Solving Monopoly with Markov chains

Business Insider's Walter Hickey did the math on Monopoly, calculating the most frequently landed-up squares (taking into account dice probability, Go To Jail events, and Community Chest/Chance cards) and conceived of a supposedly optimal strategy for buying and building upon property. I still hate Monopoly, but I suspect that this would make it less boring (for a while, at least).

How To Use Math To Crush Your Friends At Monopoly Like You've Never Done Before (via MeFi)


  1. Do you hate it because you’ve been playing it wrong?

    1. Excellent stuff. I was aware of the auction rule, but I haven’t played Monopoly in decades, because it’s a hate-worthy game. But you may be right, maybe I just never played it right.

      Also, I suspect “solving” Monopoly will not make it any more fun, in fact it will remove some of the already scarce fun. The fact is, grinding your friends slowly into poverty just isn’t much fun, even less so when you do it by adhering to an optimized formula.

    2. Maybe, the true secret of Monopoly is not what is written in the rules, but what is not written there. If none of the players buy any property, they all may circle the board, gaining $200 every time they pass ‘Go’ in their endless dance. But the moment the greed of a single player tempts them to buy a property, all players are condemned to a merciless struggle where one player inevitably bankrupts the others, only to be saddled with a fortune in useless properties that no-one can ever land on.

      (sfx: chinese flute playing ‘Kung-fu’ theme)

    3. I thought the Auction rules didn’t matter because everybody bought up every square when they landed on them and never let them go to auction? 

  2. It’s a profoundly bad game, but if you only remember it from childhood, you will be destroyed by a good player if you are ever inveigled into playing it again. 

    I should also point out that analysis of the patterns of movement based on the combination of dice, special board spaces, and cards was done many years ago.

    1. My older brother bought a fairly thick Monopoly strategy book when he was a pre-teen, then read the whole thing and followed it to brutal effect. After a while I picked up on his tactics and we would have stalemate situations that would last for hours. He did the same with Scrabble, Boggle and Risk, so I’m sure you can imagine how fun game nights were at the Roberts’ house.

  3.  I’m not sure this really helps that much. I have always noticed that being the first to get ANY of the sets of properties is a huge advantage. Of course, this ROI chart could certainly be useful when making decisions about property trades.

    They say Monopoly can generate hard feelings between players it’s got nothing on Diplomacy.

    1.  Diplomacy and Risk are higher on my hate list, stalemates and random luck, ug. Monopoly is better than those two. Not saying it’s good.

      1. The saving grace for Diplomacy is that it’s supposed to be a simulation of a brutal, pan-European, meatgrinder stalemate, so all its vices are at least accurate.

    2. I had a great game of Diplomacy once. We were living abroad and one of my friends brought a board over at great personal effort. He really wanted to show us the game, and had been talking about it for ages. He wasn’t too happy when I declared peace on another player (who accepted) and we used our collective power to bring about unity and prosperity throughout the region.

      1. There are many examples of two way draw strategies in the Diplomacy literature. There is R/T Juggernaut. the E/F Steamroller. The A/I Lepanto. The F/G Sealion ….

        But there’s always a chance for the solo stab once you get forces beyond the two way stalemate line. 

    3. I once had a guy I was dating throw a tantrum at the table because of an unfortunate move in Settlers of Catan. He then sabotaged his own chances in order to try to screw me over all while pretending his falsetto shrieks were ironic.

      I say we all stick with trivia games and never speak of strategy again.

    4. Diplomacy is a great game. Just don’t play it with friends, or with people who are friends with one another.

      1.  Friends with one another is a perfect situation to form a three member coalition. From Fall 1901 you get people to cut that off. It’s an E/R alliance? France should open with English Attack, maybe get the Germans to help with F/G Sealion. R/T Juggernaut? Give them the Lepanto.

        1. A rock-solid alliance is no fun to play, IMO. It’s much more fun to play as R or T with the other guy/gal a stranger, agree to bounce in the Black Sea the first turn as a ruse, and then roll up the rest of the map while everyone else fails to ally properly…. But it’s been so long since I actually played, I think the last time was in a FtF tournament organized by John Boardman.

  4. I bought a paperback based on similar analysis back in the mid-70s, including the probability factors and the ROI of various properties and add-ons (houses/hotels).  Since then, I suspect the process has been repeated every few years.  I’m not sure which is a worse option – that Hickey didn’t run into any of these prior works, or that he knew about them but didn’t acknowledge them.  But he did use Powerpoint, so he has that going for him.

    1. I have this book, or one very like it — it’s “1000 Ways to Win Monopoly Games”, by Jay Walker and Jeff Lehman, copyright 1975. It has tables of probabilities for landing on various color groups, describes the real rules and the importance of the auction, and various strategies employed by tournament players.

      I am astonished to learn that it’s listed on Amazon as “unavailable” and priced at almost $12000

      1. I believe that was probably it.  I’d also bet it’s still in my mother’s house somewhere. LOL

  5. That’s like saying poker is reduced to the luck of the draw.

    Also, if there is one solution and no variables, then there would no reason to play again, like a puzzle.

    1. Is there bluffing in Monopoly? Is the risk versus reward as variable? I’d say no.

      What I imagine is four players with this guy’s stats, each trying to buy and build up the same properties, in the same order. It comes down to who rolls most optimally. 

      1. There is no bluffing of course, but there are auctions and trades. If a player goes by the graph only, they will give away too many resources to capitalize, they are going to be crushed. Its the same as if a poker player would play only with a graph of winning poker hands, instead of playing the people.

