Killer tips for winning a game of Monopoly

Capitalism! Yeah! Owning money is great, it lets you buy great stuff, like fridge magnets, waffles and dignity. And if you’ve got money you can buy bits of property and then charge people rent just for walking on it. And you can build houses on top of pubs, and then build a hotel on top of that. And there’s a ship that follows, um, a top hat into the, um, bit of ground that has “Chance” written on it that lets you win crossword competitions. Yeah, the analogy kind of stopped working. Also you can make women be the iron because it’s ironic.

Of course, I’m talking about Scrabble. I mean Monopoly.

After peeking under the gusset of Noel Edmonds for my last article, I was challenged by my editor to test out his theories on Monopoly. But that posed a bigger challenge of making a friend and then convincing them to play Monopoly, with the express purpose of them losing and me taking all their money. Only a complete lunatic would agree to this. Naturally, my playing partner was Den Of Geek’s Jenny Morrill.

Firstly, our strategy. My goal was to buy all the orange properties, followed by the blues. I’ve always taken Monopoly games very seriously, and on opening up the family box for the first time in two decades I found detailed notes on the last game, including positions and finances. Yes, it was with my mother, shut up. Jenny’s goal, on the other hand… we’ll get to that. We played on a regulation 1971 Monopoly board, using original pieces. We also had proper auctions for each property we landed on, because that’s what it says in the rules.

Game 1

We quickly found out that auctions for properties no one wanted turned into games of “I’ll buy it for £1” or “how about £1.01?”, which then degenerated into “go on” until one of us (i.e. me) caved. I should have accepted Jenny’s offer for Pentonville Road of £3.78 just to see how she would have paid me (I imagine she would have needed scissors). This meant that soon the early properties were all snapped up quite quickly. I acquired the blues (my personal favourite) and the oranges (said editor’s top tip) quite quickly, while Jenny managed to get the odd station, the pinks, and the purples (her favourite). The game was afoot.

Herein we noticed an immediate benefit to my portfolio – the houses were dirt cheap to buy. So I already had houses on all the blues before Jenny could afford just one on Mayfair. And so marked the decline into the endgame. Turns out it didn’t matter at all what Jenny did now, I’d already won by getting a couple of houses on Bow Street.

Only able to find one die. we had modified the rules – instead of throwing doubles to get out of jail, you had to roll a six. Six spaces from jail is Bow Street. You end up in jail a lot in Monopoly, what with all the go to jail cards, the stupid rolling three doubles rule (ours was rolling three sixes) or the Go To Jail space, so the greatest strategy is to buy properties you will land on after escaping jail. Jenny was admittedly quite unlucky in going to jail quite as much as she did, but when she escaped, she wound up with a pricey stay in a Bow Street B&B. She’d rather she were still in Pentonville.

Her strategy of the purples alas didn’t yield as much success as she’d hoped. By focusing on one group (and a small one at that) she was able to reasonably quickly develop her properties. But that group proved to be expensive for me due to the Super Tax space, rather than Mayfair or Park Lane. There are three spaces on that side of the board that potentially don’t allow you to move – Chance, Community Chest and Go To Jail. Thus there are fewer moves that allow you to land on those spaces, and chances are, if you miss those, you’ll end up on Super Tax or Go.

In fact Park Lane is the least common square to land on, due to the Go To Jail space being seven moves back from it. Since seven is the most common throw of the dice, that’s a huge hit right there. It is also rather easy to bypass Mayfair entirely with Go To cards, vastly outweighing the one Advance to Mayfair card. Park Lane doesn’t even have a Go To card. This strategy is rather risky, relying on a lucky (or unlucky) throw of the dice.

Game B

Armed with a second die, our strategies were forming. Getting the oranges was a priority, followed by the reds (as they were a likely stopping off point after the oranges). Avoiding the expensive ones was obvious, and getting a majority of stations was another tactic we were toying with. And all that immediately went out of the window when Jenny landed on the blues and oranges and bought the lot.

Undeterred, I tried my hand at some other properties. I acquired three stations, the pinks, and the reds. Later I bought Mayfair and Park Lane. This was to be my undoing, although not at first. While the second die meant far fewer times landing on Bow Street, the oranges are still statistically more likely to be landed on than any others due to their proximity to Jail – nearly 40% in fact.

