How to win at Monopoly


As children growing up in Sri Lanka, we were addicted to the game Monopoly. When a bunch of us cousins got together during school vacations, we would play games over and over again late into the night, with a lot of shouting and laughter.

I now positively detest the game. There is something about having the goal of forcing other players into poverty where they cannot pay the rent and are forced to declare bankruptcy that strikes me as morally repugnant.

But the game does have some interesting statistical features. On the surface, one would think that the chance of landing on any particular square is the same as for any other. But there are obvious variations. For example, since everyone starts at GO, the chances of landing on the first twelve squares will follow the probability of getting that total from the throw of two dice. But in a long game that variation would be small effect. But there are other special cases, such as landing in jail or drawing a Chance or Community Chest cards that sends one to particular squares, that also introduce some non-random elements. Also rolling doubles gives you another turn, further skewing the randomness.

Now Walter Hickey has gone to the trouble of looking into the research that takes all these things into account and calculates the overall probability of landing on each of the squares. Some of the suggestions for increasing your odds of winning are those that many regular players would have intuitively realized on their own without a statistical analysis. (More on the math can be seen here and one set of tables of probabilities based on that math can be found here.)

Here are the steady state probabilities.

monopoly

What conclusions can be drawn from this? Hickey gives some tips.

  • The red and orange properties are exceptional investments.

  • Particularly earlier in the game, you’ve got to get the railroads.
  • Properties between Jail and Go To Jail get landed on more frequently than properties between Go To Jail and Jail.

Hickey also looks into the question of when one should build properties.

  • While Park Place and Boardwalk are excellent for crushing opponents, early in the game their ROI [Return On Investment] is not ideal.

  • Owning all the railroads is an exceptional position to be in.
  • The best investment in Monopoly is building the third house on the orange block of St James, Tennessee and New York.
  • Three houses is the way to go.

There’s a lot more specific advice for aficionados.

I pass this valuable information along to anyone who plays the game so that you can use it as part of your strategy.

Comments

  1. screechymonkey says

    This article seems to be getting passed around a lot lately. There’s two problems with it.

    First, it’s nothing new. When I was a kid in the 80s, I got a Monopoly strategy book from the library that made all of the same points: which spaces get landed on more often, the large jump in rent from two to three houses, etc.

    Second, although the facts it points out are sound, the way the advice is phrased is odd and seems to show a fundamental misunderstanding about the game and basic strategy. How exactly am I supposed to go about “trying” to buy the railroads or the orange properties? Barring exceptional circumstances, the proper early game strategy is to buy everything you land on that isn’t already owned. You don’t land on Park Place and say, “no thanks, I’m saving my money until I land on the oranges.” The advice is still sort of useful if you take it to mean that you should adjust how you value those properties in trades, but that’s a much more subtle point.

  2. mobius says

    I remember reading a good article by Marvin Gardener many years ago analyzing Monopoly. I don’t remember all the details, but one conclusion was that the orange properties had the best return for a modest investment. This analysis also included weighting the figures by the probability of landing on the property, considering die rolls and various “go to” cards. The best performing properties over all were the green properties, but took almost twice the investment to surpass the orange properties.

    I have found basing my strategy off of this to be pretty successful. Most people consider the orange properties to be only mediocre and tend to ignore them or let them go easily. It also helps if you have an opponent that is willing to go overboard gaining control of Boardwalk and Park Place with little cash to improve them.

    @Katherine

    Real Monopoly includes auctions on properties not purchased by the one who lands there.

    True, but then almost everyone plays the game with some house rules.

    For myself, I find it very advantageous to mortgage properties to get the cash to buy more properties after landing on them. You will almost always get enough cash in the middle stages of the game to get them out of hock, and the more properties you control the better your chances of winning.

  3. Paul Jarc says

    The Landlord’s Game was created to illustrate the darker side of capitalism. Monopoly was created as a commercialized ripoff of The Landlord’s Game. (A bit on the nose, but there it is.) So your (and lots of other people’s) distaste for Monopoly can be read as vindication of the position that games can be art and don’t need to be fun.

  4. unbound says

    Well, keep in mind that the name of the game is Monopoly, so that should tell you that it isn’t supposed to be a fair game at the end of the day.

    In fact, if you look at the history of the game (based on Lizzie Magie’s “The Landlord’s Game”), it was actually designed to teach how capitalism has some problems. An interesting discussion of the history can be found here – http://www.straightdope.com/columns/read/2986/was-monopoly-originally-meant-to-teach-people-about-the-evils-of-capitalism

  5. left0ver1under says

    Board games like Monopoly, Othello or Risk are very much zero-sum games similar to hockey, soccer or basketball – one can only win at the expense of another player. Other board games such as Life, Scrabble or Careers are independent games, much like golf. You are competing with others but not in an “I win, you lose” setting. There can be friendly rivalry without offending other players.

    Games can become unpleasant to play both because of sore losers *and* sore winners, while sessions in independent games can often be much friendlier. Computer opponents can suffice for some games when one can’t find opposing players, but not all. I enjoy Turbo Risk (a freeware game) because few people like to play the board game version, even without sore losers.

    http://www.marioferrari.org/freeware/turborisk/turborisk.html

    Just as Monopoly can be broken down and analyzed for probabilities, Risk can be seen as an exercise in graph theory – maps, adjacenies, possible paths, decision making, etc.