        I do agree that the dice have a huge influence on the game, but an experienced player will still have options, just like a poker player drawing a pair of sevens.

  6. No money in free parking speeds the game up (too much money sloshing around is the real cause of static, looong games), as does strictly adhering to the limited number of houses and hotels in the set.  Monopoly is often very skill-based, as you need to assess multiple variables (including personalities) in order to decide what risks to take.  The article is old news, everyone in our family has known that the NY and Illinois monopolies are optimal ones, but it’s also just dead wrong about the railroads.  They’ll let you survive for a while, but they aren’t going to let you win because you cannot develop them.  Baltic and Med and the light blues (especially if you can finagle the whole side of the board) can be huge strategically, because you can use them to control the supply of houses and strangle other ostensibly better properties.  I guess to each his own, but I find it very stimulating to try to come up with a trading strategy that’ll give me the best shot, especially starting from a property disadvantage. I’ve never understood why people think it’s terrible, I suspect that certain house rules may be distorting the balance of it in their games.  Might be personality as well, we’ve got a pretty competitve family.

    1. People hate it because on the surface the game seems simple and fun, but it too often degenerates into bickering and bitterness.  People don’t understand when they’re making a bad choice, and people have favorite properties that don’t want to give up on.  

      Furthermore, when these same people with a misconception on how to play end up playing someone who can play they are shocked when they’re steamrolled by what appears to be the ruthless face of capitalist.  But then…that’s been my experience.  I’m no Monopoly master, and I lose my share of games when I do play, but I love the hell out of the game.

  7. Games like Monopoly, Risk, and the like kept me from really playing board games until I was an adult.  The “classics” are horrible.  I am not saying you can’t squeeze enjoyment out of them, but it is like comparing bud lite to a well crafted microbrew.  Bud lite is fine until you have tried good beer.  

    The classic have horrible game design.  They don’t have the strategy and balance of a good Eurogame, and they lack the theme-through-mechanics and controlled risk of Ameritrash games.  

    I have converted a pile of my friends to loving board games.  It is simple.  Ask them if they like board games.  If they say no, ask them what they have played.  If they mention one of the “classics”, coerce them into playing a real board game with another couple of enthusiastic folks.  It has worked for me without fail.

      1. The key is to always make sure that you know the game forward and backward.  If you have to reach for the rules, you fail.  You can reach for rules when preaching to the converted who want to learn, but on your fast pass against non-believers, show no doubt to the heathens.

        I should preface my recommendations by saying that I am not a Eurogame guy.  Eurogames tend to be only tangentially adversarial, the theme a throwaway excuse for the mechanics, play tends to be a bit more deterministic (like chess) and reward thinking ahead (also like chess).  I prefer what is lovingly known as Ameritrash.  These games tend to have a very strong sense of theme.  The theme comes out strongly in the gameplay.  They tend to have more elements where you manage risk, rather than deterministically know the result of each move (closer to poker than chess). Spartacus, despite being a TV tie in, if you can get four people together, this game is awesome.  The rules are pretty simple and require almost no rulebook reaching by even people with poor memories.  It has a bunch of different mechanism going on at once, but all the mechanisms are simple and interesting, it self balances, and it has lots of interaction.  You will be screaming at your friends in no time.  This is my game of choice for converting people to adult level games.  It shows what a game with some good mechanics and them can be, and it does it without overwhelming them.  It requires little effort on your part to setup and manage, so it is low stress to introduce people to it.If you have friends who like Battlestar Galatica, the BSG board game is great.  You really get a strong sense of theme, and the game is semi-cooperative.  The only problem with this game is that YOU need to understand the rules pretty well and you really need to set it up before people arrive. If you have to dig into the rule manual all of the time, you are going to kill it.  If  you know the rules and can manage the game, it is a lot of fun and pretty easy to grasp.Netrunner is an awesome two player game.  It crushes the idea that all card based games are variants of Magic.  The two sides are symmetrical and the gameplay is unique.  This is my go-to two player game.The Resistance is a perfect game for people who need to be eased into the idea of playing games as an adult.  The rules are very simple, there are almost no components, and it revolves around socializing and pointing angry fingers at each other.  You can play it in a pub.  It isn’t a hardcore board game, but it is a good first step down the path.

      2. Ticket to Ride and Settlers of Catan I think are both good games to transition with. They look and feel similar to classic board games, but with better mechanics. If you want something really easy to learn, then Tsuro is great. Tsuro doesn’t even require the players to know how to read.

  8. In the real world, we’d be looking at net present value (NPV) of the investment instead of ROI.  Factoring the interest rate of a loan, we might determine that the 10 year ROI of $100,000 has a NPV of $71,000.

    The slide says “ROI time,” but I don’t think there is such a thing – I think he really means “payback period.” 

  9. Everybody should know the real way to win Monopoly is to be the banker and to embezzle all the money when no one is looking.

  10. I have to say, this is really interesting.

    But we don’t play Monopoly that way. We get out both Monopoly and Dungeon (the 1981 TSR board game) and set up rules that if you really want to buy Park Place, first you had to fight a monster.

    If your shoe-elf or thimble-superhero lost the combat, you had to leave half your cash holdings under the square on the board as “treasure.” Another player could then defeat the monster and acquire the cash (and the right to buy the property).

    Perhaps not the best in terms of game balance, but an awful lot of fun by our standards.

Comments are closed.