From a Monopoly Veteran

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I have been playing Monopoly since before 1950.

Aside from the fun, it provides one of the best ways to introduce the idea of marginal to an intro economics class; and because I’m not teaching my giant section of intro microeconomics this year (the first time since 1980/1981), I miss both teaching and Monopoly.

Each Monopoly property gives a payoff when an opponent lands, with the payoff rising from double the rent if you have a monopoly with no houses, up to a maximum total return with a hotel (five houses).

On a given property, each house costs the same; for example, on New York Avenue, my favorite property, a house is $100. But the marginal return to a house is not constant: it rises steadily with the first, second, and third houses and then falls with the fourth and fifth.

This dictates strategy: if you have two monopolies and limited resources, even though the big red hotels are pretty, you are better off building equal numbers of houses on both monopolies, rather than hotels on one and nothing on the other.

Here’s one other economics lesson that is well known to Monopoly veterans: better a monopoly on the farther end of each side of the board; the houses cost the same on each side, but the payoffs at the farther end are greater.


science minded

Dear Martin;

One more hindsight thought-

Next time you play monopoly try both approaches- bet you will win-

science minded

Dear Thomas;

I think I got your message. But frankly, never thought of myself as an oligarch. Just someone wishing to make a contribution to science- I was not the one to have brought my work out to the public eye- if I had my way- would have waited til finished- the person I shared my stuff with (needed the communication and collaboration for a bit) to finish it off- went behind my back and published- I understand his expedient need- Well, now that I have a publisher and a deadline- I have one of my own- sorry- for delay-

Dear Sallie K;

Tokens- no - I rather see it as making sure that when the book is published we all are in so much sync that it won't take 200 years, 5000 years for your work/and our work to be done- That's the motivation- a real scientific enterprise- that leaves no science and no one behind. And you can quote me on this one Robyn Ann Goldstein 2008 or call me at John Jay College of Criminal Justice. Ask for the sociology department and leave me a message as I do not have a permanent office in the department.

Sincerely--

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salliek76

Regarding the strategy in selecting tokens, I have to agree with #3 McCafferty that the proper token can have an important impact on the outcome of the game, particularly when an important part of your strategy is to "lay low" and hope the property owner doesn't notice you. In my family, the car was the most desired token, followed closely by the horse, but I always gravitated toward either the penny or the purple button. Don't remember these tokens? They're the ones that we had to use to replace the pieces that were lost over the years. Incidentally, when I bought a new Monopoly set as an adult, I was surprised to find that the thimble was an authentic token and not one of our homemade ones!

Thomas B.

We always formed a coalition right off the bat, and made deals to sell properties to others in the coalition at steep discounts from the list price.

The lesson I like in Monopoly is how oligarchs can quickly ruin the game for hard working monopolists everywhere.

science minded

Dear all;

This was a test- and one not deliberately orchestrated- a bit of a Freudian slip- for surely I could have died. There were other blogs that people responded to since 1:15 today(@ 1:37,2:41,3:41) No one of you, since 1:15, thought to ponder my fate- So I guess now you know why I will not go any further, but to say that there is a lesson many of you will need to learn from this and you won't hear it from me here. Only to say that you will need to learn it if you too have any intention of making a genuine contribution to the advance of science!

science minded

One additional point just reminded of. as far as the injustice of the situation- I am afraid that this is one in which we all fall or rise to the occasion of understanding that the one responsible is a woman of African origin. She shared her wealth. so does money = probability of winning. I guess not- since she had no money-

And liberalarts- doesnt't putting your money where your mouth is- make it possible for even the poor to benefit- as in "the poor pay more" - the rich should not have to pay less or more than everyone else for what a few of us have devoted our lives to- True-our choice- and we all paid a price-

If anything public discussion may facilitate mutual understanding betwen the arts and the sciences and religion and hence survival long-term- so I see us all benefitting in the long-run/ In the short term- time is money here in America- where I live and need to work- to support a family- so you see-- the ruling ideas are not always the ideas of the ruling class- Marx was right in the sense in which the ruling class is one to which we all are capable of belonging- and wrong in the sense in which the problems (including the one of injustice- is unavoidable- and I have paid my dues fairly and sq

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liberalarts

As mentioned in the comments, people's refusal to follow the rules on numbers of houses and hotels makes the game less strategic to play. The game also has a reputation for lasting forever, but that follows from another deviation from the rules: putting money in the middle to be won by landing on Free Parking. Putting money in the free parking pot inflates the total cash available and greatly extends games by allowing people with poor positions to stay in the game much longer.

Nichlemn

Does money approximately equal utility (defined as the probability of winning) at all stages? A hypothetical property with a rent of $10,000 is obviously not 100 times better than a property with a rent of $100. Surely some of more expensive properties would have dimishing marginal winrate increases?

Rick

I remember reading in an old issue of Nintendo Power that Illinois was the most landed on property. Not sure how the deduction came about, but I always try to own it anyway. You should also try to own the Railroads, with one on each side of the board, you have a great "chance" at $ 200 rent all around the board.

Pat

I find Monopoly to be boring. It suffers from the same fundamental design problem as most American mass-market games: too much of what happens in the game is dictated by random die rolls and card draws, leaving little room for skill or strategy.