  6. brucegee1962 says

    As an avid gamer, the main reason I hate Monopoly is that there are so many adults who say, “You play board games? I played Monopoly all the time when I was kid, until I realized how boring and unpleasant it was. Board games suck.” I reply, “You wouldn’t want to drive a car designed in the 1930s, would you? Game design has moved forward since then just as much as car design has.”

    Player elimination is a terrible mechanic, and as #7 points out, the bleak economic model of the zero-sum economy makes losing a miserable experience. Here’s a famous article from the Washington Post about how the greatest of the modern games, Settlers of Catan, not only is a lot more fun to play, but also uses an economic model (trading for mutual benefit) that is more humane and does a far better job of training kids for the modern world: http://www.washingtonpost.com/wp-dyn/content/article/2010/11/24/AR2010112404140.html

    In most modern German-style games, you don’t get the agonizing bankruptcy in loss that you have in Monopoly. Everybody builds something; it’s just that some people build a bit more than others. But even if you lose, you can tell yourself, “I built the most cities” or “I had the longest road.”

    Oh, also, whatever you do, don’t play with the “Free Parking collects all the money that’s been paid in fees” rule. A lot of folks do, and they don’t realize that’s the main reason why the game goes on for so long. And if you’re playing Monopoly, your main goal should be to finish the game as soon as possible so you can play a better game.

  7. says

    Someone needs to write an updated version of Monopoly that includes the options to rewrite the rules once you have enough power and influence.

    Aaaah, competing capitalists to see who can divide up the world! Such fun! Perhaps there should be a couple cards in which the workers get to rebel and the player with the least money gets a tumbril-ride.

  8. Mano Singham says

    And if you’re playing Monopoly, your main goal should be to finish the game as soon as possible so you can play a better game.

    That’s a good rule to keep in mind!

  9. CaitieCat says

    There’s also been a growth in games which are either fully or mostly cooperative – I’m most familiar with Arkham Horror, the Lovecraft-mythos game which is fully cooperative, but there are several others with varying levels of cooperation/competition mechanics, like Knights of Camelot and Battlestar Galactica.

    There are older versions of this type of game, too: Escape from Colditz has most of the players playing a national group of escaping officers, and one player as the prison-guard Nazis. This one is, unfortunately, not as scaleable as they’d like, since the ratio of escaper-turns to guard-turns goes up directly with the number of escaper players, and the resource availability to the guard goes down directly with the number of players, just as the escapers’ resource access stays constant (well, regresses to multiples of the mean, actually, but that’s not key).

    In the cooperative games, you’re generally working with the other players against the game, or against one player, or with all the players except for an unknown traitor (BSG, where one player can be a Cylon infiltrator). For people who don’t enjoy the zero-sum-ness of strictly competitive games (one of my partners is like this, quite strongly), the co-op games can provide a completely different experience, especially a well-designed one that allows different players to contribute to the team victory in different ways. Say someone likes fighting, while another likes doing the puzzle-challenges, and another likes the risk of a luck-based obstacle – a good co-op will let each do the thing they like, and gain victory or defeat as a team, rather than as individuals. Arkham Horror is really well scaled – not perfectly, as again the number of player-turns to monster-turns scales with the number of players, but it does scale most other parameters to the number of players fairly well.

    Just to add a different facet to the discussion. :)

  10. mobius says

    @Paul


    You’re thinking of Martin Gardner. Or possibly Marven Gardens.

    You are exactly right. Martin. I am afraid I had Monopoly on my brain.

  11. brucegee1962 says

    “there are several others with varying levels of cooperation/competition mechanics, like Knights of Camelot and Battlestar Galactica”

    I think you mean Shadows over Camelot.

  12. morejello says

    Marcus, we played a game of monopoly once with the house rule of when you pass go, you compare the value of all players (Cash + worth of non-mortgaged properties), and the top player gets to make or rescind a rule (We called this house rule ‘One Percent Monopoly). Note that they could word the rule any way they want, so it could apply specifically to them or specifically not to them. We had 3 people playing, so once around the board meant that 3 new rules were made, inevitably all by the same person. We got as far as 5 new rules before the 2 who weren’t the top player stopped playing. It’s fortunate that we had the option to quit, unlike participants in real-world capitalism. I don’t remember all the rules, but the first was that the top player got $2000 instead of 200 for passing go, and one of them was that the top player could take bank loans for no interest. Both are very realistic in comparison with capitalism, and both are unbelievably unbalancing to the game.

  13. screechymonkey says

    True, but again, best strategy is to purchase every property you land on, so this shouldn’t really happen against competent players.

    I suppose if you’ve got at least one player who doesn’t realize this, then the advice given may help you decide how high to bid in an auction.

  14. left0ver1under says

    After the fact, I was thinking about independent games and golfing handicaps, which are used with players of different abilities. It turns out that scrabble has a handicapping and rating system which allows weaker and stronger players to play one another, with points initially given to weaker players to balance play.

  15. Francisco Bacopa says

    None of this ROI stuff makes sense in Monopoly. There are dice. You land where the dice tell you to. Whoever gets a properties monopoly early tends to win.

    Diplomacy is the real board game , but it works best with 7 players. Hard to pull together, and ferocious when you do. There are many sites that host PBEM and server based games.

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