Fastest Theoretical Game!

Welcome to the Monopoly Nerd’s Blog!

This blog has been inspired by another blog post I came across claiming to have found the fastest theoretical game of Monopoly (assuming that the dice fall just right and that there are no crazy auctions done, etc). 

The post to which I refer can be found here:  http://scatter.wordpress.com/2010/05/30/the-shortest-possible-game-of-monopoly-21-seconds/

In short, their proposal involves one player getting to Park Place and Boardwalk as quickly as possible (doubles), building three houses on Boardwalk (and two on Park Place), and then the second player getting an “Advance to Boardwalk” chance card to get knocked out of the game (they have also already landed on Income Tax to put them under 1400 bucks).

Not too bad, huh?  Well, given that I am the nerd that I am, it got me thinking about whether I could improve on it…

I quickly realized what, I am sure, the creator of the game did years and years ago:  by design, it is difficult for one player to obtain a monopoly in a short period of time.  Specifically, if you look at all of the three-property monopolies on the board, you will notice that two of the three will always be on adjacent spaces.

This ensures that it is IMPOSSIBLE to purchase all three properties of a given color set in one go-round of the board (since rolling a “1” is impossible with two dice). 

That leaves the two exceptions to the rule to look for the answer:  the dark purples (also sometimes brown these days) and the dark blues.  We can quickly eliminate the dark purples from contention, since they quite simply don’t do enough damage (worst case 450 hit to the bankroll) and since you need to rotate around the board once just to land on Medditeranean (again back to the not being able to roll a “1”)!

This leaves Park Place and Boardwalk, which appears to be the solution afterall.  Or does it??

Any long-time Monopoly player knows very well of perhaps THE most shocking and painful way to lose a monopoly game:  the “go back three” card.

But first, let’s recreate the mindset and atmosphere of being in the middle of an all-out Monopoly battle.  You have hotels on the light purples and are neck-to-neck with your best friend, who has hotels on the oranges.  Unfortunately, it is your turn to roll, and you HATE where you are sitting:  St. Charles Place!! 

You pray to the monopoly gods for a safe roll and NOT for a 5, 7, or 8!  You close your eyes and roll the dice and wait for the cheers from your best friend, but instead, you simply here the “click click click” of your piece being moved!  You are relived upon opening your eyes to find a “6” and “5” on the dice; you did it!!!

You begin to greedily hope for your opponent to land on your hotel on Virginia but WAIT!  Your best friend is suddenly jumping up and down and laughing in your face (perhaps it’s time to find a new friend)!

You stare at the orange chance card but can’t believe what you see:  “GO BACK THREE SPACES”!  You watch in horror as your piece retreats to New York Avenue:  GAME OVER!

This point is this:  the only property that can be landed on as a result of “go back three” is New York Avenue, which just happens to be next to Tenessee.  And since the chance space is so close to the oranges, it is theoretically possible to obtain all three oranges (or land on all three oranges in the worst case scenario) within one turn!

To be honest, before I had a chance to look further into the idea of perhaps bankrupting an opponent with the oranges, I game across the following reply to the proposed “shortest game”:

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.

I am also looking into whether something can be done with the reds (advanced to Illinois).  We shall see…  🙂

About krusta80

I am a lover of mathematics, statistics, and games! Monopoly is the perfect storm of all of these, so I naturally I love Monopoly. :)
This entry was posted in Statistics and Analysis and tagged . Bookmark the permalink.

9 Responses to Fastest Theoretical Game!

  1. subgalea says:

    About buying the three oranges: I published that as a sequence of puzzles in 2003. I am pretty confident you will not find a way to buy all three reds from the bank in one of your own turns.

    If you like Monopoly minutiae, figure out, under the strictest reading of the rules, what card can send you to jail, other than “Go To Jail?” I’ll put the answer in my blog.

  2. John M. Hoyt says:

    Hahahah I love this =)

  3. A_Nonamus says:

    There’s a shorter, cleaner version of the orange color group “shortest game”, involving only seven rolls of the dice in two full turns, with neither player required to gain or lose money other than buying property and paying rent.

