# A simple simulation of the board game "Monopoly"

### History

NOTE: this paragraph is an excerpt
Slightly inebriated one night at Mark and Mel's back porch, our conversation swayed to the topic of the old board game Monopoly. It was theorized that night, that certain spaces on the board had a statistically higher chance of being landed on than others. This, of course, begs the question whether every space had a fixed probability of being landed on. A brute force calculation of this lead to a very, very large factor of branching, and the conversation quickly moved on to other things. So I am at home one evening and decided to try and figure this out, not by writing a program to do all the branching (this is especially hard because of the Chance and Community Chest cards), but by writing a simulation of a game of Monopoly. This simulation is simple: one person playing monopoly, takes turns, rolls dice, moves spaces. The spaces that are landed on are recorded. Chance and Community Chest cards are accounted for in the movement. The results of my simulation was too long to send as an email to a distribution list and too long to fit in a paragraph on my homepage, so they are here instead, on a page dedicated to the Monopoly simulation.

I'll apologize ahead of time for any gross errors I've made in the simulation, since I didn't have a Monopoly game set handy. In fact, it was surprisingly hard to find an official set of rules online, or even something that told me what the spaces were and what the cards were. It was much easier to find the source code for a monopoly game from the 80s written in GW Basic and just sift through it to get all the relevant information that I needed to write this simple program. There was no information about the author in the code, or any copyright notice in the program or on the website that I found the code, so I have nothing to use as an official reference.

### The Program

Being a java programmer, along with the incredible ease of use and versatility of the language, this simulation is naturally written in Java. Before you OO people start sending me email flames, let it be known the original program was only 10 lines. The results of this 10 line program was disappointing. No matter how many turns I take, the board distribution was almost steadily the same; uniform. Thus, the program got bigger, I had to add objects, I had to add more code, and ultimately, I was too lazy to make it look nice.

So now the program fairly accurately simulated a one man game of Monopoly. I could run a few thousand tests and look at some results. There's no way I would subject any of you to look over megabytes of results (if I was a little smarter, and a little less lazy, I'd stick them into a database, but alas, I am neither), so you can take this program and run it yourself to your hearts content. HERE is where you can find it.

### The Results

First, let's take a look at a typical game. Although games that I've played usually ended in arguing or the throwing of the board pieces, or even the board itself, I'd guess a typical game would take 100 turns per person. I'd like to make clear that the turns does not include having to "roll" your way out of Jail or the skipping of turns if you were in Jail. The turns in this simulation only involve movement. I'd also like to point out that, given the rules that come with the game, there is no way another person's move can directly affect where you move next. It can, however, affect your movement when your opponent(s) use Chance or Community Chest cards that alter their movement that would otherwise have altered your movement. So here is a 100 turn game:
```

GO collect \$200              = 4
Mediterreanian Ave [purple]  = 1
Community Chest 1            = 4
Baltic Ave         [purple]  = 2
INCOME TAX                   = 2
Oriental Ave       [cyan]    = 3
Chance 1                     = 1
Vermont Ave        [cyan]    = 3
Connecticut Ave    [cyan]    = 3
Jail                         = 4
St. Charles Place  [magenta] = 3
Electic Company    (Utility) = 2
States Ave         [magenta] = 2
Virginia Ave       [magenta] = 4
Pennsylvania RR     < RR >   = 4
St James Place     [orange]  = 0
Community Chest 2            = 4
Tennessee Ave      [orange]  = 4
New York Ave       [orange]  = 2
Free Parking                 = 3
Kentucky Ave       [red]     = 2
Chance 2                     = 4
Indiana Ave        [red]     = 1
Illinois Ave       [red]     = 2
B&O Railroad        < RR >   = 2
Atlantic Ave       [yellow]  = 4
Ventnor Ave        [yellow]  = 4
Water Works        (Utility) = 2
Marvin Gardens     [yellow]  = 3
GO TO JAIL                   = 2
Pacific Ave        [green]   = 2
North Carolina Ave [green]   = 4
Community Chest 3            = 1
Pennsylvania Ave   [green]   = 3
Short Line RR       < RR >   = 2
Chance 3                     = 2
Park Place         [blue]    = 3
LUXURY TAX                   = 0
Boardwalk          [blue]    = 2

Properties:
purple  = 3
cyan    = 9
magenta = 9
orange  = 6
red     = 5
yellow  = 11
green   = 9
blue    = 5
RR      = 11
Utility = 4
chance  = 7
chest   = 9
fucked  = 4

The board was traversed a total of 18 times

Rolls: (2)=4 (3)=9 (4)=8 (5)=12 (6)=12 (7)=13 (8)=11 (9)=8 (10)=12 (11)=4 (12)=7

