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]
18 Responses to “Best Charts to Compare Actual Values with Targets – What is your take?”
Great post. I can't vote, though, because the answer I want to put down is "it depends". As with all visualisations, you've got to take into account your audience, your purpose, technical skills, where it will be viewed, etc.
I'm with Andy: It depends. Some I would use, some I might use, some I won't touch with a barge pole.
Naturally I have comments 🙂
The dial gauge, though familiar, is less easy to read than a linear type of chart (thermometer or bullet). It's really no better than the traffic lights, because all it can really tell you is which category the point falls in: red, yellow, or green.
By the same token, pie charts are so familiar, people don't know they can't read them. Remember how long it takes kids to learn to read an analog clock?
Bullet charts don't show trends.
With any of the charts that have a filled component and a marker or ine component, it makes more sense to use the filled component (area/ column) for target, and the lines or markers for actual.
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I voted for #6 even though I agree with the other comments that it depends.
The majority of the votes are for the #2, thermometer chart. I still have yet to understand what happens when you are above plan/goal, which was brought up in yesterday's post.
Also, I agree with Jon in that it would be better to flip the series and make the filled part the target or goal and the line or marker the actual.
I am also a fan of using text when appropriate if the data is among other metrics in a type of dashboard. Calling it out by saying actual and % achievement is a good option.
Another "it depends" vote. Are you just looking at one or are you comparing a number of targets with actuals? You didn't include a text box. The problem with sentences is that they can get lost in a page of gray text. A text box can call attention to the numbers and line them up effectively.
I'm with Jon: "Some I would use, some I might use, some I won’t touch with a barge pole" and I'm surprised that some of your readers voted for the last group.
Jon says:
With any of the charts that have a filled component and a marker or line component, it makes more sense to use the filled component (area/ column) for target, and the lines or markers for actual.
Why does this make more sense? I like 6 the way it is, although I would use a heavy dash for the plan/target marker.
"It depends" is also my take. What I usually try to drill into my clients dashboard design is the fu ndamental difference between spot results (am I on target for this month) and long term trends.. I always try to create 3 different set of graphs to represent real perormance:
- spot results vs objectives
- cumulative results vs objectives
- long-term trend (moving average) mostly) to see where we're going
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Jon says:
With any of the charts that have a filled component and a marker or line component, it makes more sense to use the filled component (area/ column) for target, and the lines or markers for actual.
Why does this make more sense? I like 6 the way it is, although I would use a heavy dash for the plan/target marker.
I totally agree, Bob. I would normally favour a line for the target and a column for the actual, you can see quite easily then which columns break through the line, then.
[...] best charts to compare actual values with targets — den Status mal anders zeigen, z. B. als Tacho [...]
Thermometer charts: "Not appropriate when actual values exceed targets" - this is easily solved by making the "mercury" portion a different color from the border, then you can clearly see where the expected range ends and the actual values keep going.
People seem to knock gauges quite a bit in dashboarding, but trying to show comparison of realtime data between operating sites and targets for each site can easily be done with a bank of gauges that have the optimal operating points at 12 o'clock.
The human eye is great at pattern stripping, and any deviation of a gauge from the expected 12 position will quickly register with an operator and attract his attention. Using a colour background, or meter edge, will also indicate the sensitivity of a particular site.
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I am wondering how will the plotting work, for some of the targets which may have been achieved before time. E.g. for the month of Jul the target was 226 and the actual was 219. So the chart will show a deficit in meeting the target by 7 points but what if this 7 may have been completed earlier in month of June. So ideally it not a deficit.