Instead of average-case, here's a funny analysis of an extreme case, the shortest possible game:

http://scatter.wordpress.com/2010/05/30/the-shortest-possibl...

This is a fascinating breakdown. Quite a few people have covered this ground before, but I've rarely seen the raw statistics of the game explored in such depth. (Most commentaries I've seen, for example, start and stop at the probabilities of landing on any given space, perhaps coupling those with the expected ROI of improvements on X or Y properties. But those are only some of the factors in play, and you do a nice job going beyond them).

Apropos of nothing, there's a really entertaining documentary called "Under the Boardwalk" that sort of flew under the radar last year. It's about the history of the game, and the national championships (yes, apparently there are Monopoly players who take themselves as seriously as chess masters).

My dad had an article about Monopoly published in 1973 - http://www.unz.org/Pub/SaturdayRev-1973mar24-00044

Including probabilities per space, and expected return per dollar invested.

If you like this kind of stuff, here is an analysis of Chutes and Ladders http://www.datagenetics.com/blog/november12011/index.html

And another about Candyland http://www.datagenetics.com/blog/december12011/index.html

Anyone for Battleship? http://www.datagenetics.com/blog/december32011/index.html

Or Hangman? http://www.datagenetics.com/blog/april12012/index.html

Or Darts? http://www.datagenetics.com/blog/january12012/index.html

It's a hobby of mine to analyze these kind of games. Suggestions for other games to look at welcome.

(Smiles) Ah, memories of high school in 1985: writing an Apple II program to find the odds of landing on each Monopoly property, a bit surprised that (IIRC) the orange & green blocks were visited with unusual frequency.

Was thinking of a similar analysis last week when playing a simplified "kids'" version of Monopoly.

me too, my friend. Apple IIc in my case. Monte Carlo methods worked wonders for a teen who didn't know about Markov Chains and stationary distributions.

Ha... me and my friends would always play by house rules, and start out with a ridiculous amt of money (we even created more money with paper if the bank ran out), so there was no question we would buy every single property we landed in.

This is great and all, but I suspect many readers will have the same response as I: that as a 10-year-old I'd figured out the best-value spaces just by the jail and Go To Jail placements alone, along with the higher rents and bonus chance cards for some properties over others for the same building cost. It's great for someone to run the figures, but if you didn't know what the answers were largely going to be you're a terrible gameplayer and analyst of your environment!

Here's a problem for you, fellow algorithmists: http://projecteuler.net/problem=84

I have a Lisp solution to this that I wrote some years ago when I was going through Project Euler problems. https://github.com/2old2randr/Euler/blob/master/monopoly.lis...

Gah! He's using horrible US street names! Mayfair et al please! Does anyone have a translation table?

Monopoly board images:

https://www.google.com/search?q=monopoly+board&safe=off&rlz=...

Weird how this shows up today. I played Monopoly over the weekend and we were discussing the same thing!

A bit off-topic: Please note that we have much better boardgames than Monopoly these days. Have a look at boardgamegeek.com for some suggestions. Carcassone is a good beginners game.

Much to the chagrin of the BGG crowd, Settlers of Catan is a much better gateway boardgame. It's easy to learn and it has a lot of social interaction. I'd also recommend Ticket to Ride as the second-best gateway boardgame. I love Carcassone, but it's not nearly as intuitive on the first couple of playthroughs, and the scoring at the end is more than tedious.

I've generally had the opposite experience. Carcassone is simpler, and a player can generally play competently on their first game.

Catan, on the other hand, I've found difficult to teach, despite the rules being fairly obvious to me, and there's lots of edge-case rules. (I had one friend get fairly pissed at me that I didn't describe, at the beginning of the game, the rule that a new settlement can break a longest road, which is a rule that hardly ever comes up)

Edit: That said, Catan probably is a better gateway game into European-style board games in general, since it uses many of the same concepts.

Ticket to Ride would probably be my top pick now, though, for a gateway game.

Have you played Trains yet? I think that may be one of my new go-to games with new people. It's like Dominion but a lot less abstract.

Oh, Settlers of Catan is also fine. I just mentioned Carcassone as the first gateway game that came to mind.

I don't really play Settlers anymore these days. It's nearly twenty years old; the first decade was fun, but it does get old after a while. There are also a few things that a modern game would do different---but beginners will enjoy themselves very much.

I think the enduring popularity of Monopoly etc is the nostaglia factor and the ease of inter-generational play... it's quite ubiquitous and perhaps only behind Trival Pursuit in terms of "family" games.

How does that compare to Settler's of Catan?

In my opinion, Carcassone is generally simpler and friendlier.

The rules are fairly quick to pick up (although, as another commenter mentioned, scoring at the end can be a bit tedious).

Also, in a couple playgroups I've seen, Settler's of Catan can have as much, if not more, conflict than Monopoly. In Carcassone, you can't really take very aggressive action against other players.

> In Carcassone, you can't really take very aggressive action against other players.

You are playing it wrong. ;o) Carcassone, in my player groups, has much more direct conflict than Settlers of Catan.

Monopoly is almost devoid of direct conflict. At least of conflict you can have any influence one. Your hotels are targetting all players equally.

This needs some charts!