First mover advantage

January 13, 2010

Based on our previous analysis, one might be inclined to think that He-Who-Must-Not-Be-Named was not a very skilled Monopoly player. However, it is impossible to ignore the fact He-Who-Must-Not-Be-Named, who was the last player to roll, was unlucky in that he systematically landed on properties that were already owned and only owned four properties before being knocked out. To what extent does player ordering explain He-Who-Must-Not-Be-Named's abysmal market share?

Just as before, we can conduct our analysis by assuming that players purchase properties as quickly as possible. We then simulate 1000 Monopoly games until all of the properties are owned and we quantify a player's market share by the total number of properties that they own at that time (without any trades). We can then compute the average market share of a player that rolls first, second, third, and so on to see how the ordering of players affects market share.

Of course, the raw market share of each player is not entirely instructive without a proper basis for comparison. In this case, we might expect that each player has an equal chance of owning a property. Under this assumption, we would expect the distribution of the number of properties per player is given by a multinomial distribution. We can then use this null model as a basis to calculate the relative market share for each player.

Market
  share quantified by number of properties owned
Fig. 1: Market share, as quantified by the number of properties owned, relative to the multinomial null model as a function of the player order for games with 2, 4, 6, and 8 players (left to right).

This analysis clearly shows that the relative market share per player is directly influenced by their ordering during the game (Fig. 1). In fact, you can expect to lose 5% relative market share for every player between you and the first player to roll, regardless of the number of players in the game. In a game between two people, merely 0.5 properties separate the first and last players, but in a game between eight people, this disparity increases to 1.4 properties. To summarize, at least part of He-Who-Must-Not-Be-Named's trouble is a direct result of not having the same potential market share as other players in the game.

The large disparity between the first and last players in a game of monopoly illustrate that there truly is a “first mover advantage” (yuk yuk). This suggests that it might be possible to handicap Monopoly such that each individual has the same expected number of properties. Of course, a more robust handicapping system would also account for the value of properties that each player is most likely to purchase, but even this simple analysis illustrates that such a handicapping system would greatly improve the fairness of Monopoly.

contributors to this post

headshot of Dean Malmgren
Dean
headshot of Mike Stringer
Mike