```
This is the output of the Monopoly.java program. The first table shows how many times each space on the board was landed on (there are 40 spaces in all). The second table shows a summary of properties that have been landed on, including railroads, the 2 utilities, chance and community chest, and finally "fucked", which consists of paying income tax, going to jail, and paying luxury tax. The number of times a board was traversed is the times I've gone past GO. The rolls, is a summary of all the dice rolls (the total of the 2 die) I had in the game. You can see that the yellow properties gets landed on the most, whereas the purple and blue get landed on the least.

Say there are 3 other people playing with you, this can be their moves:

```

GO collect \$200              = 2
Mediterreanian Ave [purple]  = 2
Community Chest 1            = 3
Baltic Ave         [purple]  = 1
INCOME TAX                   = 3
Oriental Ave       [cyan]    = 2
Chance 1                     = 2
Vermont Ave        [cyan]    = 3
Connecticut Ave    [cyan]    = 2
Jail                         = 2
St. Charles Place  [magenta] = 2
Electic Company    (Utility) = 5
States Ave         [magenta] = 4
Virginia Ave       [magenta] = 4
Pennsylvania RR     < RR >   = 4
St James Place     [orange]  = 0
Community Chest 2            = 2
Tennessee Ave      [orange]  = 1
New York Ave       [orange]  = 5
Free Parking                 = 2
Kentucky Ave       [red]     = 2
Chance 2                     = 5
Indiana Ave        [red]     = 4
Illinois Ave       [red]     = 2
B&O Railroad        < RR >   = 1
Atlantic Ave       [yellow]  = 2
Ventnor Ave        [yellow]  = 2
Water Works        (Utility) = 5
Marvin Gardens     [yellow]  = 4
GO TO JAIL                   = 2
Pacific Ave        [green]   = 5
North Carolina Ave [green]   = 0
Community Chest 3            = 3
Pennsylvania Ave   [green]   = 1
Short Line RR       < RR >   = 1
Chance 3                     = 0
Park Place         [blue]    = 1
LUXURY TAX                   = 7
Boardwalk          [blue]    = 3

Properties:
purple  = 3
cyan    = 7
magenta = 10
orange  = 6
red     = 8
yellow  = 8
green   = 6
blue    = 4
RR      = 9
Utility = 10
chance  = 7
chest   = 8
fucked  = 12

The board was traversed a total of 17 times

Rolls: (2)=5 (3)=8 (4)=11 (5)=10 (6)=8 (7)=26 (8)=10 (9)=12 (10)=7 (11)=1 (12)=2

GO collect \$200              = 4
Mediterreanian Ave [purple]  = 1
Community Chest 1            = 2
Baltic Ave         [purple]  = 2
INCOME TAX                   = 3
Oriental Ave       [cyan]    = 3
Chance 1                     = 6
Vermont Ave        [cyan]    = 1
Connecticut Ave    [cyan]    = 1
Jail                         = 4
St. Charles Place  [magenta] = 2
Electic Company    (Utility) = 5
States Ave         [magenta] = 1
Virginia Ave       [magenta] = 1
Pennsylvania RR     < RR >   = 2
St James Place     [orange]  = 1
Community Chest 2            = 8
Tennessee Ave      [orange]  = 4
New York Ave       [orange]  = 1
Free Parking                 = 4
