Without further ado, here it is (note that there are several variations not covered by the example, but they are accounted for in my calculations).  I leave it to the reader to figure out what they all are, or of course you can just message me:

Player 1, Turn 1:

Rolls 5,5 -> just visiting ($1500 liquid)
Rolls 6,6 -> Chance -> advances to nearest utility and purchases it ($1425 liquid)
Rolls 5,4 -> purchases park place ($1075 liquid**)

Player 2, turn 1:

Rolls 3,1 -> pays 10% income tax ($1350)

Player 1, Turn 2:

Rolls 1,1 -> purchases boardwalk ($675 liquid)
Rolls 2,1 -> com chest -> Bank error in your favor +200 ($1075 liquid)

Player 1 builds three houses on Boardwalk, two houses on Park Place ($75 liquid)

Player 2, Turn 2:

2,1 -> Advanced to Boardwalk (GAME OVER)

** Note that my definition of “liquid” includes mortgage value of Water Works as well as cash. It does NOT include mortgage value of park place and boardwalk, since we need to build on them.
__________________________________________________

According to my calculations, the probability of any seven-roll game of monopoly occuring (assuming that it can only be done with PP and BW) is to follow. BIG PROPS TO BLUE MONSTER for finding a way to make seven rolls work with the oranges!!! New post to follow:

(1/36)*(1/36)*(1/16)*(1/9)*(1/18)*(1/36)*[(1/18)*(1/8)*(1/18)*(1/15) + (1/9)*(2/15)*(1/18)*(1/14)]

+

(1/36)*(1/36)*(1/16)*(1/9)*(1/9)*(1/36)*[(1/18)*(1/8)*(1/18)*(1/15) + (1/9)*(2/15)*(1/18)*(1/14)]

+

(1/36)*(1/36)*(1/16)*(1/9)*(1/18)*(1/36)*[(1/18)*(1/8)*(1/18)*(1/15) + (1/9)*(1/15)*(1/18)*(1/14)]

+

(1/36)*(1/36)*(1/16)*(1/9)*(1/9)*(1/36)*[(1/18)*(1/8)*(1/18)*(1/15) + (1/9)*(1/15)*(1/18)*(1/14)]

+

(1/36)*(1/36)*(1/16)*(1/9)*(1/6)*(1/15)*(1/36)*[(1/18)*(1/8)*(1/18)*(1/14) + (1/9)*(1/7)*(1/18)*(1/13)]

+

(1/36)*(1/36)*(1/16)*(1/9)*(1/6)*(1/15)*(1/36)*[(1/18)*(1/8)*(1/18)*(1/14) + (1/9)*(1/14)*(1/18)*(1/13)]

+

(1/36)*(1/36)*(1/16)*(1/9)*(1/6)*(2/15)*(1/36)*[(1/18)*(1/8)*(1/6)*(1/14) + (1/9)*(1/7)*(1/6)*(1/13)]

+

(1/36)*(1/36)*(1/16)*(1/9)*(1/6)*(2/15)*(1/36)*[(1/18)*(1/8)*(1/6)*(1/14) + (1/9)*(1/14)*(1/6)*(1/13)]

+

(1/36)*(1/36)*(1/16)*(1/9)*(1/6)*(1/15)*(1/36)*[(1/18)*(1/8)*(1/36)*(1/14) + (1/9)*(1/7)*(1/36)*(1/13)]

+

(1/36)*(1/36)*(1/16)*(1/9)*(1/6)*(1/15)*(1/36)*[(1/18)*(1/8)*(1/36)*(1/14) + (1/9)*(1/14)*(1/36)*(1/13)]

+

(1/6)*(1/16)*(1/36)*(1/18)*(1/15)*(1/36)*(1/14)*(1/16)*(1/36)*(1/18)*(1/13)*(1/18)

+

(1/6)*(1/16)*(1/36)*(1/18)*(1/15)*(1/36)*(1/14)*(1/36)*(1/13)*(1/16)*(1/18)*(1/18)

~=

 So a bit better than 185 billion to 1. 

PS – I would like to give a special thanks to my best friend and fellow Monopoly nerd, Stephen Priester, for helping me point out the “sneaky” first move possibility for player two of rolling a seven and going back three!!  “The problem is dead, Jim.”

Player 1, Move 1: 

Rolls 1,1 -> Bank Error in Your Favor +200 (1700)
Rolls 6,6 -> Buy Virginia (1540)
Rolls 5,3 -> Advance to St. Charles / Purchase (1600)

Player 2, Move 1: 

Rolls 4,3 -> Get Out of Jail Free Card

Player 1, Move 2: 

Rolls 1,1 -> Buy States (1460)
 Rolls 4,3 -> Free Parking
 Builds hotels on St. Charles and Viginia and 4 houses on States (60)

Player 2, Move 2: 

Rolls 2,2 -> -750 (750)
Rolls 2,1 -> -900  (GAME OVER)

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…