What's the probability of an endless Monopoly game? (simulating 1.000.000 games in Python) - zigjogos.com

# What’s the probability of an endless Monopoly game? (simulating 1.000.000 games in Python)

Games Computers Play
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Monopoly is known to have a nasty tendency of getting endless. I have built a Python simulator that will uncover whether it is really so – and what factors are at play here. 5 different experiments, 1000000 games simulated, multiple graphs plotted, ppt slides created.

(Spoiler: it is actually rather low, if you play the game the right way).

Souce code:
As always, sorry it’s messy.

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1. Thekingoflorda Games says:

was that rimworld running in the background?

2. Tiler says:

It's a shame you can't run the simulations with auctions

Auctioning off properties that someone can't or chooses not to buy speeds the game up so much. Incidentally, ignoring the standard rules is what makes games take so long. I know from when I was younger that introducing more money into the game economy feels like it's more fun, but you're really just dragging out the game. Monopoly isn't supposed to be fun. It's not supposed to feel fair.

Let's say I'm winning. Let's also say I land on Boardwalk (unowned), and I own Park Place. I easily have \$400 to buy it, but I choose to pass on it anyway. Why? Because I know you only have \$24 in front of you, so I can get Boardwalk for dirt cheap if I auction it off. Is it fair? Not really. But the game was designed to show how poor our economic system is. The rich get richer, and the only way the poor survive is from literal handouts like Free Parking from house rules. If you play monopoly by the standard rules, you have a much more manageable game length on your hands.

Though if I might make a recommendation, play a version where money is kept track of electronically. Paper money slows the game down too

3. Sir_ComA says:

Monopoly can't be endless. Eventually people get feed up and make awful trades to end the game quickly. Or both are too stubborn and the board gets flipped or something.
In any case, human nature will attempt to prevent this shitty game from continuing.

4. Dragon Brendan says:

Could you simulate the computer playing risk and see how good it gets? Also quality video

5. Nohri says:

Monopoly games often do reach an end, but the final stretch to that end is very drawn out, when people just run around until eventually one player gets enough bad rolls

6. Cheesy Lizzy says:

A few years ago my lil sister Joy and I decided to play Monopoly using our My Little Pony plushies.
5 hours later Rarity, Rainbow Dash, and Applejack were bankrupt. Fluttershy had so many monopolies and Twilight was just doing her best to survive and hope Fluttershy lands on one of her few remaining spaces. And Pinkie Pie had miraculously never landed on a single property throughout the course of the game. My sister and I had no idea how to explain it, Pinkie Pie would always land on chance, tax, free parking, jail, pass go, literally anything except property spaces, and she kept it up the whole time! Because of this she gained and lost very little money and her total stayed around \$1,500 the whole time, she may as well have not played at all for how much she contributed to the game! Unfortunately we didn't get to see how long Pinkie's weird luck would last as our mom made us put away the game after 5 hours. We declared Fluttershy the winner and Twilight 2nd place even though she had less money than Pinkie, because at least Twilight actually contributed to the economy.

Final results for anyone curious:
1. Fluttershy
2. Twilight
3. Pinkie
4. Applejack
5. Rainbow Dash
6. Rarity
Rarity had some really terrible luck early on and had a very dramatic breakdown.

7. Huxley Leigh says:

You could implement some rudimentary scheming in trading:

If one was to make a property trade
that benefits the other Player more than you (eg: you have already got 1 of the colour you need and they have 2) then the trade shouldn't go through.

And of course people are less likely to trade with people who are richer than them

8. Benjamin Anderson says:

Saying a game that reaches 1000 or even 10000 turns is endless is like saying that rolling two dice 10000 times and never getting a 12 means you'll never get a 12. Surely you'll get one eventually, you've just gotten unlucky so far.

9. electriKal_ shoK says:

wait, monopoly games can end?

10. Roger Cruz says:

In Brazil we have "banco imobiliário", it's a rip off that changes names of properties

11. Lockrime says:

Ngl, we practically never traded for monopoly because it usually just was too dangerous.

12. Aarantula says:

Hello, saw this in my recommendations and watching to help it in the algorithm. Love videos like this.

