Hack 51. Pass Go, Collect 200, Win the Game

Hack 51. Pass Go, Collect $200, Win the Game

Monopoly is a game of chance (and Chance cards). As such, the best strategies for winning capitalize on probability.

Winning the popular Parker Brothers board game Monopoly requires negotiating skill, clever money management, and insightful investment planning. It also requires a little bit of luck.

As two six-sided dice (and a randomly shuffled pile of cards) are the primary determinants for deciding what square you land on, luck pays more than just a small role in the outcome. Competitive statisticians such as you and me (or, at least, me) are drawn to any game in which probability plays a key part because, by applying a few probability basics, we should win more often than your average, run-of-the-mill railroad baron.

Monopoly Statistical Basics

Let's start by examining the simple effects of rolling two dice. Figure 5-1 shows the most common squares landed on in the first couple of turns for everyone.

Figure 5-1. Likely opening rolls

Imagine the start of the game, when everybody is on Go. With two six-sided dice, there is a 44.5 percent chance that a 6, 7, or 8 will be rolled, with 7 as the most likely outcome (16.7 percent). For your first two dice rolls, then, some squares are more likely to be hit (e.g., the light blues and Virginia Avenue) and some less likely (Baltic Avenue or Income Tax). Based on opening dice rolls alone, not all squares are equally likely to be landed on.

Poor Mediterranean Avenue cannot even be landed on when starting at Go, because a dice roll of 1 is not possible with two dice. Have you ever noticed that it is almost always one of the last properties still available for purchase?

The Go square is a good starting point to begin calculating the various likelihoods for landing. Not only does everyone start there at the beginning, but there is also a Chance card that sends players there. On the other hand, if a player hits the "Go to Jail" space, she goes directly to jail, bypassing Go. So, the probability for landing on Go is affected by not just the possible permutations of dice rolls, but also the various Chance cards, which send players various places, and the rules of the game itself, which include squares that make things happen, going to jail situations, and getting out of jail situations.

Key Properties

I've been using Go as an example square, but, of course, Go isn't even a square we can purchase. What we really want to know is what properties to buy or trade for and where to build first. We want high traffic areas; the secret to real estate success is "location, location, location" (and, apparently, for some reason I've never understood, a nice wooden deck).

Table 5-4 shows the top 20 most landed-upon squares, taking all rules into account. The table also shows the chance that a player will come to rest on any one of those squares. Keep in mind that an "average" square has a 2.5 percent chance of being your final resting place (40 squares divided by 100 is 2.5).

Table Best real estate in all of Atlantic City
Square	Rank	Chance of ending your turn on it
Jail	1	11.60 percent
Illinois Avenue	2	2.99 percent
Go	3	2.91 percent
B & O Railroad	4	2.89 percent
Free Parking	5	2.83 percent
Tennessee Avenue	6	2.82 percent
New York Avenue	7	2.81 percent
Reading Railroad	8	2.80 percent
St. James Place	9	2.68 percent
Water Works	10	2.65 percent
Pennsylvania Avenue	11	2.64 percent
Kentucky Avenue	12	2.61 percent
Electric Company	13	2.61 percent
Indiana Avenue	14	2.56 percent
St. Charles Place	15	2.56 percent
Atlantic Avenue	16	2.54 percent
Pacific Avenue	17	2.52 percent
Ventnor Avenue	18	2.52 percent
Boardwalk	19	2.48 percent
North Carolina Avenue	20	2.47 percent

Table 5-4 is derived from information provided by Truman Collins on his web site at http://www.tkcs-collins.com/truman/monopoly/monopoly.shtml. Clever Mr. Collins developed both probability trees and a computer simulation to verify these values, and offers them for two situations: when players wish to remain in jail as long as possible (to earn rent and not have to pay rent) and when they wish to get out of jail as quickly as possible (to buy still available properties). I reported the values that apply to the former strategy.

You can draw some important tactical conclusions from this data:

Capitalize on the jailbirds: A remarkable 12 percent of the time, your opponent will begin a turn on the Jail square. Clearly, owning and developing the land that recently released parolees are most likely to land upon is a wise goal. This amounts to the orange properties (St. James and his brothers) and, to a lesser extent, the reds (e.g., Illinois Avenue) and the purples (St. Charles and friends).
Own the oranges: All three orange properties are in the top 10. About 1 out of every 12 rolls will result in a hit on Tennessee or New York Avenue or St. James Place. Getting the monopoly with these properties and developing quickly would seem to be the strategy that a pure statistician would choose.
Avoid the far side: Properties on the far side of the boardthe greens, Boardwalk, and Park Placeare less likely to be landed upon, even deep into the game. Only Boardwalk and Pacific Avenue rank high, and Boardwalk is there, no doubt, because there is a Chance card that sends players there. These properties are also the most expensive to develop, so including these monopolies prominently in one's game plan is a bit risky.

Importance of the Monopoly Prison System

Without a statistical analysis, it might not be so clear the crucial role that the Jail and "Go to Jail" squares play in the overall true value of real estate. One wishes it was for sale. Players will start or end their turn on the Jail square more often than they will land on any monopoly on the board. A constant stream of released prisoners flood across one side of the board, increasing the opportunity to collect rents on properties all the way up to Illinois.

Jail can also provide a welcome respite from having to travel the streets paying rent to other players, though early in the game, Jail can prevent you from buying up your dream properties. A final observation on the importance of Jail: there is only one square that you can never end your turn on. Can you name it? Go to Jail.