Kentucky Ave       [red]     = 0
Chance 2                     = 2
Indiana Ave        [red]     = 2
Illinois Ave       [red]     = 2
B&O Railroad        < RR >   = 1
Atlantic Ave       [yellow]  = 5
Ventnor Ave        [yellow]  = 5
Water Works        (Utility) = 5
Marvin Gardens     [yellow]  = 2
GO TO JAIL                   = 2
Pacific Ave        [green]   = 1
North Carolina Ave [green]   = 2
Community Chest 3            = 3
Pennsylvania Ave   [green]   = 2
Short Line RR       < RR >   = 5
Chance 3                     = 4
Park Place         [blue]    = 1
LUXURY TAX                   = 2
Boardwalk          [blue]    = 3

Properties:
purple  = 3
cyan    = 5
magenta = 4
orange  = 6
red     = 4
yellow  = 12
green   = 5
blue    = 4
RR      = 10
Utility = 10
chance  = 12
chest   = 13
fucked  = 7

The board was traversed a total of 19 times

Rolls: (2)=3 (3)=3 (4)=4 (5)=10 (6)=15 (7)=20 (8)=13 (9)=14 (10)=16 (11)=1 (12)=1

GO collect \$200              = 2
Mediterreanian Ave [purple]  = 2
Community Chest 1            = 3
Baltic Ave         [purple]  = 2
INCOME TAX                   = 6
Oriental Ave       [cyan]    = 3
Chance 1                     = 2
Vermont Ave        [cyan]    = 2
Connecticut Ave    [cyan]    = 2
Jail                         = 6
St. Charles Place  [magenta] = 0
Electic Company    (Utility) = 5
States Ave         [magenta] = 1
Virginia Ave       [magenta] = 1
Pennsylvania RR     < RR >   = 5
St James Place     [orange]  = 3
Community Chest 2            = 2
Tennessee Ave      [orange]  = 3
New York Ave       [orange]  = 5
Free Parking                 = 1
Kentucky Ave       [red]     = 2
Chance 2                     = 4
Indiana Ave        [red]     = 2
Illinois Ave       [red]     = 6
B&O Railroad        < RR >   = 4
Atlantic Ave       [yellow]  = 3
Ventnor Ave        [yellow]  = 4
Water Works        (Utility) = 0
Marvin Gardens     [yellow]  = 3
GO TO JAIL                   = 2
Pacific Ave        [green]   = 2
North Carolina Ave [green]   = 2
Community Chest 3            = 1
Pennsylvania Ave   [green]   = 5
Short Line RR       < RR >   = 1
Chance 3                     = 4
Park Place         [blue]    = 2
LUXURY TAX                   = 1
Boardwalk          [blue]    = 2

Properties:
purple  = 4
cyan    = 7
magenta = 2
orange  = 11
red     = 10
yellow  = 10
green   = 9
blue    = 4
RR      = 11
Utility = 5
chance  = 10
chest   = 6
fucked  = 9

The board was traversed a total of 18 times

Rolls: (2)=5 (3)=7 (4)=5 (5)=5 (6)=16 (7)=11 (8)=9 (9)=11 (10)=18 (11)=9 (12)=4

```
Already you can see where most of the action is just by looking at the properties summary: yellow and the railroads. These numbers by no means can indicate a possible winner, or a possible loser; it only shows the number of times spaces have been landed on. If we were to combine the 4 players property summaries, we would have this:
```purple  = 13
cyan    = 28
magenta = 29
orange  = 29
red     = 27
yellow  = 41
green   = 29
blue    = 17
RR      = 41
Utility = 29
chance  = 34
chest   = 36
fucked  = 32

