OK, since no one is posting, you get to endure another Monopoly post!
After our recent attempt to play the shortest actual game of Monopoly on record, we started to wonder about what the shortest THEORETICALLY POSSIBLE game of Monopoly would be. That is, if everything went just the right way, with just the right sequence of rolls, Chance and Community Chest cards, and so on, what is the quickest way one player could go bankrupt? After working on the problem for a while, we boiled it down to a 4-turn (2 per player), 9 roll (including doubles) game. Detail on each move given below. If executed quickly enough, this theoretical game can be played in 21 seconds (see video below).
Player 1, Turn 1:
Roll: 6-6, Lands on: Electric Company
Action: None, Doubles therefore roll again
Roll: 6-6, Lands on: Illinois Avenue
Action: None, Doubles therefore roll again
Roll: 4-5, Lands on: Community Chest “Bank error in your favor, Collect $200”
Action: Collects $200 (now has $1700)
Player 2, Turn 1:
Roll: 2-2, Lands on: Income Tax
Action: Pay $200 (now has $1300), Doubles therefore rolls again
Roll: 5-6, Lands on: Pennsylvania Rail Road
Action: None
Player 1, Turn 2:
Roll: 2-2, Lands on: Park Place
Action: Purchase ($350, now has $1350), Doubles therefore rolls again
Roll: 1-1, Lands on: Boardwalk
Action: Purchase ($400, now has $950), Doubles therefore rolls again
Roll: 3-1, Lands on Baltic Avenue
Action: Collect $200 for passing GO (now has $1150), Purchase 3 houses for Boardwalk, 2 for Park Place ($1000, now has $150)
Player 2, Turn 2:
Roll: 3-4, Lands on: Chance, “Advance to Boardwalk”
Action: Advance to Boardwalk, Rent is $1400, only has $1300 = Bankrupt
GAME OVER
scatterplot 
Hmm. I thought, “Come on, Dan! Clearly this can be shortened.” But, lo, I cannot see how.
I look forward to the shortest possible game of Risk.
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Official Monopoly rules:
“If he does not wish to buy the MONOPOLY property it is sold at auction by the Banker to the highest bidder.”
The following properties were landed on and went unpurchased and didn’t go through an auction either (which is a rule violation):
Winning Player:
Electric Company
Illinois Avenue
Baltic Avenue
Loosing Player
Pensylvania Railroad
What the looser purchases is irrelevant since he is destined to go bankrupt anyway…
But the winning player would have either
spent some of his money, and therefore wouldn’t be able to afford the houses to bankrupt player 2
or
they would have had an auction which would have taken up more time.
If you want to be stupid about it… which they already were since the players weren’t buying valid properties… I can legally bankrupt player 2 on his first role, and accomplish it in 5 seconds (I didn’t make a video, but I did it).
Player 1: rolls a 1:2, lands on Baltic avenue, doesn’t want it, declares auction. Player two offers $1450 for it. Player 1 declines, player 2 tosses the cash and gets the card, and now has only $50.
Player 2 roles a 1:1 and lands on community chest “Pay School Tax: $150” Player 2 bankrupt. Game over… legally.
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Several people have pointed out this auctioning thing, but it’s not right. Someone doesn’t HAVE to buy it. All players can refuse to bid. The property goes unsold. We didn’t bid. Auction over. The wild auctioning have been taken up previously as well–and I think that is completely valid. Likewise, someone else pointed out an even shorter, completely legal, strategy on another blog which is that one player just immediately quits! Nothing in the rule preventing that!
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One optional rule of monopoly is that no player may purchase properties until passing Go. This is a common rule at my house.
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(Although, when you write this up for publication, I think the proper move for Player 2 is to pay the 10% rather than the $200 on Income Tax, even though it isn’t enough to save her/him.)
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You are absolutely correct about the income tax. I can’t believe we missed that after everything we went through to get it down to this point. And, while there are obviously other ways to do this in the same number of rolls, I also can’t think of how to get it shorter than this. Risk, Parcheesi, Life, Candyland…the possibilities are endless…
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Two things – actually, current Monopoly boards have the income tax as $200 – 10% is not an option. Second, when you land on an unowned property, “none” isn’t a realistic action. If the player who lands on a property chooses to not buy it, the property goes up for auction (if, of course, you’re playing by the rules). While it *is* possible that no one would buy the property, even for a $1, I don’t think it’s very likely. If we’re going to consider unrealistic possibilities, consider this:
Player 1, Turn 1:
Player rolls anything that lands them onto a property. Doesn’t buy it – it auctions. Both players bid until Player 2 bids $1,500. P2 gets the propert.
