Monopoly as a Markov Chain | Hacker News Reader

Monopoly as a Markov Chain

koaning.io

95 pointscantdutchthis36 comments

A very interesting little experiment! Based off this, the author notes that the orange streets will provide a steady stream of income, and this is useful information.

But the trick in Monopoly is to get hotels on your properties as quickly as possible, because this not only provides you with a revenue stream (and fastest return on investment), but also takes money away from your competitors, who would have used it to buy/upgrade their own properties. An important factor is therefore how quickly you can acquire all the streets in a block so you can start putting up hotels, and p * rent of a single street is only one part of that equation.

Instead of hotels, put 4 houses as quickly as possible so there are no houses left for other people to build. Only upgrade to hotels when you can afford to put the houses that will become available onto another of your properties. Other people's sets are worthless to them if you own all the houses.

Combine this strategy with the fact that the highest ROI on most properties is 3 houses, and you have a winning strategy against most non-experts.

1. Do whatever it takes to get cheap sets (other than risking somebody else getting the red or orange set). This is where blues and purples are very useful.

2. Put as many houses as you can as quickly as possible.

3. Wait for desperate people to trade with you to get the oranges or reds.

4. Spread your houses across the sets you own with 3 on each property, prioritising the reds and oranges.

NB - nobody likes me at Christmas.

But what about the street repairs card?

IIRC it is only 2-3 times the price of a house for a hotel.

Hope that you don't pick it up! In the end, Monopoly is a game of luck. Sometimes you lose because you constantly get sent to jail, and never land on unbought properties. All you can do is improve your odds, and this is the most surefire way I've found of doing that.

You can improve your odds of not picking it up slightly by never using the 'or take a chance' cards, and if all the properties are bought, stay in jail as long as possible.

That last line is the rub here. I used to play Monopoly as if my life depended on it. Now I don't, because no one will play Monopoly against me anymore.

Agreed. I've found the best way to play games against friends is to disconnect my competitive spirit and anlytical mind and just sit back and enjoy the conversation. I have fun, and those folks who are hyper-competitive get another "victim", so it's good for everybody.

That, however, means a monopoly game can easily last 5 hours.

The only way to play monopoly is to be brutal and eliminate everyone as quickly as possible.

(Ignoring the best way to win is to not play, and play any of the very much better games)

Really? Maybe a couple of hours. I just buy whatever I land on. Others usually follow suit and fairly quickly the board is divvied up. Then it's horse-trading and luck.

I think that with a few simple heuristics the game moves along quickly enough. I have family members who are so nice they try to prevent doing things the other players don't like. These games take forever. Geesh.

I haven't played in quite a while, so I may be remembering the game moving along faster than it actually does.

Side note: we've been playing Machi Koro at home over the last few weeks. Very simple concept, mostly luck, and interesting enough for a somewhat fun 30 minutes or so.

Monopoly requires player elimination. That's seen as "mean", whereas winning isn't seen as mean. That's the main reason Monopoly isn't a good game. The other reason is that people have house rules, which often have the effect of reducing the risk of player elimination, which then increases the playtime to stupid lengths.

There are a bunch of great, easy to understand, easy to play games that are much better.

(HN search might find a few, there have been several threads before. Board Game Geek tends to skew toward the more complex end, but there's probably good lists of great family games.)

There are some interesting variations of the game, using a standard Monopoly set. One I've seen allowed things like Lynch Mobs - if enough of the players agree, they can send someone to prison, remove their assets, or even eject them from the game. You could also institute a rule like "90% tax on cash holdings" or "those with assets under $200 receive an extra $1000 when they pass Go". It sort of combined Werewolf with Monopoly, because it required more skill at the human level to persuade your fellow players to vote with you.

"...Lynch Mobs - if enough of the players agree, they can send someone to prison, remove their assets, or even eject them from the game"

AKA democracy ;-)

Sounds like "Monopoly: Regulatory Capture Edition".

  > Monopoly requires player elimination.

Absolutely. I love Monopoly, and when I mention this, people always say "but it lasts so long!" It only lasts so long because just as someone is about to get knocked out, someone else loans them money to stay in the game...

  > There are a bunch of great, easy to understand, easy to play games
  > that are much better.

My favorite with family is either Carcassonne (I even have a tattoo) or Ticket to Ride.

Carcassonne and Ticket to Ride are brilliant games!