```
To get larger samples for our results, instead of combining 500+ players taking 100 turns, we'll just have 1 player take a LOT more turns. So lets look at a few 1000 turn games:
```

GO collect \$200              = 23
Mediterreanian Ave [purple]  = 19
Community Chest 1            = 15
Baltic Ave         [purple]  = 24
INCOME TAX                   = 22
Oriental Ave       [cyan]    = 18
Chance 1                     = 23
Vermont Ave        [cyan]    = 20
Connecticut Ave    [cyan]    = 25
Jail                         = 37
St. Charles Place  [magenta] = 24
Electic Company    (Utility) = 19
States Ave         [magenta] = 27
Virginia Ave       [magenta] = 25
Pennsylvania RR     < RR >   = 35
St James Place     [orange]  = 29
Community Chest 2            = 25
Tennessee Ave      [orange]  = 31
New York Ave       [orange]  = 21
Free Parking                 = 26
Kentucky Ave       [red]     = 33
Chance 2                     = 23
Indiana Ave        [red]     = 31
Illinois Ave       [red]     = 30
B&O Railroad        < RR >   = 32
Atlantic Ave       [yellow]  = 30
Ventnor Ave        [yellow]  = 28
Water Works        (Utility) = 25
Marvin Gardens     [yellow]  = 24
GO TO JAIL                   = 26
Pacific Ave        [green]   = 31
North Carolina Ave [green]   = 31
Community Chest 3            = 23
Pennsylvania Ave   [green]   = 25
Short Line RR       < RR >   = 30
Chance 3                     = 21
Park Place         [blue]    = 24
LUXURY TAX                   = 26
Boardwalk          [blue]    = 32

Properties:
purple  = 43
cyan    = 63
magenta = 76
orange  = 81
red     = 94
yellow  = 82
green   = 87
blue    = 56
RR      = 125
Utility = 44
chance  = 67
chest   = 63
fucked  = 74

The board was traversed a total of 174 times

Rolls: (2)=24 (3)=64 (4)=89 (5)=109 (6)=147 (7)=161 (8)=139 (9)=96 (10)=89 (11)=56 (12)=26

GO collect \$200              = 40
Mediterreanian Ave [purple]  = 20
Community Chest 1            = 18
Baltic Ave         [purple]  = 19
INCOME TAX                   = 25
Oriental Ave       [cyan]    = 19
Chance 1                     = 26
Vermont Ave        [cyan]    = 22
Connecticut Ave    [cyan]    = 26
Jail                         = 25
St. Charles Place  [magenta] = 28
Electic Company    (Utility) = 21
States Ave         [magenta] = 29
Virginia Ave       [magenta] = 28
Pennsylvania RR     < RR >   = 29
St James Place     [orange]  = 26
Community Chest 2            = 25
Tennessee Ave      [orange]  = 23
New York Ave       [orange]  = 38
Free Parking                 = 33
Kentucky Ave       [red]     = 22
Chance 2                     = 27
Indiana Ave        [red]     = 27
Illinois Ave       [red]     = 29
B&O Railroad        < RR >   = 16
Atlantic Ave       [yellow]  = 27
Ventnor Ave        [yellow]  = 32
Water Works        (Utility) = 36
Marvin Gardens     [yellow]  = 31
GO TO JAIL                   = 27
Pacific Ave        [green]   = 18
North Carolina Ave [green]   = 27
Community Chest 3            = 28
Pennsylvania Ave   [green]   = 22
Short Line RR       < RR >   = 26
Chance 3                     = 25
Park Place         [blue]    = 30
LUXURY TAX                   = 20
Boardwalk          [blue]    = 22

Properties:
purple  = 39
cyan    = 67
magenta = 85
orange  = 87
red     = 78
yellow  = 90
green   = 67
blue    = 52
RR      = 107
Utility = 57
chance  = 78
chest   = 71
fucked  = 72

The board was traversed a total of 181 times

Rolls: (2)=29 (3)=51 (4)=73 (5)=110 (6)=134 (7)=161 (8)=166 (9)=103 (10)=77 (11)=60 (12)=36

GO collect \$200              = 34
Mediterreanian Ave [purple]  = 26
Community Chest 1            = 23
Baltic Ave         [purple]  = 21
INCOME TAX                   = 21
Oriental Ave       [cyan]    = 25
Chance 1                     = 25
Vermont Ave        [cyan]    = 20
Connecticut Ave    [cyan]    = 19
Jail                         = 27
St. Charles Place  [magenta] = 27
Electic Company    (Utility) = 32
States Ave         [magenta] = 19
Virginia Ave       [magenta] = 19
Pennsylvania RR     < RR >   = 22
St James Place     [orange]  = 30
Community Chest 2            = 34
Tennessee Ave      [orange]  = 32
New York Ave       [orange]  = 29
Free Parking                 = 35
Kentucky Ave       [red]     = 34
Chance 2                     = 25
Indiana Ave        [red]     = 29
Illinois Ave       [red]     = 28
B&O Railroad        < RR >   = 40
Atlantic Ave       [yellow]  = 27
Ventnor Ave        [yellow]  = 23
Water Works        (Utility) = 25
Marvin Gardens     [yellow]  = 22
GO TO JAIL                   = 36
Pacific Ave        [green]   = 21
North Carolina Ave [green]   = 28
Community Chest 3            = 35
Pennsylvania Ave   [green]   = 16
Short Line RR       < RR >   = 28
Chance 3                     = 30
Park Place         [blue]    = 17
LUXURY TAX                   = 13
Boardwalk          [blue]    = 26

Properties:
purple  = 47
cyan    = 64
magenta = 65
orange  = 91
red     = 91
yellow  = 72
green   = 65
blue    = 43
RR      = 117
Utility = 57
chance  = 80
chest   = 92
fucked  = 70

The board was traversed a total of 173 times

Rolls: (2)=32 (3)=61 (4)=85 (5)=111 (6)=137 (7)=156 (8)=148 (9)=126 (10)=77 (11)=51 (12)=16

