It was 2am, and despite my physical exhaustion- I couldn’t sleep. I had touched down from London a few hours prior, and my body-clock was spun.
Laying bed, my delerium led me to ponder all the locations I had visited that appear on a classic Monopoly board. Americans may be surprised to learn that the standard editions of Monopoly sold in Commonwealth nations all used locations in London as the properties- Trafalgar Square, Pall Mall, etc.
Hacking Monopoly
It may be argued that despite it’s appearance, Monopoly is still intrinsically a luck based-game due to the linear way players progress around and around the same board, all controlled by the random element of dice-rolls. Assuming players are all of an equal understanding of the rules, it’s down to just ‘dice’ in the end.
In-fact, there is readily available source-code for simple programs which simulate billions of dice-rolls and moves across the board within all applicable Monopoly rules, even accounting for anomalies like chance cards and jail stays. Using a the aid of programs like this to create transition matrices revealed quite detailed statistics such as:
Spaces pieces end their turns on most:
• Jail is (unsurprisingly) the space that players most often end their turns on. A player can be directed to jail in three ways: by landing on the Go to Jail space, by drawing a “Go to Jail” Chance or Community Chest card or rolling three doubles.
• Illinois Ave. (a red property) is the second-most popular space.
• Go is the third most commonly finished-on space.
• A piece finishing on a Chance space is extremely rare- only likely to happen once per game if at all (because the Chance cards almost always move you somewhere else).
Average number of opponent dice rolls to recoup cost of each property (including incremental costs of adding houses/hotels):
• Paying off St James Place (a $180 orange property) would take ~460 opponent dice-rolls if it’s the only orange space you own, a greatly improved ~106 rolls if you own all four orange properties (which provides a rent bonus), and only ~17 rolls if you put a hotel on it. Note that this isn’t how many times an opponent needs to land on the space to pay it off, it’s how many times any opponent needs to have a turn.
• B&O Railroad takes ~234 opponent rolls to pay off it’s $200 cost if it is the only Railroad you own. But if you own all four rail-roads (providing a bonus), the opponent only needs to roll the dice ~13 times before you have paid it off.
Using these transition matrices, we can instantly see within the naked ‘inner-workings’ of Monopoly’s carefully constructed probabilities, and ‘play’ accordingly
Monopolising Exploits
There are a more than a few elements presented by the ‘human’ element of Monopoly that prevent it from being entirely a game of luck; and they aren’t as easy to model with a computer. Whether it be simple strategies (Get out of jail quickly early in the game, but stay in jail as long as you can later in the game as moving around the board becomes more dangerous), or more advanced tactics fostered by specific limitations of the game itself (as there is a specific limited number of physical house and hotel pieces, rush to build four houses on cheap properties quickly to create a building shortage, hurting other players’ chances to build). It’s also interesting to note several ‘broken’ aspects of Monopoly, which players can take advantage of:
Statistically the ‘Jail’ space is where a-lot of players will often be, as no other space has so many rules that send players to it. Once you leave jail, the ‘Orange’ properties are 6, 8 and 9 spots away on your first roll- statistically you’re likely to roll these numbers with two dice 1/3rd of the time, and any roll less than ‘6’ still puts players at risk of hitting Orange on their next move. There’s also the ‘move back 3 spaces’ Chance card, which also plays into these odds (I won’t bore you with the numbers) making the middle-priced ‘Orange’ spaces the most lucrative in the game- not the expensive ‘Blue’ spaces.
Perhaps these aren’t exploits- but rather features the creators of Monopoly deliberately inserted as a commentary on the plight of middle-class renters in the face of a capitalist society (as Monopoly’s predecessor, The Landlords Game was created to “Let the children once see clearly the gross injustice of our present land system”). Much more realistically- players have simply analysed Monopoly over the years to discover the most ‘mathematically sound’ strategies, and it is knowledge of nuances like this which separate a ‘pro’ player from the rest.
Always keep in mind that players will act irrationally. As rivalries develop, and emotions are on the high- the probability sheets fly out the window. Such is the most compelling part of playing Monopoly- learning to hate your friends. A player can win Monopoly by making the most statistically informed decisions; though one would need to ask themselves if they ‘played Monopoly’ or rather just wasted hours sitting through something that resembled a high-school maths class.
Changing the game...
I didn’t know it at the time; but these jet-lagged hallucinations of Monopoly would be the spark that ignited a proverbial fire within me. Pictured above is the first draft I made of a modified ‘Monopoly’ board in Google Sheets. This game would enable players to control multiple pieces that could move both backwards and forwards over the spaces. Additionally, instead of having just one linear path around the board- there were four distinct ‘islands’ that players would be able to transfer between by paying a ‘fare’ as a penalty.
The rules changes grew and grew until I had something different on my hands entirely; a totally new tabletop role-playing experience. I had taken some game-design classes at University; but now for the first time I had ‘my own’ project that I found myself strangely passionate about, and I could put my learned theory into practice.
Prototyping the game physically proved cumbersome- which is why I turned to Google Sheets, but this is a tale for another time…
Read more about ‘Island Kingdoms‘…