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]
12 Responses to “Analyzing Search Keywords using Excel : Array Formulas in Real Life”
Very interesting Chandoo, as always. Personally I find endless uses for formulae such as {=sum(if(B$2:B$5=$A2,$C$2$C$5))}, just the flexibility in absolute and relative relative referencing and multiple conditions gives it the edge over dsum and others methods.
I've added to my blog a piece on SQL in VBA that I think might be of interest to you http://aviatormonkey.wordpress.com/2009/02/10/lesson-one-sql-in-vba/ . It's a bit techie, but I think you might like it.
Keep up the good work, aviatormonkey
Hi Chandoo,
You might find this coded solution I posted on a forum interesting.
http://www.excelforum.com/excel-programming/680810-create-tag-cloud-in-vba-possible.html
[...] under certain circumstances. One of the tips involved arranging search keywords in excel using Array Forumlas. Basically, if you need to know how frequent a word or group of keywords appear, you can use this [...]
@Aviatormonkey: Thanks for sharing the url. I found it a bit technical.. but very interesting.
@Andy: Looks like Jarad, the person who emailed me this problem has posted the same in excelforum too. Very good solution btw...
Realy great article
"You can take this basic model and extend it to include parameters like number of searches each key phrase has, how long the users stay on the site etc. to enhance the way tag cloud is generated and colored."
How would you go about doing this? I think it would need some VB
Hi,
I found the usage very interesting, but is giving me hard time because the LENs formula that use ranges are not considering the full range, in other words, the LEN formula is only bringing results from the respective "line" cell.
Using the example, when I place the formula to calculate the frequency for "windows" brings me only 1 result, not 11 as displayed in the example. It seems that the LEN formula using ranges is considering the respective line within the range, not the full range.
Any hint?
@Thiago
You have to enter the formula as an Array Formula
Enter the Formula and press Ctrl+Shift+Enter
Not just Enter
Thank you, Hui! I couldn't work out how this didn't work
is there a limit to the number of lines it can analyse.
Ie i am trying to get this to work on a list of sentances 1500 long.
@Gary
In Excel 2010/2013 Excel is only limited by available memory,
So just give it a go
As always try on a copy of the file first if you have any doubts
Apologies if I am missing something, but coudn't getting frequency be easier with Countif formula. Something like this - COUNTIF(Range with text,"*"&_cell with keyword_&"*")
Apologies if I missed, but what is the Array Formula to:
1. Analyze a list of URL's or a list of word phrases to understand frequency;
2. List in a nearby column from most used words to least used words;
3. Next to the list of words the count of occurrences.