13. Mark Hendryx says:

Since you brought up Civilization…I have long dreamed of a Civ V simulator that would predict the optimal starting strategy through some limited timeframe or until some early stage goal (e.g. 30 turns or fewest turns to build Petra). Obviously, a full simulator that could deal with optimal settling locations, warring opponents, etc. is not feasible. However, I am hopeful that you could reduce the scope of the simulation to make it technically viable, but still have relevant/applicable learnings. One way to do this would be to consider one player in a vacuum (no opponents, no barbarians, no city expansions) with an already settled city. In this scenario, the only choices to make are your building queue (likely limited to buildings, workers, or fishing boats), research queue, cultural policies, and what tiles to improve. The fitness of each build strategy could be evaluated by adding up the total science, culture, gold, faith, production, food, etc and choosing the strategy with the highest overall output. The relative weightings of science, culture, gold… may have to be tweaked in order to make sure the optimal solution predicts a strategy that best positions the player for success. We could also use this simulator to study simple questions like "Is a food or production trade route the most effective way to build a new city?".

14. Ben Prather says:

1) The common Free Parking house rule adds much more money to the game than your proposed increase in salary. This makes games endless, barring spiteful trades to become a kingmaker as you spiral out of the game.

2) Suppose you have multiple monopolies, and are building houses. Which should be your preference? My gut says Blue > Orange > ??? > Red > Green. There are 8! permutations of preferences. Which is the best?

3) With a \$500 start, it might be interesting to revisit the value of not buying properties in your other video.

15. RipleySawzen says:

Why would people trade? Clearly trading puts one person at a disadvantage compared to another (unless it's in desperation). Your evidence actually proves this. So I think not trading is completely reasonable, at least for 2 players.

16. Joshua Wenninger says:

How are there still endless games when trading is allowed?

17. Arman Aryan says:

honestly i kinda hate monopoly its not very fun imo

18. Cool Taylor says:

Bankrupcy handled by the bank ruins the game.

Property of a bankrupt player is supposed to go to their creditor. Im sure you'd find less endless games using that rule.

19. Gelatin says:

It’s a paradox. There is an infinitely small chance that a monopoly game would be endless. The more turns you go through, the smaller the likelihood that the game is endless gets. This is because at any turn a sequence of events that could end the game could happen; The odds of that never happening get smaller and smaller as the game goes on because all previous turns must also have not ended the game.

20. Steven Cow-Meat says:

U should try having an AI play monopoly against a bot

21. Étourdie says:

The one house rule I think would guarantee that the game will end is the one where you get to build houses on any property you own, regardless of whether or not you have the Monopoly

22. Mj1343 says:

Business 2000 looks a lot snazzier than monopoly. I’d be down to play something like that

23. The Hint says:

Are you playing with an infinite bank?

24. Wandering Bishop says:

Came for monopoly-based math, but now I'm really interested in trying that Business 2000 game.

25. E Stolee says:

The two rules you changed may not seem like that big of a deal at first glance, but they would have drastically changed your results had you kept them in. Strong players being able to buy off auctioned properties from a bankrupt player saves a tremendous amount of time.

26. Whitequill Riclo says:

There is another thing that would keep the game from being endless which is that there are only 30 of each bill.
30 ones,
30 fives,
30 tens,
30 twenties,
30 fifties,
30 one-hundreds,
30 five-hundreds

a grand total of \$15,140.
There is always some strategy in what denominations you have even if the rules aren't followed correctly.

27. ZeldaFreak says:

There is a lot to improve.
House rules are that thing that makes games long. As a child I played with house rules and games went on for days. A rule around free parking is interesting. This brings more money into the system. I've played it that 2k (the game where 10k is the highest note) goes into the middle and everything that the bank usually would collect, goes into the middle. There is no money that leaves the board.

Also tactics can change. Usually a player wants to buy at least one street of every color. A player can be more willing to trade properties with no option for houses. You don't want to give a other player a property where he can build a house on. Also you don't want someone with a lot of money to give the option to get more money.

Let's not forget that this is a game for the family. Kids usually are not intelligent enough to master the game and parents don't want to destroy the child and want to extend the game, so no clear winner will be there.

There is a lot of possibilities. I think I can program such a simulator. It would be a nice small project. I may even try to implement an AI to the game. AI is something I didn't done yet and is something I won't do at work.

28. Lydia Spire says:

Do my eyes decieve me? Is that a 999: 9 Hours, 9 Persons, 9 Doors reference?

