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]
17 Responses to “Custom Number Formats – Colors”
You are right, Chandoo. I was playing with the colour numbers last week and some of them don't appear different from each other. Others are totally different from yours.
@Duncan
Each version of Excel, post 2003, renders colors slightly differently
Different language versions may also have different default color palettes
Hello in french
excel 2010
colo1 = couleur1 = black
[couleur1]; [couleur2]; etc..
@Hui, thank you very much again for this great post.
However - under Excel 2007, Hungarian version your solution does not work with color names. I've tried both English and Hungarian names, but drops an error message "not valid formats"
Do you have any idea how to solve this issue?
thanks in advance
@Andras
Without a Hungarian version of Excel 2003 I don't think I can assist
Have you tried using the colour numbers? I couldn't get the names to work (despite using an english version of excel). but it did work with the numbers though. I left out the "u" and was easily able to produce burgundy using [color9]
Here a possible solution: find an English version of Excel, write there the formats using English names, then open the file in the Hungarian version and see the translation.
In Excel 2007 I can't get the colour names to work e.g Sea Green but the numbers do e.g color3 - colour3 does not work so I must bow to the country that has stolen my language (ha ha!)
Hey chandoo, nice Tip!
Wouldn't be easier just apply some conditional formatting for negative numbers and another for positive numbers? Or there's some cases that you can't do that?
Unfortunately the TEXT function doesn't color the cell as number formatting does.
Hi Hui,
Great post Sir, love the new way of formatting with color numbers.
I am using 2007, and it leads me to the last color number 56.
Thanks Hui.
[…] explains how to set up custom number formats with a wide array of […]
Thanks Hui - works a treat!
Thank you, very helpful.
Trying to figure out if it is possible to apply color only to a part of the cell?
E.g. I have a value formatted as Accounting with a currency symbol.
Those I find somewhat distracting though necessary. If I could make them less obtrusive by coloring them gray while the number would stay black, that would be great. Tried tinkering with the format string, but didn't get the desired result. Single color for complete cell value works, but coloring just part of it could not be achieved. Maybe somebody managed that?
Exactly what I was looking for - thank you!
colour in the Australian doesn't work - we have to go American and no problem.
I always thought is was 56 colours notice you have 57. Cool.
thanks
Analir Pisani
Customised Microsoft Office Training Specialist
Sydney - Australia
http://www.azsolutions.com.au
Thank You!