Player 2, Turn 1:
Player 2 rolls and lands on Income Tax (on a current board) and has to pay $200. Game over.
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Very good! I’m definitely going to remember your strategy the next time I want to get out of a Monopoly game quickly!
Using insane auctioning, I think I can do you one better though: Player 1 rolls double 4s–landing on Vermont–declines to buy and auctioning begins. Since you can bid on a property you declined to buy, the auctioning continues and Player 1 ends up buying Vermont for $1500. Then the second roll based on doubles is a 4-5, community chest and its any card where you have to pay. Player 1 is bankrupt and Player 2 never even had a turn!
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I also think you can do the same thing without landing on any actual properties, thus eliminating auctioning:
P1: 5-5 Jail, 6-6 Chance, 5-6 Community Chest
P2: 5-5 Jail, 4-3 Comm Chest (pay 150)
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@blue monster
You Player 1 bankruptcy isn’t realistic (as unrealistic as this all is). The auctioning doesn’t begin until the landing player opts to *not* buy the property.
Why then, would this player decide to purchase it within the auction process for a much more expensive price.
Although, I guess he could be trying to get it for cheaper (doesn’t buy it, and Player 2 is only willing to risk $1 on the purchase, so Player 1 gets it for $2).
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@walesmd – It *is* possible. I’ve let stuff go to auction thinking I could shave a few bucks off when another player decides to drive the price up. Now, it is *unlikely* that the price would get driven up to $1,500… ;)
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The hidden assumption here is that the rules are being followed. In my family it was perfectly possible to have games of Monopoly that ran a good deal shorter than 21 seconds given the propensity of some players to steal all your money or turn the board upside down or throw your top hat down the stairs. To be honest I’d always thought the real purpose of Monopoly was not so much to be a proper board game but rather to serve as a focus for sibling conflict.
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Indeed. The quickest game I ever played was the one where I caught my brother hiding a couple of $500 bills under his corner of the board before the game even started!
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The real purpose of Monopoly is to gauge the temperament of a potential boyfriend/girlfriend/spouse. After playing the game once with said person, you may not wish to continue the relationship.
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Without insane auctioning, but by allowing P2 to purchase a property, you can do a bit better:
P1,T1
(same as above; 3 turns)
P2,T1
3-4 -> Chance -> Advance to Illinois
Action: Purchase Illinois (-$240, but effective -$120 because of ability to mortgage: total: $1380)
P1,T2
2-2 Park Place, purchase
6-4 Chance (+$200 for passing GO), advance to Boardwalk, purchase property and houses
P2,T2
6-6 Chance
Action: Pay $50 to each player (total $1330)
1-2 Boardwalk; GAME
8 turns instead of the above 9
Cool post.
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Brilliant! I doff my cap to you, sir!
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Faster perhaps. But less likely. Four and a half times less likely than the 9 move version… (once every 1,184,866,161,131,520.00 trials)
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Well, roll #7 is completely irrelevant as long as it’s a double in the 2-2 to 6-6 range; and the Chance card doesn’t matter. I guess that was just icing, because P2 is already low enough on cash before hitting that final chance.
Still, even considering that, it’s less likely.
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Here’s another way that takes only 8 moves and two turns per player, and does not require Boardwalk and Park Place. In fact, neither player touches the fourth side of the board. Also, there are no insane auctions, and Player 2 does not get to make any decisions at all about buying property.
Player 1, Turn 1:
1-1 -> Community Chest, Bank Error in Your Favor, collect $200 (Player 1 now at $1700). Doubles, so roll again.
5-3 -> Visiting Jail.
Player 2, Turn 1:
3-1 -> Income Tax, Pay $200 (Player 2 now at $1300, or $1350 if 10% of assets ($150) is allowed as in the older games – it really doesn’t matter).
Player 1, Turn 2:
3-3 -> St. James Place, Buy for $180 (Player 1 now at $1520). Doubles, so roll again.
1-1 -> Tennessee Avenue, Buy for $180 (Player 1 now at $1340). Doubles, so roll again.
3-1 -> Chance, Go Back 3 Spaces -> New York Avenue, Buy for $200 (Player 1 now at $1140).