29. The Golden Stalfos says:

as someone who made a whole video about how to win monopoly I found this rather fascinating however the exclusion of auctions greatly increases the chances of a game running long or endlessly. auctions can reduce the cost of territories and speed up territory acquisition. in the official rules a property once landed on is always either purchased or auctioned removing this means that some areas will not be taken on first landing. this not only makes monopolies harder but gives each player fewer titles to trade. it's also worth noting that in the base game bankrupt players give their property to the player who they owed too much money to this creates a snowball effect which can speed up games although snowball effects are often viewed as unfun/unfair they do shorten games and I feel like you would get shorter results if you included these mechanics. however I do recognize that these may be too difficult/time-consuming to program for this video and don't hold it against you in any way I just feel that this may bias the results.

30. Red X says:

No simulation of the free parking rule?

31. Benjamin Burnett says:

YOU GREW UP WHERE?

32. Raresh C. says:

I think that auctions make the game way more difficult. this is probably a variable that might change most results since the person with the least amount of money cannot bid and you end up selling indigo for 10 monopoly each.

33. chettha javanapong says:

In Thailand เกมเศรษฐี, there’s a card that just said you’re bankrupted ถังแตก so the probability of game going endless is 0%

34. jcb3393 says:

6:18 50-60 turns is more like 9-10 laps around the board. If the average die roll is 7 and the length of a lap is 40, then you will complete 1 lap approx every 5.7 turns. (This, of course, does not account for the effects of chance and community chest cards sending you to other locations – including "Go" – which would complete a lap faster. It also does not account for the "go to jail" space and cards, which slow your progress in completing a lap.)
With a lap completed every 5 or 6 turns, 50-60 turns is about 10 laps.

35. esotericVideos says:

The biggest thing that keeps Monopoly going is people who have house rules that say you get money on free parking.

36. jasonbail says:

just print more money so no one goes bankrupt and you have an infinite monopoly oh wait that's just MMT

37. Pining for the fjords says:

I would have thought that Monopoly would have been actively encouraged in the Soviet Union. Monopoly is basically designed to highlight the failures of capitalism.

38. Jeff Power says:

How do you trade? In my family, wed put conditions on the trades. For example, if were trading and I think your monopoly is worth more than mine, Ill ask for some cash to 'sweeten the deal'. Usually enough to stop them from building too much until they hit go again

39. Qermaq says:

Wish you checked the Free Parking reward. This is a popular house rule that just stretches the game out insanely. If you're unfamiliar, it goes like this:

When landing on the Luxury or Income Tax space, or when drawing a Chance or Community Chest card, if a player is directed to pay money to the Bank, they would instead put this money in the center of the board.

Of course, if the card awards money to the player, that still comes from the bank or the other players accordingly, and any other costs, such as paying \$50 to get out of Jail, also go to the Bank.

Whenever a player lands on Free Parking by exact dice roll, they collect whatever money is in the center of the board.

Consider the assessor card or the property tax card….

40. Toby Hall says:

Absolutely love this. Thank you

41. Thomas Lindner says:

I need to agree with other comments.

Auctions and the transfer of all assets of a bankrupt player to the player that needs to be paid, are the two factors, that make the game quick and basically impossible to go forever. It will have a definite winner.

The third “rule” to speed up games and make clear winners is the limitation on how many houses and hotels are available. They are limited and who builds last might not build at all.

The game is tedious, because people don’t play by the rules.

Implement all rules and your outcomes will differ dramatically.

42. Sehnsucht says:

Interesting that the USSR made their own Monopoly. Monopoly was originally known as the Landlord's Game and is supposed to show how capitalism inevitably leads to monopolies. I would've thought they'd have liked to keep the original.
Also: no auction rule is normally why it lasts so long. It's supposed to be quick and high intensity.

43. Ranibow Sprimkle says:

Numbers don't have double decimal points, please stop with using decimal points as commas

44. J Lyf says:

Love the science, but philosophy solves the problem quickly. An endless game of Monopoly is impossible because there will be an eventual heat death of the universe. Assuming that never comes the players will eventually die. if it is simulated power will eventually be lost. It cannot last forever.

45. RupertMDoc says:

Its difficult for me to imagine Monopoly (without house rules) actually ending in a stalemate. Having a reasonable monopoly and building houses on is so powerful that competent players will find deals to make that happen. That may involve a 2-1 trade (balanced with a of money), or an interim trade to grab 2 of a kind first, but the player or two who figure it out will be light years better than those who do not.

46. Eidenhoek says:

I thought it was ideal to only get 3 hourses, and to mortgage if necessary to build up the monopoly that's 6,8,9 from the jail.

