Monopoly as a Markov Chain

http://koaning.io/monopoly-simulations.html

by cantdutchthis • 11 years ago

95 36 11 years ago

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.

blowski3• 11 years ago

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.

TheAnimus• 11 years ago

But what about the street repairs card?

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

jon-wood3• 11 years ago

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.

davidgl• 11 years ago

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...)

captn3m0• 11 years ago

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).

toolslive• 11 years ago

This is also solves project Euler assignment 84.

edem• 11 years ago

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

cantdutchthis6• 11 years ago

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.

admiralpumpkin2• 11 years ago

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.

cantdutchthis6• 11 years ago

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

admiralpumpkin2• 11 years ago

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

___

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

takk309• 11 years ago

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...

mizzao• 11 years ago

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?

cantdutchthis6• 11 years ago

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

rrggrr• 11 years ago

Using the Python Seaborn library one line sounds about right:

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

DenTheRed• 11 years ago

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

iraphael• 11 years ago

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

Monopoly as a Markov Chain

Related Stories