I’ve been in plenty of Monopoly games that dragged on for hours, with one or two bankrupt players sitting on the sidelines, bored to death. But a few intrepid gamers decided to figure out the shortest theoretically possible Monopoly game. Their solution is explained here and depicted in the video below. While extremely unlikely, it’s theoretically possible that it could happen. It takes only nine rolls of the dice.
But what’s more interesting is this comment thread in which several other Monopoly theoreticians propose slightly shorter games — several eight-roll versions and even one seven-roll game. There’s also a two-roll solution that involves a strategy known as “insane auctioning” which seems even more unlikely (since it involves a player making remarkably stupid choices when buying properties), but hey, it’s theoretically possible so I say it’s valid. There is also, of course, a theoretical “shortest game” in which one player simply defaults (typically by throwing the board across the room). That requires no rolls and is thus mathematically optimal. But let’s be civil.
Anyway, here’s the 9-move, 21-second game that started the discussion. Behold the nerdiness!
(Via Metafilter, which has its own awesomely nerdy comment thread.)
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The odds of getting the correct dice rolls (which don’t necessarily have to be the exact rolls set out in the video, as some allow more than one combination) is about 19.5 billion to one.
There are 16 Chance cards, so the odds of getting the right card is 16 to one, making the odds of being able to play the 21-second game about 313.5 billion to one. And that requires both players to make the “right” choices.
posted by Jon. on 6-16-2010 at 1:31 pm
Whoops, I missed one of the cards – so multiply that last number by 16! (A little over 5 trillion to one.)
posted by Jon. on 6-16-2010 at 1:46 pm
There’s some more math on this (and an additional solution video) here: http://monopolynerd.wordpress.com/
posted by Chris Higgins on 6-16-2010 at 1:48 pm
Holy friggin crap!!!!!!!!!!!!!
posted by J.S. on 6-16-2010 at 4:53 pm
Jon, that also considers that the players are moving fast enough to hit the 21-second mark, which is also unlikely.
posted by Eli on 6-16-2010 at 10:37 pm
Never Tell Me the Odds!!
posted by Jonathan on 6-16-2010 at 11:52 pm
i feel like a nerd watching this :P
posted by cassy on 6-17-2010 at 12:37 am
@cassy – I feel like a nerd for laughing at this!
posted by Edward Jensen on 6-17-2010 at 1:58 am