The Shortest Possible Game of Monopoly (2010) (opens in new tab)

You don’t even need that second roll. If, in that auction, a player bids more than the cash they have, they go bankrupt immediately (https://www.hasbro.com/common/instruct/monins.pdf doesn’t say such bids are disallowed, and does say “The buyer pays the Bank the amount of the bid in cash” and “You are declared bankrupt if you owe more than you can pay either to another player or to the Bank.”)

This can happen after the first player rolled a double, so the first player’s turn doesn’t even have to be over for a player to go bankrupt.

You’d be surprised how few people know about the rule for auctioning property that is not purchased. I’m guessing most people learned to play without reading the actual rules. It’s just passed down by copying the actions of your older siblings.

I think the idea is that this is the shortest game where the loser makes no mistakes. The four turn game in TFA has the loser making no decisions whatsoever.

Of course it ignores the auction rule, but it could be amended to say the loser buys each auctioned property for a dollar (or whatever amount.) The only decisions the loser makes in this case are their bid prices which are irrelevant. The outcome is the same.

Edit: Actually it's a bit more complicated than this, as buying all of the auctioned properties and mortgaging them would give Player 2 enough money to afford the rent on Boardwalk. Player 1 would have to bid close to the mortgage price for each property. That way if they win the auction they can mortgage it to get their money back to afford houses, and if they lose the auction it doesn't help Player 2 afford rent on Boardwalk.

This isn't right. After turn 1, player 2 has say $200 worth of assets (depending on what they buy). They can mortgage that for $100. Then they need to pay 10% income tax on their assets ($20). No problem.

You would pay 10% of your wealth for income tax, so you could always mortgage your one property and pay the 10% of the mortgage value.

Well played! And this strategy is actually easy to execute.

The probability for executing this strategy is: P(3)+P(5)+P(6)+P(8)+P(9)+P(11)+P(12) * P(4).

Plug in the numbers from https://statweb.stanford.edu/~susan/courses/s60/split/node65...

(0.0556+0.1111+0.1389+0.1389+0.1111+0.0556+0.278)*0.0833 = 0.07407036

So 7.4%.

Wait... if you land on a property and don’t buy it it goes to auction where other players can bid (and start a bidding war)? My childhood has been shattered.

whaaat? I never knew there were auctions if another player didn't purchase. does it occur when a player doesn't have the money to purchase yet too?

the fandom wikipedia page says "Interestingly, this is one of the most-often overlooked aspects of the game." ya don't say.

The only memories of playing monopoly I have are with family.

I hope that’s not the same for you

Many years ago I was at a church singles retreat, and someone suggested playing Monopoly. At 11:30 at night. With an early worship service scheduled the next morning.

A couple of people groaned about the late hour and how long the game would take.

So I suggested some simple rule changes that make for a faster game.

The pastor's daughter said "we can't do that." She pulled out the Monopoly rules, pointed to the relevant chapter and verse, and said "Look. It Is Written."

People drifted off to do other things or just call it a night.

In hindsight, maybe I should have gone along with her literal interpretation of the rules. After everyone else gave up, it would have been just her and me playing until the wee hours. That might have been nice!

My favorite variation included these rules:

1 - Double 1s or double 6s: steal any property from any player. 2 - you can build on any property you own. You’re not forced to build evenly and you’re not forced to own a monopoly on that color.

A 2 player game would last an hour, maybe 2 tops. 4 player still took some time but was still fun and exciting :P

Also, with these rules the balance of the game shifted. BW/PP are good, but not the best. Utilities and railroads are pretty lame. The winning properties seemed to me to be, from best to less best: Orange, Red, Pink, Yellow, Green. Orange and red because they’re properties most likely to be landed on after leaving jail. :)

No one is required to purchase during an auction, everyone could pass.

Simply insert in the directions in the appropriate places "...put the property up for auction and everyone passes immediately."

That's when you sneeze or find some other reason to bump the table hard enough to lose the places of all of the pieces. "Ooops, I guess we'll have to pick this game up later"

For families I recommend Monopoly Deal since the games are quicker and the theme is similar.

I played that version, for real. The lawyers got all the money and now everybody in the family hates each other. It took years.

No doubles just means the player rolls again after resolving the action.

Incoming complaints about how it's obviously tool-assisted

The comments of the article are full of people coming up with ways to play entirely rationally and still end the game in 8 moves, they're worth reading.

There's nothing irrational about this. Choosing not to buy properties is not irrational. Choosing to buy Park Place and Boardwalk and then put houses on it as soon as possible is not irrational. In fact, my strategy when I play is to get a color set as quick as possible while saving my money by buying as few other properties as possible, then spending all that money on houses/hotels for those few properties I have.

I also agree but it’s still _possible_ in theory

The specific sequence of rolls has 5 doubles (which can only occur one way) and 4 unequal pairs (which can occur two ways). Each double has a 1/36 chance of happening while the unequal pairs have a 1/18 chance. So that's 1/36^5 * 1/18^4 = 1/6,347,497,291,776 or about 1.5 times ten to the minus thirteen.

It's interesting that the last four digits of the denominator of the probability of the shortest game of Monopoly are 1776. I'm sure that has some kind of cosmic significance.

0 in practice, who decides to buy nothing? And even if player one declines to buy, player two can buy it via the auction.

If we say it’s nine rolls of two dice, and the probability of getting any particular pair of numbers in each roll is 1/36 (underestimate since we sometimes only care about the sum), then getting any specified sequence would be like (1/36)^9, around 1e-14. Of course then we’d have to get the gameplay right too

A breadth first search?

You most likely weren't following all the rules. Monopoly shouldn't take more than about 45 minutes of game play if you follow all the rules.

For once: very apt username :) And congratulations. Not sure if I would have the patience for that.

Because your understanding is wrong. The game uses 2 dice.

lol we find the person with the worst monopoly family rules of all time

You can't roll doubles to get another roll with a single die

Added above. Thanks!