47. Yoni Yakub says:

Awesome and well done video! Have you ever experimented with machine learning/ai (tensorflow) to make playable bots?

48. gdrgsgdgdfsfgrgdfh says:

wait…. CAN YOU TRADR CARDS ?! I PLAYED WRONG ALL MY LIFE!

49. Rainbow says:

Okay, so, I'm not really that much into board games, but I have multiple friends who are and I've even watched them play on occasion, and their bad opinion of Monopoly has less to do with the lenght a single game can be, and more to do with the simplicity and chance factor of it. To put it simply, there's very few things one can actually do differently while playing Monopoly, and unless you're employing some sort of fancy strategy (and even then, really), chance determines practically all you'll be able to do with dice rolls and cards. There's just many alternatives that are designed way better and are actually more entertaining to play. The only things Monopoly has going for it is that it's very easy to play for vast majority of people, and pretty much everyone who lives in places where monopoly made cultural impact knows about it, and, well… if you're into more fancy and obscure board games, you're already dealing with the fact that most people that aren't probably won't want to play with you anyways, especially if they have to spend time learning how to.

While I didn't read all the comments, I saw a couple of people referencing roots of Monopoly as a criticism of capitalism, but none of them seemed to mention the part of the story that honestly struck me the most when I read about it some time ago – the version of Monopoly Hasbro will sell you isn't how the game was originally designed, they modified it to be more fair in order to sell it as a family game. In the original, each player started with different amount of money, with one played having significantly more than all the others, to basically represent bourgeoisie, and to make a point about how you already own property, means of production, or just money (all of which are often inherited), you have infinitely bigger chances at making it in the capitalist system. It is still rather basic stuff, but a lot of people actually have trouble grasping stuff like this unless it affects them directly and/or because they can't see the full picture, so a small scale simulation like this that you can experience and fully grasp actually seems like a rather useful tool for education. Of course, it's a shame that the original intention behind creation of the game is mostly not remembered, but you have to admit that taking a criticism of capitalism and transforming into a product to be sold by capitalists has to be one of the most capitalist things that can happen.

Since this comic ended up becoming much more of a wall of text than I intended, have a "joke" – the only truly endless thing about Monopoly is the number of different versions they make. (most people don't realize just how many of those are, not only is there pretty big chance that any relatively known francise that you can think of will have a Monopoly version made after it, there's also a bunch of really obscure regional editions that most people won't be able to know about).

I hope you don't get discouraged from all the comments trying to "well, actually" the endless thing. There's probably some people who were genuinely well meaning, but… well, there has to be a large degree of ignorance to assume you meant '*actually* endless' when it's pretty clear you were going for 'practically endless', or to just think that you, as a person who programmed and ran all those simulations, didn't know of limitations or potential problems with this method of determining things when you very clearly know what you are doing. The video is very good and despite some complications when it comes to different rules people use, you did a very good job getting the answer to the question stated.

Also, while I don't know if we had Business 2000 here in Poland, a bootleg Monopoly I got from my family that is from the ""communism"" times is Eurobusiness, though I don't know if it was something specific to Soviet-controlled parts of the Europe, or if it was just a European verson of Monopoly that found its way here at some point.

50. Dethneko says:

The two major house rules I've always known in Monopoly, and didn't even know were house rules until years later is the Free Parking money and the ability to bypass houses and go straight to hotels.

The Free Parking money works by sending all money that should be paid to the bank from things like Chance, Community chest, and spaces on the board like Luxury Tax into the middle of the board, to be paid out to the next person to land on Free Parking. Really doesn't matter who gets that money, if the influx is high enough they're probably going to win the game, or else the Free Parking money just aids in the game becoming endless.

Bypassing houses and going straight to hotels works by having enough cash to buy all the houses necessary to build a hotel AND the money for the hotel(s) themselves. If there's only 4 houses in the bank then you need enough to buy 12 houses and 2 hotels at least to build 4 houses on one property and two hotels on the other two. Except, as kids, I'm not sure we knew all properties needed houses (and they had to be spread out evenly) before hotels could be built, I didn't learn that until the Monopoly game on the NES. Slightly less problematic, this one, as this tended to make the game end much quicker, only going "endless" if enough high traffic squares were controlled by enough different players that money kept changing hands. On the other hand, if that many houses were already on the board, with enough people having enough money to buy straight to hotels, feels like we should already have been in endless territory.