December 29, 2018
Ahhh, it’s that ❄ time ❄ of year again - a break from work with lots of time with the family.
(In other words - do you have that specific in-law you just can’t wait to see defeated?)
* well this is the post for YOU my friend! *
For my family at least, we’ll play Monopoly at least once during the Christmas - New Year’s week (What other time of year do you have 4+ hours to spend duking it out with one of the world’s most loved1 games?)
So, in a recent bout (like, last Wednesday 😂), my brother had snagged both the brown / dark purple properties (Mediterranean and Baltic) as well as the light blues (Oriental, Vermont, and Connecticut). If a player owns both of these adjacent monopolies, we cherishingly call them the ‘slum lord’).
My girlfriend ended up with the greens and blues, what we call the ‘high roller’ properties. I initially thought she had the advantage. But as the game went on, we realized just how high maintenance (the properties, not my girlfriend 😂) those expensive green and blue properties are. First, they cost a fortune to buy, and at $200 dollars per house, cost another fortune to build on. There’s the additional detriment that Boardwalk and Park Place are only a two-property set.
In the end, my girlfriend was actually one of the first players to go out, while my brother lasted until the end, securing 2nd place (I actually ended up winning due to massive luck with the magenta properties: Virginia, States, and St. Charles Place).
So, now the question: was our intuition that more expensive properties were the better properties to seek as you play the game? Or is it at least true that some properties and property groups have an inherently better profit margin, regardless of how much they cost to buy and build on?
Turns out, it couldn’t be more true! (Or interesting!)
I call a ‘rent style’ property any of the non-utility or railroad properties, i.e., any of the properties you can build houses or hotels on.
I calculated the percent return on investment (ROI) for these properties as follows:
I calculated and plotted this value changing the number of times a player lands on the property, for 1,2, and 3 times:
(Sorry for the non-interactive .svg, Gatsby 2.0 currently has no way of including bar charts easily - or at least I spend a few hours trying to find a way. Though I may consider reopening this pull request on mermaid2 and doing it myself.)
If you’re a table kind of person, here’s all the same data in a table, just as shown, from lowest ROI to highest:
|Property||Return on Investment After 1 Land||Return on Investment After 2 Lands||Return on Investment After 3 Lands|
|North Carolina Avenue||-1.92||96.15||194.23|
|St. Charles Place||17.18||134.37||251.56|
|St. James Place||39.70||179.41||319.11|
|New York Avenue||42.85||185.71||328.57|
And, looking at that data per monopoly:
|Monopoly Set||Return on Investment After 1 Land (Averaged)||Return on Investment After 2 Lands (Averaged)||Return on Investment After 3 Lands (Averaged)|
This analysis of the expected return on a property shows us that the light blue properties are the best investment in terms of expected return. However, it’s not yet a complete picture of the game. We need to consider locations on the board and how players move around the board to complete our analysis.
First, a crucial takeaway from the monopoly board layout is that a large sink of player location on the board is the jail. There is ‘speeding’ or rolling doubles 3 times in a row, the fact that all Chance and Community Chest spaces have a small chance of sending you there as well, and then of course the ‘Go To Jail’ space will send you there. So assuming that jail is one of the most common spaces on the whole board for a player to be on during a game, let’s look at the roll probabilities from the jail space to the following 2-12 spaces, at least in terms of rentable properties.
Note the roll probability of two dice:
Yes, landing on Community Chest from jail is actually the most likely single roll of 7 at 16.667% from a two dice, but the combined probability of the orange properties Tennessee, St. James, and New York Avenue with rolls of 6, 8, and 9 at 13.889%, 13.889%, and 11.111%, respectively, is an overwhelming net of 38.889% chance of a landing on an orange property from a single role from jail. The possibility of landing on a purple property by rolling a 3 or 4 at States and Virginia is 5.556% and 8.333% respectively, or 13.889%, and for the slim chance of a roll of 11 to the red property Kentucky, only 5.556%.
From both this analysis and have a lot of experience being a huge Monopoly nerd as a kid, I can draw a few conclusions:
So, a fair rank for the rent-style properties is as follows:
I ranked the greens above the browns because there are three of them, and the hotel prices that come with the browns at 450 just usually aren’t enough to do much damage late game4. The blues could perhaps be a bit higher, maybe above the reds or the yellows in terms of rank, but again, the blues are only a two-property set, and they are after that jail ‘sink’ space, not to mention all the other Chance and Community Chest spaces that can send a player to jail (or anywhere). It would take a full board analysis to truly place the middle monopolies amongst one another.
To make it really simple, let’s categorize the 8 monopolies into ‘best’, ‘better’, ‘good’, and ‘bad’, with 2 monopolies each:
Of course, in the end, Monopoly is a game highly based on chance, so after all this analysis, actual game outcomes and mileage explained here will always vary.
However, by subscribing to these general concepts, I’ve had great success playing Monopoly (and this holiday season) 😉. Have fun, and good luck if you’re playing any time over the holidays!