At the end of his turn, Player 1 puts 4 houses on St. James Place ($400), 3 houses on Tennessee Avenue ($300), and 4 houses on New York Avenue ($400), for a total cost of $1100 (Player 1 now at $40 cash on hand).
Player 2, Turn 2:
6-6 -> St. James Place, with 4 houses is $750 (Player 2 now at $550 or $600, depending on the income tax square). Doubles, so roll again.
2-1 -> New York Avenue, with 4 houses is $800.
GAME.
There are several variations to this sequence of events that ultimately produce the same result. Player 1’s first turn could be land on Community Chest, get Advance to Go Collect $200, then get a 6-4 to visit jail. Or, after obtaining $200 from Community Chest via bank error or going to go, visiting jail could be reached by doubles (4-4 in my original scenario or 5-5 in the alternate scenario). In this case, a 4-2 or 5-1 gets St. James on Player 1’s first turn, and he/she simply buys Tennessee Avenue and New York Avenue via the same rolls and methods as listed above in his/her second turn.
And yes, I spent way too much time figuring this all out. Oh well, I really enjoyed thinking about it – excellent idea for a post!
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This is elegant insofar as it gets to the end in 8 moves without requiring any bad decisions either in prospect or retrospect by the losing player.
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Gorgeous solution! I love it!
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This certainly looks like the most elegant solution. The proviso in all the fast games is that people are actually suicidal: not keeping any capital for further property purchases.
That early in the game it’s unlikely, but in later stages of the game improving your properties in the hope of a windfall is decidedly more prevalent. Especially if you’ve got a few squares that are going to bankrupt you anyway, and there is nothing left to buy except houses.
One interesting tactic is for two players deciding not to build hotels. That can lead to a shortage of houses, blocking those further behind in development from buying any – you have a finite number of houses in the set. Well worth it when you’re against the in-laws.
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Thought you might like to know that this is now linked on MetaFilter: http://www.metafilter.com/92602/There-can-be-only-one
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Since I’m sure you were curious about the odds of this particular game taking place if we allow one to get, e.g the 7 in P2T2 any which way (one in 6 rolls), and taking chance as 1 in 16, then 1 in 15 (there are 16 chance cards), it’s:
1/36*36*9*16*36*18*36*36*18*6*15. That’s once every 253,899,891,671,040 games. (once in every 250 trillion games or so)
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See now, this is the kind of serious, important content that can be derived from something a frivolous as the original post!
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So this leads to the question of what is the total probability (_all_ the ways) that P1 could defeat P2 without P2 having any choice in the matter (i.e., without the option to buy any properties, etc.).
Which would be a much harder question to answer.
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thank you for the number crunching it makes it seem even more surreal
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In addition to the people commenting about the land auction rules above, I also remember a rule that you couldn’t actually buy property until you went around the board once. It could be that this was a house rule, but my memory is telling me otherwise.
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To my knowledge, that is an common house rue, but it is not part of the official monopoly rules: http://www.hasbro.com/common/instruct/monins.pdf
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Even in your own example, the second roll of player 2, turn 1 is unnecessary. The first roll can be 1-3 instead of 2-2, thereby ending the turn since it isn’t a double. And on player 2’s second turn, s/he can still land on Chance and be directed to Boardwalk.
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For more realism in your example, so that no properties go unpurchased: player 1, turn 1, roll 1 could be 5-5, placing them on visiting Jail. Roll 2 could be 6-6, placing them on Chance (doesn’t really matter what card they get as long as it doesn’t move them backwards or cost them too much). Roll 3 could be 5-6, still placing them on Community Chest.
Player 2, turn 1, roll 1 would then be 1-3, ending their turn.
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Don’t forget you can only buy houses/hotels at the beginning of your turn; not in the middle of doubles.
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Not correct. Per official rules, you can buy houses and hotels at any time *except* during another player’s turn. So, anytime during your own turn or in between the turns of other players.
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well, per the rules we’re both wrong http://www.hasbro.com/common/instruct/monins.pdf
HOUSES… When you own all the properties in a color-group you
may buy houses from the Bank and erect them on those properties.
If you buy one house, you may put it on any one of those
properties. The next house you buy must be erected on one of the
unimproved properties of this or any other complete color-group you
may own.
The price you must pay the Bank for each house is shown on your
Title Deed card for the property on which you erect the house.
The owner still collects double rent from an opponent who lands on
the unimproved properties of his/her complete color-group.
