Roll the Data: How to win board games (based on science!)
Authors: Ethan Rauchwerk (Project Lead), Leo Carozo, Ryan Barney, Disha Beeraladinni, Johan Chua
Introduction
Let’s Roll the Data! We all know that numbers and data can be used to optimize so many things in the modern world, but can we use the power of data to beat our friends in games and puzzles? We will try to answer that question as we examine trends in the world’s most popular board game, Monopoly, and the world’s most iconic daily puzzle, the New York Times Crossword Puzzle. By analyzing the numbers and probabilities in Monopoly, we can pinpoint just which strategies give us the best chance of success. Then with our newly found data-driven knowledge of the game, we can play the game like a statistician and know just which properties, monopolies, and houses are the mathematical bests. Similarly, by identifying trends in the answers to New York Times Crossword puzzles over time, we can get a better sense of which types of words might appear more often in the future, and have a better informed basis of knowledge when trying to crack these puzzles. Like Billy Beane from Moneyball, we’re going to see if we can conquer the gaming and puzzling world using data!
Monopoly
Monopoly is one of the all-time classic board games that nearly everyone has heard of. Plenty of people have had the opportunity to play and experience the joy and frustration that comes along with simulating the buying and trading that takes place in a capitalist economy. Due to its wild popularity, it’s natural to wonder what strategic advantages one can give themselves if they were to study the underlying properties of the game. In that way, some insight can be gained as to how to best approach the game.
Because of the inherent competitive and strategic nature of the game, there are many who have attempted to formulate the optimal strategy to win. Here, through the use of Monopoly simulations, we hope to do the same and develop a deeper understanding of what it takes to win in Monopoly.
In this first plot, we first wanted to conduct some preliminary analysis on the squares most frequently landed on in Monopoly. Here, we see that the most frequently landed on square is the Jail square by far. This could be due to the multiple ways to end up in Jail, including through event cards or by simply landing in the Jail corner. Beyond this, the majority of the most landed on squares are mainly comprised of event spaces like Go, Free Parking, and Community Chest, Red and Orange properties, and Railroads. It isn’t until the 14th most common space that we get a magenta square that deviates from this pattern.
Naturally, we extended this to look at which families of squares were most commonly landed on during a game of Monopoly. Again, we see a similar result where Corners, which include spaces like Go and Jail, along with Red and Orange properties and Railroads, are the most common families. Considering that Corners do not help with bankrupting other players and Railroads don’t have a high return on investment in the long term, it’s clear to see that Red and Orange properties may be good investments.
In a game of Monopoly, it is often the property squares that will result in a win, as they have the highest return on investment that scales well for the game long term. Considering that Red and Orange have the highest frequency of being landed on out of the different families of properties, we next wanted to observe their rent to see whether or not they would be a good investment.
From the plot above, we see Red and Orange again as having a high frequency, but they also have a decent rent, being in the middle of the pack. This makes them more consistent and stable sources of money during a given game, as they’ll be landed on frequently while allowing the owner to net a decent amount of money through rent. Meanwhile, other families, like Purple, Light Blue, or Magenta, have a low frequency of being landed on and low rent, making them bad choices overall. On the other side of the spectrum, the Dark Blue family has a high rent but is not frequently landed on, making it high risk but high reward. It appears that the Yellow and Green families are also good options, as they have higher rent than Red or Orange but a slightly lower chance of being landed on. This makes them somewhat riskier, but they are still good options to try and obtain.
To ensure that the prior plot was not being skewed by individual properties with good qualities, we plotted each individual property against its rent. Again, we see that Red and Orange are the front runners, being at the peak when it comes to having high frequency of landing and decent rent.
Another aspect of Monopoly is the ability to upgrade a property, spending money in order to increase rent when players land on it in the future. To do this, a player must own an entire family. At this stage of the game, it is important to manage resources in order to best bankrupt other players while avoiding getting bankrupt yourself. As such, we wanted to investigate how to best upgrade properties once a player has obtained a family of squares.
To do this, we looked at the rent increase ratio, or the amount the rent increases for how much money is spent to upgrade the property. From the plot, we found that making three upgrades, which is equivalent to placing three houses on a property, results in the biggest gain in rent increase ratio. This means that, if a player owns a set, it is wise to try and upgrade it to having three houses, as this is the stage where there is the biggest jump in rent when other players land on it. The only situation where this doesn’t hold is the Purple family, where it’s wise to try and upgrade 5 times, or all the way to a Hotel. However, the Purple family should try to be avoided anyway, as it has a bad return on investment.
Crosswords
A crossword puzzle is a series of questions and answers, placed onto a square board where each 1x1 square represents a character in the answer. In 1942, the New York Times launched their version of the crossword puzzle, which uses a 15x15 board and became the gold standard for American crossword puzzles. In this article, we aimed to see if there are any strategies that people can use to optimize their crossword puzzle solving skills, as well as if crossword puzzles have changed over the years of our data (1993–2021).
This plot shows the five most common crossword answers over the years. The graph gives insight to two clear factors. First, common crossword answers tend to be three or four letters. Of the 25 most common crossword answers, 21 of them are three-letter answers, and the remaining 4 are four-letter answers. In fact, 51.6% of all crossword puzzle answers contain three or four letters. The second trend is that the most common words contain lots of vowels. Of the twenty-five most common words, 24 of them contain at least two vowels, which is why words such as ere that are more obscure can make lots of appearances. Vowels being prominent corresponds well to crossword structure, since often letters from words are used to form other words in the crossword puzzle.
As time goes on, both crossword answers and clues are getting longer, although the trend is much more linear for crossword clues. Clue length has almost no relationship with answer length, which suggests that one getting longer is not necessarily resulting in the other getting longer. While we were unable to identify why clues and answers are getting longer, one possible explanation is that many of the easier clues have already been written, so the Times has been forced into expanding into more complex prompts and words.
Conclusion
As we can see, we can learn a lot about household games and puzzles from their data. Besides being interesting, we can take away some of these facts into our own arsenal of strategies the next time we play. Make sure to place extra value on the orange and red monopolies and try to get exactly three houses on your monopolies next time you play, and you’re likely to have an advantage against your friends. While it’s very difficult to predict the types of words that appear on the next crossword and really gain a tangible advantage, the long term trends in how word and clue length are increasing over time is interesting to see and provides fascinating insight on how the New York Times Crossword is evolving with modern society and words.