The double dice severely skew the average dice throw to the middle-ish values, between five and nine. They also are reasonably cheap to develop at £100 each. Since the average income around the board (taking into account money from Go, fines, taxes and rents) is £170 per trip, there’s scope to buy a house or two every circuit. Consider that most individual properties cost more than that, and you can see the attraction.

The blues have the same relationship with the Go as the oranges do with jail. They are also very cheap to develop, and the average player could develop the whole set each turn, if they so desired. The effect of buying both is devastating, as if you do manage to avoid the blues, you’ll end up near jail, and we both know where that leads. To be honest, if a player gets both of those groups you might as well give up.

Jenny started building houses which quickly meant I was handing over quite a bit in rent every trip around the board, but I mostly was breaking even with the stations, and little bits here and there from my diverse portfolio. This went on quite a long time, with neither of us really making enough to expand significantly. I bought a house on Pall Mall and Trafalgar Square (as they had Go To cards), but it made little difference. It is at this point I should mention Jenny’s winning strategy… get all the £1s.

Jenny, bless her, has never been one for hardcore Monopolising. Instead she was far happier to annoy me by denying me access to the bank by sitting on it, and making me regret charging her for rent when she insists on paying in odd denominations. This strategy was only marginally successful the previous time, but here it really started to pay off. I thought we were both more or less even financially, with me having the larger portfolio but her having more capital. It’s just that her capital was mostly stored in ones and fives in a rough pile (at most points she actually had all the ones), making it impossible to tell how much money she had. Mine however was neatly arranged in piles, in sensible denominations. Out of nowhere, she bought extra houses for all her properties. Turns out she had a lot more money than I thought.

The result was a painful slide, each trip round the board whittling down my money, forcing me to mortgage, and finally having to sell properties. Of course, at that point the balance sharply tipped, and within a few turns I was utterly bankrupt. And that’s after I cheated by embezzling several thousands of pounds from the bank. After that I wasn’t allowed to be the banker.

There is actually nothing in the rules that says you have to let other players see your cash. Hiding or otherwise obfuscating your cash is a very lucrative strategy when it comes to property auctions, as you can easily gazump other players, or just stop them from picking up a bargain. Tournament play positively encourages obfuscating your cash on hand in order to introduce a poker style element to auctions.

I can’t believe she beat me at Monopoly.

Game 111

Now our key strategies were in place:

1) Buy properties five to nine moves from common squares (i.e. the oranges, and the blues)

2) Buy the stations (all four net you £200, which will keep you in the game for a long time)

3) Avoid properties in the first half of any side of the board – they cost the same to develop as the latter half but give far less rent.

It is at this point that I should mention the yellows and greens, because I suppose someone has to.

The greens are the most expensive set to buy and develop. In addition to there being more of them, they also cost exactly the same per property to develop as the purples. As a result, early game players are almost entirely locked out of this route. In fact, the greens are most commonly used in the game as bartering chips.

The yellows on the other hand, while being reasonably cheap to develop, are landed on far less than the other sets, or at least that’s what we’d experienced in our games. The yellows and greens are neither near a common space nor have a Go To card. They are also likely to be bypassed by other Go To cards, which greatly favour the first half of the board. So naturally, the focus of the third game was to see if these properties could ever be leveraged to victory.

The game proceeded mostly as previous ones have. The blues got snapped up early, there was a rush for the oranges, and the stations were bought at the earliest opportunity. I decided to wait for the yellows and greens though, which Jenny (now calling herself “The Land Baron”) happily obliged with. It was a disaster.

In order to buy just one house for each of the greens costs £600. That’s three trips around the board assuming no fines, rents or purchases. After three trips around the board most players can expect to have one decent development, or a range of properties, and I had neither. The more I waited, the more the rent kept piling up which meant more waiting. I was bankrupt before I’d put my second house on.

In theory…

Of course any game of Monopoly will be affected by chance (the concept, not the space) more than anything else. So, in an ideal world what should you look at? Andrey Markov. Markov is best known (well, as well known as stochastic mathematicians can be) for inventing the statistical analysis method the Markov chain. His first teaching post was the title “extraordinary professor” which I’m only mentioning because it sounds like something from Harry Potter. The Markov chain is a method that allows you to work out the long term probability of a chain of events, in this case the chance that your turn will end on a particular square.