```
Now we get a better idea of where we land the most on the board. It seems the magenta, orange, red, yellow, and green properties get landed on the most, and the railroads have the trump in getting landed on (perhaps this is the way to go to win games). However, with only these 4 sets of results to look at, Orange, red, and yellow seems to have a higher rate than magenta and green. So lets kick it up a few notches, then a few more notches, and perhaps even a few more after that.....

We have here, 500,000 turns:

```

GO collect \$200              = 13439
Mediterreanian Ave [purple]  = 10979
Community Chest 1            = 11021
Baltic Ave         [purple]  = 11065
INCOME TAX                   = 11910
Oriental Ave       [cyan]    = 11332
Chance 1                     = 11692
Vermont Ave        [cyan]    = 11863
Connecticut Ave    [cyan]    = 11699
Jail                         = 14105
St. Charles Place  [magenta] = 13628
Electic Company    (Utility) = 13203
States Ave         [magenta] = 11976
Virginia Ave       [magenta] = 12215
Pennsylvania RR     < RR >   = 14413
St James Place     [orange]  = 13640
Community Chest 2            = 14227
Tennessee Ave      [orange]  = 14119
New York Ave       [orange]  = 15018
Free Parking                 = 14220
Kentucky Ave       [red]     = 14086
Chance 2                     = 13970
Indiana Ave        [red]     = 13617
Illinois Ave       [red]     = 16080
B&O Railroad        < RR >   = 15392
Atlantic Ave       [yellow]  = 13700
Ventnor Ave        [yellow]  = 13192
Water Works        (Utility) = 13992
Marvin Gardens     [yellow]  = 12988
GO TO JAIL                   = 13058
Pacific Ave        [green]   = 13390
North Carolina Ave [green]   = 13251
Community Chest 3            = 13490
Pennsylvania Ave   [green]   = 12651
Short Line RR       < RR >   = 12254
Chance 3                     = 11717
Park Place         [blue]    = 11156
LUXURY TAX                   = 11094
Boardwalk          [blue]    = 13537

Properties:
purple  = 22044
cyan    = 34894
magenta = 37819
orange  = 42777
red     = 43783
yellow  = 39880
green   = 39292
blue    = 24693
RR      = 57041
Utility = 27195
chance  = 37379
chest   = 38738
fucked  = 36062

The board was traversed a total of 89061 times

Rolls: (2)=13823 (3)=27456 (4)=41649 (5)=55730 (6)=69357 (7)=83727 (8)=69779 (9)=55376 (10)=41624 (11)=27736 (12)=13743

