Uncategorized October 14, 2016 James 2 comments

What is the “best” Monopoly property?

What is the best Monopoly property?

It really depends on what you consider to be “best”. We’re actually going to answer 5 separate questions, each asking the same question a different way:

  1. Which property has the best Return on Investment, before hotels and after?
  2. Which property is most frequently landed on during the game?
  3. Which color of properties are most frequently landed on during the game?
  4. Which property has the highest revenue, before hotels and after?
  5. Which color of properties have the highest revenue, before hotels and after?

The Tools and Methods

We’re going to be doing all of these calculations using Python 3 with pandas in Jupyter Notebook.

For the hit frequency and revenue analysis, I’m going to be running a Monte Carlo Simulation on Monopoly. This simulation is going to be focused strictly on movement in the game. It does take into account: rolling doubles, various ways to go to jail, and chance and community chest cards. It will not simulate buying properties, banking, players dropping out, etc. What the simulation will do is run 10,000 games of Monopoly with 4 players 100 rounds in each game. Then we’re going to count how many times each property has been landed on, and use that in our calculations.

Let’s get started!

A Copy of the American Game Board

Free Parking

Kentucky Avenue
$220
Chance Indiana Avenue
$220
Illinois Avenue
$240
B&O Railroad
$200
Atlantic Avenue
$260
Ventnor Avenue
$260
Water Works
$150
Marvin Gardens
$280
Go To Jail

New York Avenue
$200
MONOPOLY
Pacific Avenue
$300
Tennessee Avenue
$180
North Carolina Avenue
$300
Community Chest Community Chest
St. James Place
$180
Pennsylvania Avenue
$320
Pennsylvania Railroad
$200
Short Line
$200
Virginia Avenue
$160
Chance
States Avenue
$140
Park Place
$350
Electric Company
$150
Luxury Tax
(pay $100)
St. Charles Place
$140
Boardwalk
$400
In Jail/Just Visiting Connecticut Avenue
$120
Vermont Avenue
$100
Chance Oriental Avenue
$100
Reading Railroad
$200
Income Tax
(pay $200)
Baltic Avenue
$60
Community Chest Mediter-ranean Avenue
$60
Go
(collect $200)
Monopoly Go Arrow.png

Which property has the best Return on Investment, before hotels and after?

What do we mean by “Return on Investment”?  Simply put, our ROI is how many times must another player land on this property before we get our money back we put into it.

ROI = (Cost of Property) / (Rent)

We’re going to calculate the ROI without any buildings, and then with hotels.

Top 10 with 0 Buildings

Board Position Property Name Low Cost Low Rent Low ROI
28 Water Works 150 28 5.357143
12 Electric Company 150 28 5.357143
25 B&O Railroad 200 25 8.000000
15 Pennsylvania Railroad 200 25 8.000000
5 Reading Railroad 200 25 8.000000
39 Boardwalk 400 50 8.000000
35 Short Line 200 25 8.000000
37 Park Place 350 35 10.000000
34 Pennsylvania Avenue 320 28 11.428571
31 Pacific Avenue 300 26 11.538462

From a ROI stand point, before buildings are put out on the board, Utilities and Railroads are the way to go. They recoup their cost faster than the traditional colored properties. Let’s take a look at the results when we add hotels into the mix.

Top 10 with Hotels

Board Position Property Name High Cost High Rent High ROI
9 Connecticut Avenue 370 600 0.616667
8 Vermont Avenue 350 550 0.636364
6 Oriental Avenue 350 550 0.636364
19 New York Avenue 700 1000 0.700000
39 Boardwalk 1400 2000 0.700000
18 Tennessee Avenue 680 950 0.715789
16 St. James Place 680 950 0.715789
14 Virginia Avenue 660 900 0.733333
11 St. Charles Place 640 750 0.853333
13 States Avenue 640 750 0.853333

 Since Utilities and Railroads can’t have buildings, their ROI becomes unchanged, so are actually a worse investment long term in the game. The best property for a good ROI is Connecticut Avenue, with costs $370 to build up to a hotel, but returns a whopping $600 when a player lands on it! Well worth the investment it seems.

ROI is great, but it doesn’t give the best picture. Certain properties get hit more than others, and therefore will generate money more often.