Obviously, if you’re on Go there’s a zero probability you’ll land on Park Lane in one turn, but still, for looking at the big picture it is invaluable. For technical details involving matrices and beards see the link at the end. I have used the data from that article, but bear in mind there will be minor differences in the UK. Interesting trivia: there is no equivalent of the “Go back to the Old Kent Road card” in the US version. Okay, maybe not that interesting.

In Jail (far right) is obviously the most occupied space, so let’s remove that (but not Just Visiting).

The proximity to jail and the Go To card make Trafalgar Square the most landed on square on the board. Aside from Go and Free Parking, the next two most common properties are Fenchurch Street Station and Vine Street. What about the colour groups as a whole? For no reason other than I like pie, let’s put this one as a pie chart.

Interestingly, you’re most likely to not land on a property at all. The stations are the most likely properties. Reds are the next most likely, followed by oranges and yellows. Blues are surprisingly far down the list.

However, this is all well and good, but considering the different rental yields and development costs probability is just part of the equation. So, I collated the different colour groups, multiplied the probability by the rental yield to give an expected value. Then I divided the this expected value by the total cost of the properties at different points in the game (buying the whole group, developing them to three houses, and then to hotels). Technically this is the inverse of the payback time of the investment, but it gives a good indication of which properties are the best value for money (hence the lack of numbers on this one). Here:

You can see lots of things here. Firstly, the stations (black) are fantastic in the early game, and hold their own in the mid game. The late game sees them dropping off a little in value but still not by much considering how they require no development. Obviously, the value is much less if you don’t get all of them. The utilities are great early on but rubbish once houses start being built. Look how little extra value hotels add though. In the cases of the greens and purples, it actually removes value.

Putting this all together, we can see a clear strategy.

– Buy any stations you can as soon as you can and keep them all game.

– Buy the oranges and put at least three houses on them ASAP. Don’t bother going any higher unless you’ve already developed other properties.

– For the next ideal set, I’d plump for four houses on the blues, as they give the next best bang for your buck. There’s a sneaky reason not to upgrade to hotels I’ll tell you in a bit.

– If you can’t grab the oranges or blues, get the reds or yellows. The reds are cheaper to buy and are landed on more often, however yellows have better development costs versus rental income. They average out about the same so either or both are good. Three houses maximum – don’t put hotels on these ones; hotels don’t actually add any value.

– If you own a set that has a go to card, always develop that property first. Otherwise develop the last property on the row first.

– The pinks are only any good with serious development, so unless you’re planning to develop quickly I would avoid them.

– Mayfair itself is a very good square, but it is severely dragged down by forcing you to develop Park Lane, the worst square on the board. Worth it as a punt only, and don’t develop it too much.

– Avoid buying the greens as a development, but do consider them for trades late in the game.

– Buy the utilities early but trade them in later.

– Don’t buy the Old Kent Road unless you’re playing Jenny’s strategy of hoarding all the £1s.

There are some other strategies that bear mention too, but less to do with the stats and more to do with underhanded tactics. You know, the best kind of tactics.

– There is a limited supply of houses, so it actually pays to not buy hotels, because it returns houses to the pool. In two player games this is a non-tactic, but once you get to about four players this is definitely something to consider. The advantage of owning the oranges is blunted considerably if you stop them building houses.

– Deliberately go to jail. Jail is the only place you have a hope in hell of staying for the next turn. And while in jail you can’t pay rent to anyone. In the early game it’s wise to try and get out of jail quickly to buy properties, but in the late game it’s actually something of a refuge. In tournament play they often introduce three dice, and throwing a triple lets you travel anywhere you want. The majority of players choose Go To Jail.

– Don’t have house rules. Most people play using the rules their parents taught them, which normally means no property auctions, and putting all the fines on Free Parking as a sort of lottery. All this slows down the game; with the official rules the average game only lasts about an hour. If you must modify the rules, turn Free Parking into Wheel Clamping and charge £100 for it – it considerably speeds up the game.

It’s only after putting all this together that the moral of Monopoly emerges. Capitalism sucks balls. The haves get more money, the have nots just keep paying out more and more. There’s profit in creating a housing shortage. Privatisation of the railways leads to price fixing. Being in jail is great if you’re rich. Poor areas stay poor for a reason. All your earnings get paid out in tax at some point. Playing Monopoly is like an Aesop’s fable on big business – the only way to not lose is to already be winning.

Of course, the real London rarely has free parking.

Data source

Find more from Alex at World Of Crap, here.

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