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This video claims that the fastest game of monopoly involves 4 turns and 9 rolls of the dice. I am wondering if this is actually the shortest game or can we do better in theory? What is the probability of this game happening in real life?

https://www.youtube.com/watch?v=gHJkTz6Ej3U

For reference, the moves in the above video are as follows:

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 favour, 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

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    $\begingroup$ What version of monopoly? The UK version? The US version? $\endgroup$ – Daniil May 25 at 11:09
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    $\begingroup$ No idea if that is the shortest game but I would have said the probability for that game is 96/(36 ^ 9) * 1/(16 ^ 2) which is 96 / 25999348907114496 or one in 271 trillion - based on i.stack.imgur.com/7MP4F.png $\endgroup$ – Martin Smith May 25 at 12:00
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    $\begingroup$ I think the video answers it all, this link agrees: scatter.wordpress.com/2010/05/30/… $\endgroup$ – Daniil May 25 at 13:13
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    $\begingroup$ Can you provide a short summary of the moves in the video? If the video gets taken down or something, future users won’t be able to view it. $\endgroup$ – boboquack May 25 at 13:58
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    $\begingroup$ o.O I'm puzzled by the rules applied here! Are these the official ones? We always did it like that: no buying until you passed Go once. Buying houses only if you're sitting on your own street. Only one house at the time. Well, it seems I just learned, why Monopoly always took us hours and hours ^^ $\endgroup$ – Jessica May 26 at 15:24
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If you are trying to lose the game as quickly as possible then you can do it in 1 turn and 2 rolls of the dice. This is using the UK version as I'm not sure about the US one.

Roll 1:

You get a double 3 (a six) which lands you on The Angel, Islington. You don't buy this but put it up for auction. You then go up to M1500 in the auction.

Roll 2 (Because of the doubles):

You roll 11 and this takes you to the community chest. Out of these you need to get Pay a M10 fine or take a chance card. You need to choose the chance card then you need the Pay school fees of M150. You will not be able to pay this as you have no money and your assets can only mortgage to give you M50. Your opponent wins the game.

The chance of this is:

Getting double 3s: 1 in 36
Getting the right community chest card: 1 in 16
Getting the right chance card: 1 in 16
Getting an 11: 1 in 18

So the total is: 1 in 165888 or 0.0006028% (which is a lot more likely that the example Dmitry Kamenetsky gave

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  • $\begingroup$ I think you can get more likely (but no shorter) by rolling a double six to land on Electric Co,, doing the same action, and then a 10 to land directly on chance, bypassing the Community Chest. $\endgroup$ – DJClayworth May 25 at 19:37
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    $\begingroup$ I think the video shows a game where the other player isn't intentionally trying to lose, which makes for a somewhat more complex puzzle. $\endgroup$ – Bass May 25 at 20:49
  • $\begingroup$ Here is another version of intentionally trying to lose, found by Robert Manning: www2.stetson.edu/~efriedma/mathmagic/1112.html $\endgroup$ – Dmitry Kamenetsky May 26 at 1:39
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    $\begingroup$ the chance aspect of this is complicated — what is the chance of the selling price being $1500? (Probably not very high) $\endgroup$ – JDL May 26 at 8:17
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    $\begingroup$ @NuclearWang: It was an illegal action so it was rolled back like any illegal action. $\endgroup$ – Joshua May 26 at 20:01
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No, the game given in the OP is not the shortest possible Monopoly game (using the American edition). As with the UK edition solution given by William Pennanti, a two-player game can be lost in a single turn with two rolls of the dice:

Player 1, turn 1, roll 1:

The player starts with \$1500 and rolls a 3 and a 3, advancing to Oriental Avenue. The player declines to buy the property outright and so it goes up for auction. The bidding ends with Player 1 buying the property for \$1500, leaving them with \$0.

Player 1, turn 1, roll 2:

The player rolls a 5 and a 6, advancing to Community Chest. The player draws the "Pay hopsital \$100" card. The player is bankrupt because they have no money, and even mortgaging Oriental Avenue for \$50 would not be enough to pay the fee.

The probability of this game:

Rolling 3–3: 1 in 36
Rolling an 11: 1 in 18
Drawing the right Community Chest card: 1 in 16
Total: 1 in 10,368, or 0.00964506…%

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  • $\begingroup$ It doesn’t have to be only that community chest card - it can be any with a cost > 50. Are there any others? That could change the probability. $\endgroup$ – Tim May 27 at 9:28
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A two player game can be lost in a single dice roll. As long as the first player lands on a deeded property on their first roll, they can allow the property to go up for auction. Now they just have to bid more money than they have, and their own bid will force them into bankruptcy. Game over.

This can happen so long as the first player lands on a property that can be bought on their first turn, which excludes rolls of 2, 4, 7, and 10, which have a combined probability of 13/36. Therefore, the first player can bankrupt themselves on their first roll in 23/36 cases (63.8% of the time).

See: https://boardgames.stackexchange.com/questions/39455/in-monopoly-what-happens-if-the-auction-winner-cannot-pay-his-her-bid

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    $\begingroup$ Is it possible to bid more than you have?! $\endgroup$ – Dmitry Kamenetsky May 26 at 14:18
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    $\begingroup$ @DmitryKamenetsky There's nothing that would prevent it - you just incur a debt that you cannot afford to pay, just like any other way of going bankrupt. In practice, the only way to prevent this would be to have each player calculate their total worth before each auction in order to set an upper limit for each player, which would be awfully cumbersome, and isn't mentioned anywhere in the rules. $\endgroup$ – Nuclear Wang May 26 at 14:25
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    $\begingroup$ This isn't the only way to prevent it. In practice people manage to play monopoly all the time without bankrupting themselves. It is only necessary to perform the cumbersome "exact" calculation if you are bidding something close to your net worth. Otherwise it just needs a cursory rough check $\endgroup$ – Martin Smith May 26 at 14:52
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    $\begingroup$ @MartinSmith regardless, it sounds like the rules do not prevent it, and do not allow for backing out of a bid once made. $\endgroup$ – Ben Barden May 26 at 15:40
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Technically, the shortest Monopoly game can be achieved with

ZERO rolls

by simply

forfeiting the game before even starting to cast the dice.

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  • $\begingroup$ Best answer so far. I wonder if you can go with less turns hmm... $\endgroup$ – Yanko May 27 at 10:33
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In the https://scatter.wordpress.com/2010/05/30/the-shortest-possible-game-of-monopoly-21-seconds/ someone found a faster way that doesn't use auctioning (or other non-playing scenarios):

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
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