Which property is most frequently landed on during the game?

 For this calculation, we’re going to run the Monte Carlo simulation. You can find the notebook used to run the simulationand the output from the code on Github. I also have the results from this simulation available in a zip file. Warning, this unzipped file is 219MB. Be aware before opening.

After running the simulation, here’s what we got.

Top 10 most frequently landed on properties

 Board Position Property Name Count Percent of Total Count
10 Jail 295199 5.6890 %
25 B&O Railroad 179864 3.4663 %
0 Go 146917 2.8314 %
19 New York Avenue 146168 2.8169 %
5 Reading Railroad 144861 2.7917 %
35 Short Line 142711 2.7503 %
15 Pennsylvania Railroad 141960 2.7358 %
17 Community Chest 141822 2.7332 %
18 Tennessee Avenue 139522 2.6889 %
28 Water Works 136729 2.6350 %

It should come as no surprise, but most of the time people are in jail. There are many ways to go to jail, from rolling multiple doubles, to chance or community chest cards, to another space on the board telling people to go there! What’s interesting is that B&O took the #2 spot. My first guess would’ve been the Community Chest in position 17, since it is 7 spaces away from jail. But it is actually all the way down in 8th place.

Why is this? My best guess is Chance cards. There is a Chance spot 12 spaces from Jail and there are two “Advance Token to the Nearest Railroad” cards in the Chance deck. Meaning you have a 1/36 chance of rolling a 12 from jail and landing on Chance. Then a 1/8 chance of advancing to the nearest railroad. This sequence has a 1/288 or 0.347 % chance of happening. It might’ve been enough to squeak by the Community Chest. Chance would also explain why New York has a higher hit chance, due to the “Go back 3 spaces” Chance card.

That being said, the reason as to why is a guess without actually digging into the data further. Again, those results are available here. Feel free to dig in!

Which color of properties are most frequently landed on during the game?

Now that we know which individual properties are landed on the most, let’s take a look at which colors are landed on the most.

Color Count Percent Total Count
Railroad 609396 11.7442 %
Orange 420237 8.0988 %
Red 389019 7.4971 %
Yellow 369199 7.1152 %
Pink 367658 7.0855 %
Green 356539 6.8712 %
Light Blue 342688 6.6043 %
Utility 264425 5.0960 %
Blue 224215 4.3210 %
Dark Purple 207779 4.0043 %

Excluding the properties that can’t be owned, which were ~31.5% of total hits, Railroads are landed on most frequently. This isn’t surprising, since there are 4 of them and have Chance cards that drive that number higher.

But frequency isn’t everything. Properties have different rent rates. Even though some properties are landed on more often, that doesn’t mean they will always be the highest earners.

Which property has the highest revenue, before hotels and after?

What do we mean by revenue?

Revenue = (Count of property hits) * (Rent)

Top 10 Revenue earners before hotels

 Board Position Property Name Count Low Rent Low Revenue Percent Total Low Revenue
39 Boardwalk 123026 $50 $6,151,300 8.7312 %
25 B&O Railroad 179864 $25 $4,496,600 6.3825 %
28 Water Works 136729 $28 $3,828,412 5.4341 %
5 Reading Railroad 144861 $25 $3,621,525 5.1404 %
12 Electric Company 127696 $28 $3,575,488 5.0751 %
35 Short Line 142711 $25 $3,567,775 5.0641 %
15 Pennsylvania Railroad 141960 $25 $3,549,000 5.0375 %
37 Park Place 101189 $35 $3,541,615 5.0270 %
34 Pennsylvania Avenue 115034 $28 $3,220,952 4.5718 %
31 Pacific Avenue 121587 $26 $3,161,262 4.4871 %

It seems like Railroads again are a great early game investment. They have a high ROI, are landed on frequently, and are great early game, pre-buildings, investments. What’s interesting is that Boardwalk is a great revenue stream, even though it’s not even in the top 10 of most frequented properties. It’s actually number 22! But that high rent rate really bumps its Revenue.