```

And here, 5,000,000 turns:

```

GO collect \$200              = 133627
Mediterreanian Ave [purple]  = 110591
Community Chest 1            = 110524
Baltic Ave         [purple]  = 110034
INCOME TAX                   = 118184
Oriental Ave       [cyan]    = 114261
Chance 1                     = 115851
Vermont Ave        [cyan]    = 117553
Connecticut Ave    [cyan]    = 117284
Jail                         = 139455
St. Charles Place  [magenta] = 137919
Electic Company    (Utility) = 131796
States Ave         [magenta] = 119429
Virginia Ave       [magenta] = 122145
Pennsylvania RR     < RR >   = 143604
St James Place     [orange]  = 136364
Community Chest 2            = 142688
Tennessee Ave      [orange]  = 142471
New York Ave       [orange]  = 151075
Free Parking                 = 141636
Kentucky Ave       [red]     = 140387
Chance 2                     = 139276
Indiana Ave        [red]     = 137373
Illinois Ave       [red]     = 160604
B&O Railroad        < RR >   = 152977
Atlantic Ave       [yellow]  = 135006
Ventnor Ave        [yellow]  = 134519
Water Works        (Utility) = 140234
Marvin Gardens     [yellow]  = 129202
GO TO JAIL                   = 131351
Pacific Ave        [green]   = 133603
North Carolina Ave [green]   = 131624
Community Chest 3            = 136263
Pennsylvania Ave   [green]   = 125823
Short Line RR       < RR >   = 122887
Chance 3                     = 116660
Park Place         [blue]    = 111934
LUXURY TAX                   = 111789
Boardwalk          [blue]    = 134780

Properties:
purple  = 220625
cyan    = 349098
magenta = 379493
orange  = 429910
red     = 438364
yellow  = 398727
green   = 391050
blue    = 246714
RR      = 569052
Utility = 272030
chance  = 371787
chest   = 389475
fucked  = 361324

The board was traversed a total of 889460 times

Rolls: (2)=139801 (3)=278237 (4)=416267 (5)=555867 (6)=694580 (7)=832936 (8)=693904 (9)=556018 (10)=415260 (11)=277690 (12)=139440

```

Here we have 27,500,000 turns:

```

GO collect \$200              = 739347
Mediterreanian Ave [purple]  = 607144
Community Chest 1            = 606528
Baltic Ave         [purple]  = 607940
INCOME TAX                   = 649767
Oriental Ave       [cyan]    = 626785
Chance 1                     = 639207
Vermont Ave        [cyan]    = 646760
Connecticut Ave    [cyan]    = 646728
Jail                         = 765009
St. Charles Place  [magenta] = 757955
Electic Company    (Utility) = 724859
States Ave         [magenta] = 653113
Virginia Ave       [magenta] = 673943
Pennsylvania RR     < RR >   = 788540
St James Place     [orange]  = 746121
Community Chest 2            = 788431
Tennessee Ave      [orange]  = 784728
New York Ave       [orange]  = 830138
Free Parking                 = 781180
Kentucky Ave       [red]     = 771629
Chance 2                     = 765658
Indiana Ave        [red]     = 755331
Illinois Ave       [red]     = 881532
B&O Railroad        < RR >   = 842609
Atlantic Ave       [yellow]  = 744444
Ventnor Ave        [yellow]  = 734936
Water Works        (Utility) = 773184
Marvin Gardens     [yellow]  = 710868
GO TO JAIL                   = 725135
Pacific Ave        [green]   = 739169
North Carolina Ave [green]   = 723850
Community Chest 3            = 746269
Pennsylvania Ave   [green]   = 691468
Short Line RR       < RR >   = 674851
Chance 3                     = 643829
Park Place         [blue]    = 613300
LUXURY TAX                   = 614119
Boardwalk          [blue]    = 740317

Properties:
purple  = 1215084
cyan    = 1920273
magenta = 2085011
orange  = 2360987
red     = 2408492
yellow  = 2190248
green   = 2154487
blue    = 1353617
RR      = 3129714
Utility = 1498043
chance  = 2048694
chest   = 2141228
fucked  = 1989021

The board was traversed a total of 4892247 times

Rolls: (2)=763983 (3)=1527255 (4)=2293362 (5)=3055411 (6)=3819372 (7)=4581062 (8)=3819029 (9)=3055509 (10)=2292849 (11)=1527455 (12)=764713

