What's the Best Monopoly Strategy?

TABS Monopoly is the type of board game that brings families together for a night of fun, only to have everyone in that family hating each other because Susie won with all four railroads. I have played this game countless times with my family, and almost every time I end up losing to one of my older brothers because they threatened to beat me up if I didn’t give them Boardwalk. However, throughout the years I have always wondered what the best strategy is for beating my family, and it turns out that going for the most expensive properties doesn’t give you the best chance at winning.

TABS The first Monopoly ever created started production in the early 20th century, and has gone through a lot of remodels to get to be where it is today. The earliest strategies of Monopoly didn’t have the different rules that we have today, so original Monopoly was believed to be fair and equal. Ian Stewart, who has written multiple papers on this probability wrote about the fairness of Monopoly back in 1996. His conclusion was that it was equally proportional, “So, with a little help from Markov, we can prove that a game as complicated as Monopoly is fair, in the sense that—in the long run—no particular square is more or less likely to be landed on.” With evolutions in computer programming, and a better understanding of the game and its rules, we can now show that there is an unequal probability to which squares get landed on more.

TABS The most popular spaces to land on are, in no particular order: GO, JAIL, Illinois Ave., Pennsylvania Railroad, and B&O Railroad. This wild phenomenon of the probabilities is explained using something called the Markov Chain. Ian Stewart uses the Markov chain theory to explain, “The theory of Markov chains tells us that the evolution of this probability distribution is given by the sequence of vectors v, Mv, M2V, Mlv and so on: each throw of the dice corresponds to the matrix M operating on the vector v.” He basically goes on to say that you need a basic computer to compute the 1,600 transition probabilities that stretch across a Monopoly board.

TABS Stewart uses some basic rules when determining the probabilities for each of the squares. First off, the double dice rule. Each person on their turn throws two dice, and if they get double numbers, meaning two 5’s or two 3’s, they get to roll again. However if they get a double on their third roll, they go to jail. This determines that the greatest distance possible in one turn is 35, but the most likely distance to be rolled is 7.

TABS The M vector described earlier gets extremely complicated when the “Jail” space is added in. Jail is the most landed on space on any monopoly board, because there are so many ways to get sent there. For instance, one player can visit jail, land on the “Go to Jail” square, draw a Chance or Community Chest card sending them to jail, or roll doubles on dice. He didn’t take the different ways to end up in jail during his first conclusion.

TABS The most shocking thing I learned while researching this topic is that jail is almost twice as likely to be landed on as any other square. Jail has a 5.89% chance of being landed on, whereas the next highest probability of 3.18% belongs to Illinois Avenue. B&O Railroad has a staggering 3.06% chance of being landed on, Reading Railroad has a very close 2.99% chance, and Pennsylvania Railroad has 2.91%. Boardwalk, the square with the greatest rent value, has a landed on probability of 2.63%, and Park Place only has a 2.19%.

TABS Now where do we implement the business side to Monopoly? Because after all the math is done, the object of the game isn’t to have the most properties, but instead to bankrupt the other opponents. Friddell dove deep into the property market behind Monopoly. He outlines when the best times to buy houses and upgrade to hotels. His strategy assumes that houses can be bought from the start, but in most house rules you need all three properties before you can build even one house. Friddell describes that even though it might be more difficult to buy houses early, the point in which you will start to make money will be achieved sooner. Likewise, with only two houses on your properties it will take roughly 20 turns for you to reach even. Now, if you can add another house to make three, the time it takes to reach even and start making money drastically shortens. He also points out that between Go and Indiana Avenue, breaking-even can be reached on spot New York Avenue in only 10 turns.

TABS Tim Darling outlines the four best ways to achieve total monopoly. The first of the four positions is to own all four railroads if at all possible. It is the best way to stack up on cash, and there is no need to pour money into the railroads to add houses. The next three strategies all include 3 houses on the following colors: orange, light blue, and light purple/magenta. “I would trade Boardwalk to get St. James Place. Sure, you don’t want your opponent to have the chance to build houses and hotels on Boardwalk, but they’ll never be able to do it unless they have houses on cheaper properties generating cash. Meanwhile, you’ll be able to throw 3 houses on each of the orange.”

TABS The next time you are playing one of the 600 versions of Monopoly, try one of these strategies out and see how it fares with you. You might be able to bankrupt your older brothers, and the rest of your family.

Stewart, Ian. "How Fair Is Monopoly?" Scientific American (1996): 104-05. Print.

"Monopoly Revisited by Ian Stewart." Mathematical Recreations. Web. 16 Nov. 2015.

Friddell. "Markov and Mr. Monopoly Make Millions." 2010. Web. 16 Nov. 2015.

"How to Win at Monopoly ® - a Surefire Strategy." How to Win at Monopoly ® - a Surefire TABSStrategy. 1 Nov. 2007. Web. 16 Nov. 2015.