Top 10 Revenue earners after hotels

 Board Position Property Name Count High Rent High Revenue Percent Total High Revenue
39 Boardwalk 123026 $2000 $246,052,000 8.7678 %
34 Pennsylvania Avenue 115034 $1400 $161,047,600 5.7387 %
31 Pacific Avenue 121587 $1275 $155,023,425 5.5241 %
32 North Carolina Avenue 119918 $1275 $152,895,450 5.4482 %
37 Park Place 101189 $1500 $151,783,500 5.4086 %
19 New York Avenue 146168 $1000 $146,168,000 5.2085 %
26 Atlantic Avenue 126095 $1150 $145,009,250 5.1672 %
29 Marvin Garden 119011 $1200 $142,813,200 5.0890 %
27 Ventnor Avenue 124093 $1150 $142,706,950 5.0852 %
24 Illinois Avenue 127213 $1100 $139,934,300 4.9864  %

Not surprisingly, Boardwalk stays put at the number 1 Revenue earner. Most of these properties are in the last half of the board, with the one exception of New York Avenue. It seems New York Avenue crossed that threshold where its high frequency actually made up for the lower rent.

Now, known individual property revenues are great, but to get those high earners, you need to build hotels. To build hotels, you need to own all of one color.

Which color of properties have the highest revenue, before hotels and after?

Revenue per color before hotels

Color Count Low Revenue Percent Total Low Revenue
Railroad 609396 $15,234,900 21.6245 %
Blue 224215 $9,692,915 13.7582 %
Green 356539 $9,500,082 13.4845 %
Yellow 369199 $8,360,400 11.8668 %
Utility 264425 $7,403,900 10.5091 %
Red 389019 $7,256,768 10.3003 %
Orange 420237 $6,175,654 8.7657 %
Pink 367658 $3,916,082 5.5585 %
Light Blue 342688 $2,284,224 3.2422 %
Dark Purple 207779 $627,174 0.8902 %

Not surprisingly, Railroads early game are the real winners. Before houses and hotels get started, they really are the best investment.

Revenue per color after hotels

Color Count High Revenue Percent Total High Revenue
Green 356539 $468,966,475 16.7111 %
Yellow 369199 $430,529,400 15.3414 %
Red 389019 $414,830,600 14.7820 %
Orange 420237 $406,533,550 14.4863 %
Blue 224215 $397,835,500 14.1764 %
Pink 367658 $293,706,150 10.4659 %
Light Blue 342688 $194,180,800 6.9194 %
Railroad 609396 $121,879,200 4.3430 %
Dark Purple 207779 $59,351,310 2.1149 %
Utility 264425 $18,509,750 0.6596 %

And here it is, the best Revenue color is Green. While the count is actually less than the next 3 earners, the higher rent from the properties really make up the difference.

Conclusion

Everyone has a different opinion on how to play Monopoly. This study doesn’t take into account many different ways to play the game and strategies that really can destroy an opponent. From a strict movement perspective, early game, go for the Railroads, maybe pick up Boardwalk if you can. For a long game strategy, I’m going for the Green properties next time we play.

Update – 10/20/16

After posting this article on Reddit, I received some excellent feedback on my analysis from the competitive Monopoly player, Minus-Celsius, and insight as to why my original conclusion of Green properties being valuable is incomplete.

Essentially, potential Revenue is not the best lens to view Monopoly properties. While Green has the potential for ~2.3% more revenue over time, Orange properties are a better investment in practice. The metric overlooked was the cost for houses. The prices of houses and hotels for Orange are half the price for the Green properties. This allows for a faster setup of the board and an earlier advantage in play. The halved cost of property setup greatly outweighs the small increase in potential Revenue.

This is a clear example of how domain knowledge of a study is invaluable. While I have played Monopoly, without the competitive experience, I missed an opportunity for a more nuanced view of the game. It’s exciting to get feedback from an expert, as it allows for an opportunity for growth and learning new ways to look at and interpret data.

2 thoughts on “What is the “best” Monopoly property?

  1. What about card events? Advance to St. Charles Place, advance to Illinois Avenue, advance to Boardwalk, take a ride on the Reading.

    What about players who leave jail? Certainly orange and red properties will get landed on more often from people leaving jail.

    1. Card events are taken into consideration. That’s my best guess as to why railroads and utilities rank so highly on the most frequently hit properties.

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