Furthermore, the economic theme of the game is pure anti-capitalist propaganda. In Monopoly, you have to pay rent to a property owner not because you have voluntarily entered into a rental contract, but because forces beyond your control have caused you to randomly land on that property. This is a ridiculous distortion of how real estate works in the real world.

The game also offers a bizarrely inaccurate definition of success: in Monopoly, you cannot succeed unless you drive everyone else into bankruptcy. Free markets do not work that way. And the requirement that you crush every other player in order to win makes the game poorly suited for friendly social play. I greatly prefer games like Power Grid or Empire Builder in which you win by building your own successful business, not by destroying everyone else's.

It's also worth noting that some of the better-designed modern games, like Settlers of Catan or Parthenon: Rise of the Aegean, you have to trade with the other players in order to succeed. Trading for mutual benefit is a vitally important element of economics that Monopoly blithely ignores.

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PMcCafferty

Another tip: Use the iron as your token. The iron has the lowest profile so the other players are less likely to notice when you land on their properties.

Martin

You are partly wrong, and I can mathematically prove it. Here is a situation where putting all your houses on one monopoly will maximize your expected profit more so than evenly distributing the houses.

Say you own the light purple and the orange monopoly. For both, the cost of a single house is $100. Further assume you have enough money to purchase 9 houses. What should you do?

After many rolls (this is known through computer simulation with chance cards) the probability of landing on New York Ave, Tenn, and St. James on a given turn is 2.81%, 2.82%, and 2.68% respectively. And the probability of landing on Virginia Ave, States Ave, and St. Charles is 2.43%, 2.17%, 2.56%.

So here are two strategies and their expected revenue in any given term (note that each strategy cost the same amount once you already have paid for the monopoly).

Strategy 1: Build 9 houses evenly, and for extra houses, put them on the properties with the highest pay off. Then you put 2 on all the oranges and 1 on all the purple. On any given term, your expected pay off is a little over $21 per roll of your opponent (I cannot show the excel spreadsheet I made to prove this, but if you email me, I will gladly give it to you).

Strategy 2: Build all 9 houses on only the orange (3 each), and leave the light purple undeveloped. The expected revenue at this point is nearly $48 per turn of your opponent.

Thus, building evenly may be optimal after you already have 3 houses on every property, but not before. The reason for this is the jump from 2 to 3 houses is the greatest. It's a lot better than the jump from 0 to 1 or from 1 to 2. So if you have two undeveloped monopolies, it usually makes more sense to build one monopoly up to three houses on each property (leaving the other undeveloped until you do this), and the repeat the process for all the remaining monopolies (focusing on getting one monopoly up to three houses before you even start to build on another). Perhaps this is a good lesson on how marginal returns can be increasing at first, and that diminishing returns only happens eventually.

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frankenduf

the real profound question is: what's better pacific/nc/pa or pp/bw? (please expedite answer- I've lost serious sleep on this one)

Ian

to HM

You are so very right about the light blues. I played the fastest game of Monopoly ever. My brother got all the light blues in only three trips around the board! He did not need to put even one house on them because I flipped the board. We have a rule that when someone flips the board, it counts as two wins but the winner has to clean up the game.

Craig

The problem with (and beauty of) the 3-houses-per-property strategy is that there is a fixed number of houses available (32), and if there are no houses available, you can't build one. Thus if you have the properties and cash, you can starve your opponent of houses. Alternatively, you may find that you have to build hotels in order to free up houses for your other properties.

MPD

@11 MBirchmeir - That's a good way to analyze the data. Maybe I'll waste more time at work and look at this more.

Nick

Who plays monopoly any more? All Hail Settlers of Catan!

MBirchmeier

@6 MPD:

I found the markov analysis interesting, but the probability of landing on a spot does not address the issue of which is better to own.

In a situation where resources are infinite the greens are better, but what if money is scarce. The additional 50% cost to improving the greens vs. the blues might effectively price them out of being as effective as the blues until the very later stages in the game.

At $2000 invested (hotels) the blues gain an average of $80.55 a turn, however the greens at $2000 invested lag behind at an average of $73.19 a turn. (the worst disparity is at $1200 invested, where the greens lag the blues by a 47% margin)

Until the green's have 4 houses each (total cost $2400) they return less than the blues.

Greens are better in the end game, but I've found games are usually decided before properties are fully developed.

-MBirchmeier

You're welcome to check my numbers as I did my calculations here and might have missed something:

https://spreadsheets.google.com/ccc?key=pl96fF2sMuYePJIdKqykRHA&hl=en

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HM

Craig and Jake,

I couldn't agree more! I was banished from family monopoly games as a child for using this strategy. I pointed to the rules, but family members said that it was unfair! I was hoping that other readers of this blog would point that out. My favorite are the light blues - you can lay claim to 12 houses very cheaply.

Marc Brodeur

Monopoly is quite outdated in the world of board games. If you really want to see some awesome economics in a board game try the excellent game Power Grid.

http://www.boardgamegeek.com/game/2651

Also one of my favorite new games: Carcassonne.

http://www.riograndegames.com/games.html?id=48