41", "Column42", "Column43", "Column44", "Column45", "Column46", "Column47", "Column48", "Column49", "Column50", "Column51", "Column52", "Column53", "Column54", "Column55", "Column56", "Column57", "Column58", "Column59", "Column60", "Column61", "Column62", "Column63", "Column64", "Column65", "Column66", "Column67", "Column68", "Column69", "Column70", "Column71", "Column72", "Column73", "Column74", "Column75", "Column76", "Column77", "Column78", "Column79", "Column80", "Column81", "Column82", "Column83", "Column84", "Column85", "Column86", "Column87"},Combiner.CombineTextByDelimiter("|", QuoteStyle.None),"Merged"),
    #"Split Column by Delimiter" = Table.ExpandListColumn(Table.TransformColumns(#"Merged Columns", {{"Merged", Splitter.SplitTextByDelimiter(";", QuoteStyle.Csv), let itemType = (type nullable text) meta [Serialized.Text = true] in type {itemType}}}), "Merged"),
    #"Added Prefix" = Table.TransformColumns(#"Split Column by Delimiter", {{"Merged", each "|" & _, type text}}),
    #"Replaced Value1" = Table.ReplaceValue(#"Added Prefix","||","|",Replacer.ReplaceText,{"Merged"}),
    #"Split Column by Delimiter1" = Table.SplitColumn(#"Replaced Value1", "Merged", Splitter.SplitTextByDelimiter("|", QuoteStyle.Csv), {"Merged.1", "Merged.2", "Merged.3", "Merged.4", "Merged.5", "Merged.6", "Merged.7", "Merged.8"}),
    #"Removed Columns" = Table.RemoveColumns(#"Split Column by Delimiter1",{"Merged.1"}),
    #"Removed Duplicates" = Table.Distinct(#"Removed Columns")
    in
    #"Removed Duplicates"

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