```

And finally, 981,000,000 turns:

```

GO collect \$200              = 26336343
Mediterreanian Ave [purple]  = 21657969
Community Chest 1            = 21659726
Baltic Ave         [purple]  = 21648104
INCOME TAX                   = 23167646
Oriental Ave       [cyan]    = 22329843
Chance 1                     = 22782665
Vermont Ave        [cyan]    = 23085121
Connecticut Ave    [cyan]    = 23075286
Jail                         = 27322284
St. Charles Place  [magenta] = 27049006
Electic Company    (Utility) = 25863212
States Ave         [magenta] = 23361722
Virginia Ave       [magenta] = 23952723
Pennsylvania RR     < RR >   = 28154971
St James Place     [orange]  = 26651787
Community Chest 2            = 28083445
Tennessee Ave      [orange]  = 27970375
New York Ave       [orange]  = 29636076
Free Parking                 = 27862206
Kentucky Ave       [red]     = 27556121
Chance 2                     = 27319952
Indiana Ave        [red]     = 26940750
Illinois Ave       [red]     = 31397430
B&O Railroad        < RR >   = 30083285
Atlantic Ave       [yellow]  = 26547562
Ventnor Ave        [yellow]  = 26269833
Water Works        (Utility) = 27535179
Marvin Gardens     [yellow]  = 25394301
GO TO JAIL                   = 25857895
Pacific Ave        [green]   = 26339850
North Carolina Ave [green]   = 25837777
Community Chest 3            = 26662061
Pennsylvania Ave   [green]   = 24626889
Short Line RR       < RR >   = 24089683
Chance 3                     = 22967934
Park Place         [blue]    = 21879795
LUXURY TAX                   = 21879011
Boardwalk          [blue]    = 26442357

Properties:
purple  = 43306073
cyan    = 68490250
magenta = 74363451
orange  = 84258238
red     = 85894301
yellow  = 78211696
green   = 76804516
blue    = 48322152
RR      = 111718858
Utility = 53398391
chance  = 73070551
chest   = 76405232
fucked  = 70904552

The board was traversed a total of 174521061 times

Rolls:
(2)=27260742
(3)=54487062
(4)=81778998
(5)=108986492
(6)=136260674
(7)=163452346
(8)=136277811
(9)=108978095
(10)=81786605
(11)=54476258
(12)=27254917

```

### Conclusions

Based off of all the results I've gathered, we do know this: All the spaces on the board have pretty much the same probability of being landed on, with a relatively small standard deviation. Illinois Ave, New York Ave, B&O Railroad, and Reading Railroad consistantly have higher numbers than all the rest. The first 10 spaces, with the exception of Reading, have consistently less frequent numbers. I can account for Reading Railroad because one card will directly move you there, and two cards will move you there if you land on the very last Chance (advance to nearest railroad). I can account for the orange, red, and yellow properties because of the number of times you have to go to Jail (2 cards takes you there and one fairly frequently landed on space), and from the Jail space, I'm most likely to roll a 6, 7, or 8.

As far as the playing of the game, it seems Illinois Ave is a sure winner, getting the monopoly on the orange and red properties is also a sure winner, and owning all 4 railroads can possibly outweigh the penalty of not being able to build houses/hotels on them and having the rent charge be upped by a factor of 10. I'm sure the creator of the game had come to the same conclusions, and balanced the game accordingly, leaving the dominant factor of the game up to luck. That doesn't mean you can't manipulate the game, perhaps by stacking the Chance and Community Chest decks to your favor or against your opponent(s) favor? But I'm sure we've all done that before, even without having seen these numbers.

I think you should run this program and draw your own conclusions. I've run this program thousands of times across many multiprocessor machines. One day, if I get bored enough, I might parallelize it so i can run it across many machines all at once, perhaps running a simulation with some octillion turns; but probably not.

Filed under: Computers, Sports & Games