    Player 1, Turn 1:
    6-4 -> Just Visiting

    Player 2, Turn 1:
    6-4 -> Just Visiting

    Player 1, Turn 2:
    3-3 -> St. James Place, Buy for $180 (Player 1 now at $1320). Doubles, so roll again.
    1-1 -> Tennessee Avenue, Buy for $180 (Player 1 now at $1140). Doubles, so roll again.
    3-1 -> Chance, Go Back 3 Spaces -> New York Avenue, Buy for $200 (Player 1 now at $940).
    At the end of his turn, Player 1 puts 3 houses on St. James Place ($400), 3 houses on Tennessee Avenue ($300), and 3 houses on New York Avenue ($300), for a total cost of $900 (Player 1 now at $40 cash on hand).

    Player 2, Turn 2:
    6-6 -> St. James Place with 3 houses, rent is $550 (Player 2 now at $950).
    Per the rules, a player may buy and/or sell houses between moves of other players. Having sufficient cash now on hand, Player 1 interrupts Player 2’s turn, paying $400 to upgrade Tennessee and St. James to 4 houses each and New York Ave. to a hotel.
    Player 2 rolled Doubles, so he rolls again.
    2-1 -> New York Avenue with hotel, rent is $1000. Bankrupt.

    • krusta80 says:

      Very nice, and thanks for pointing out one of the less-known rules of Monopoly (for the casual player anyway): a player may buy houses at ANY time, except between a player’s roll and his/her moving the piece to the rolled-upon property. This is the key to your elegant strategy, and it is very nice indeed.

      PS – Might wanna fix your player 2’s second roll to 3-3. 🙂

  4. Lori Dalrymple says:

    I’m kind of making a Christmas present for my Dad. I am using a computer game of Monopoly. I’ve been keeping stats since I started on October 23. I have played about 20 games of different and same varieties. I am playing against the computer. I’m showing my Dad how when I changed strategies, I improved or lowered my chances of winning. I am missing data to give to him. With the Monopoly rules as printed, what is the statistics of winning against a 2 player, 3 player, or 4 player game? I just wondered if it was straight 50%, 33%, 25%. On an interesting note when I changed a variable of making Free Parking to $500 my odds of winning went down. At $250 my odds of winning went up. At $0 my odds of winning was between the odds of $500 and $250. Just thought that note might interest you.

    • krusta80 says:

      Hey there, Lori! I’m sorry for taking so long to get back to you. I think it’s great that you’ve taken such an interest in the odds and probabilities behind Monopoly. I’m sure that your dad will appreciate all of the time and effort too when Christmas comes!

      That said, it’s important to keep in mind that just like other games involving chance, each Monopoly game’s winner is highly dependent on luck.

      I’m not sure if you’ve had a chance to take a look at my Monopoly simulator yet, but please do if you get the chance. But remember this: every time the simulator is run, a computer plays out literally 10,000 games of Monopoly to figure out the odds of winning! And even the numbers that the computer comes up with need to be taken with a grain of salt, because they are assuming that no trades are being made.

      Part of what makes Monopoly such a great game is that there are so many little things that can change the game’s outcome. Some of these things (like trading or building strategy) we have control over, but the most critical parts of the game are impossible to predict (the dice and cards in the middle or even our opponents’ decisions).

      I would love to give you the perfect statistics of winning for 2, 3, or 4 players, but I’m not sure that exact percentages can even be calculated without taking the players into account. BUT, if you assume that every player is equally skilled and follows the same strategy, your question becomes a little easier to answer.

      If, for example, all players agree to never trade with each other for the entire game, the percentages of winning can be found here on my blog! See my post about the importance of going first in Monopoly for the actual numbers. Of course it would be silly to play Monopoly without trading — after all that’s the best part of the game — but no matter what strategies are used, going first in Monopoly definitely helps. This is because if you go first, you have the first chance at getting properties, whereas the people behind you have a higher chance of landing on a property that you already bought. So the numbers are very close to 50% for 2 players and 33% for three players, but they get a little more skewed as the number of players increases.

      You were asking about putting money on Free Parking, and that’s a fun way to change the game up of course. BUT, there really is no significant impact on the winner of the game. There is, however, an impact on how long the game takes to finish! This is because the goal of Monopoly is to bankrupt your opponents, but if they can get an extra $500 of $1500 by landing on Free Parking, it will take longer to bankrupt them.

      I hope my reply isn’t too long and drawn out, but it’s important to keep in mind that trying different strategies and determining which is best requires a lot more than 20 or even 50 games. 🙂

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