Following the above rules, you may buy and erect at any time as
many houses as your judgement and financial standing will allow.
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I found a 7-roll solution!
P1:
5,5 -> just visiting
6,6 -> adv to nearest utility (1350)
5,4 -> buy park place (1000)
P2:
3,1 -> income tax (1350)
P1:
1,1 -> buy boardwalk (600)
2,1 -> Bank error +200 (1000)
Three houses on Boardwalk, Two houses on Park Place (0)
P2:
2,1 -> Advanced to Boardwalk (GAME OVER)
I also found a solution involving the light purples in eight rolls (see my blog here on wordpress)!
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http://monopolynerd.wordpress.com
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Following up on this excellent work by Monopoly Nerds, we came up with a couple of other 7-roll games.
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great game that is simply amazing….
http://www.snyxius.com
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great post man
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Hey guys! Monopoly nerd here…just wanted to mention that I’m thinking of developing a series of blog posts on Monopoly statistics and strategy (and maybe even eventually a book).
To help generate these numbers and probabilities, I am also working on a Monopoly simulator. Hopefully it will eventually be able to help solve some of the more interesting problems we have come up with. :)
Check out my most recent post. It’s just the tip of the ice burg, but it’s a start. http://monopolynerd.wordpress.com
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Here’s how to calculate the shortest game of Chutes and ladders http://www.datagenetics.com/blog/november12011/index.html
Here’s Candyland http://www.datagenetics.com/blog/december12011/index.html
Battleship http://www.datagenetics.com/blog/december32011/index.html
Hangman http://www.datagenetics.com/blog/april12012/index.html
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My brother and I were just discussing this, we googled “shortest possible monopoly game” and found this. I think I can do four rounds/eight rolls.
Player 1:
1-1: Community Chest. Bank Error in your favor +$200 ($1700)
5-3: Just visiting.
Player 2:
6-4: Just visiting.
Player 3:
3-3: Buys St James Place -$180 ($1520)
1-1: Buys Tennessee -$180 ($1340)
1-3: Chance. Go back 3 spaces Buys New York -$200 ($1140)
Buys 11 houses (4 on St. James, 3 on Tennessee, 4 on New York)
Player 2:
3-3: St James. Pays $750.
1-2: New York. Pays $800.
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Shorter Game (2 rounds, 5 rolls):
Round 1:
Player 1 lands on Baltic. Refuses to buy. It goes to auction. Player 2 buys it for ALL his/her money.
Player 2 lands on Baltic.
Round 2:
Player 1 rolls snake-eyes, lands on Reading Railroad, buys it.
Player 1 rolls again (because of the doubles), lands on Pennsylvania Railroad, buys it.
Player 2 lands on Reading, but has no money, and the mortgage value of Baltic is less than the $50 he/she owes.
Game over, player 1 wins.
Player two played very stupidly, of course, but the rules were followed, and nobody quit.
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Your article is easy to understand, simple communication is accessible to most people. I will keep track of your posts regularly
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My shortest possible game of Monopoly is also my longest possible game of Monopoly, which is zero seconds, because Monopoly is a terrible game and no one should ever play it under any circumstances.
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My one roll solution:
Player 1 rolls 3, 5, 6, 8, 9, 11, or 12.
Player 1 says they don’t want the property and it goes up for auction.
Player 2 bids $1,500 and wins the auction.
Player 1 buys the property from Player 2 for $1 and then mortgages it.
Player 1 sells the property to player 2 for $1.
Player 2 after coming into possession of the property can’t afford to pay the 10% interest on the mortgage and goes bankrupt.
Player 1 wins.
Odds of this game happening are 23/36. The odds are actually better when you consider if Player 1 lands on Chance (a 1/6 chance), there are six chance cards that will send them to a property.
You might be asking why someone would pay $1,500 for a property? The same could be asked why someone would land on an unowned property and not bid at least a $1? The answer to both is, they’re trying to play the shortest game of Monopoly.
My biggest question is, why would a respectable news outlet like NPR report on this story without first having a someone read the Monopoly rules.
And yes, I’m still annoyed by this twelve years later.
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I can say that for the MonopolyNerd, 7-roll variation, the assumption is that players are acting reasonably.
After all, I can give a 0-roll solution and say that player 2 resigns after player 1’s first roll.
That all said, I’ll be thinking about your analysis for cooperative shortest game.
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