I'd utterly forgotten about house rules, but you're right, they're infuriating. The combination of not auctioning off properties when passed up and free parking make games go on forever.

Those are the two house rules that drive me nuts too. To the point I insisted when I started playing again that those can't be in play. Once the few people I started playing with realized how much it changed the game from a 4 hour marathon into something far better balanced in an hour they've not brought it up again.

Hm, "Free Parking" - do you mean something like?:

https://en.wikibooks.org/wiki/Monopoly/House_Rules#Free_park...

It's been a long time since I played, but I can't remember "mandatory auction" was part of the core rules. Then again, who knows what changes may have been made to the Norwegian version.

This one really gets me, because no on ever believes its in the rules until I get them out and point it out.

> Whenever you land on an unowned property you may buy that property from the Bank at its printed price. You receive the Title Deed card showing ownership. Place the title deed card face up in front of you. If you do not wish to buy the property, the Bank sells it at through an auction to the highest bidder. The high bidder pays the Bank the amount of the bid in cash and receives the Title Deed card for that property. > Any player, including the one who declined the option to buy it at the printed price, may bid. Bidding may start at any price.

From http://richard_wilding.tripod.com/monorules.htm#buyingproper...

That rule alone completely changes the dynamic of Monopoly, transforming it from a dirge like plod around the board desperately hoping you'll roll the right number for the property you want, into a game in which people will near bankrupt themselves to buy a property they don't want an opponent to pick up.

To be clear, I certainly didn't doubt you were right -- I can barely remember the last time I played. We had an old busted up version at our cabin. I certainly can't remember the last time I read through the rules booklet.

Also bare in mind the original game that evolved into Monopoly was designed to be upsetting, to teach the dangers of monopolies (https://en.wikipedia.org/wiki/History_of_the_board_game_Mono...)

did not know. interesting!

Another thing is to note is that the highest ROI generating properties are the stations, if you can get a monopoly on them. The surest way to win is to just get the orange and the transport monopoly, and the game breaks down because you are earning far more than any other player can.

I try to focus on one of these groups at the early game, and add the other one as soon as I can. Unless I'm playing with good players, in which case I need to hedge bets and maybe go for a Red. I rarely, if ever, go for anything above Red (So anything on the second half of the board).

hi all, glad to hear you guys like it. im the guy that wrote that post, didnt imagine that it might be trending.

some of the comments here are indeed very valid. the fact that you can push all the houses to your deeds actually might make it more interesting to push for the the cheap investment places that otherwise don't give too much of a return.

my main goal was to figure out which house yields the best return on investment. which was a problem that had been bugging the back of my mind for a while.

ill add strategies that ive missed and give credit to it when i recheck the blog for spelling.

This is also solves project Euler assignment 84.

Another cool article from this website: http://koaning.io/canvas-trees-and-communities.html

A comment on the display of the data: more decimals don't make your results look better.

Only show a relevant number of decimal places. In the case of this data most of it needed 0 to 2 decimal places.

fair enough. the reason why there were so many numbers was lazyness, i just copied the R output directly.

options(digits = 3) is our friend. :-)

___

Also I should have said, "nice simulation!" instead of just nitpicking.

no worries. this way i've learned something. +1

I have read about some of this before in the book "Luck, Logic, and White Lies: The Mathematics of Games"

https://www.crcpress.com/Luck-Logic-and-White-Lies-The-Mathe...

I was playing around with this Java simulation recently that does include Chance and Community Chest cards http://tesuji.org/monopoly.html

Not to nitpick, but it seems like what you did would have been much more suited for an IPython (Jupyter) notebook directly outputting with matplotlib rather than writing Python code to generate data for R?

out of curiosity, how many lines of code do you need in matplotlib to generate http://koaning.io/theme/images/monopoly_plot3.png? in R, you'll only need one. also i have done this work in a python notebook, you can specify R cells to take pandas dataframes allowing you to still use ggplot2 for plotting. see old video of mine: https://www.youtube.com/watch?v=ZW8Aei2wlsM

Using the Python Seaborn library one line sounds about right:

http://stanford.edu/~mwaskom/software/seaborn/examples/scatt...

thats not a facet grid though, in a facet grid you'll have split data across different cells. this is a cross plot across 4 columns. i did find this tho: http://stanford.edu/~mwaskom/software/seaborn/examples/facet...

"players can go bankrupt" is listed twice at the end.

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