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[tl;dr] Go to section «The Question», at the end...

In 1936 and 1937, Parker Brothers published a «Stock Exchange» add-on for Monopoly, Easy Money, and Finance; it was re-released for Monopoly, by Chessex, in 1992. This add-on replaces the «Free Parking» square with a «Stock Exchange» square.

Board Game Geek : Monopoly Stock Exchange

Also, see The Monopoly Stock Exchange Add-On Is the Only Way to Play

The Card Decks

The add-on adds «Advance to Stock Exchange» cards to each of the Chance and Community Chest decks. The 1936 version added 3 cards to each deck. In the 1992 version, the number of Advance to Stock Exchange cards used varies according to the number of players Also added to the Chance card deck is a «Go To Jail» card that applies only if you own stock.

The Probabilities

The probability of landing on any of the squares in Monopoly has been well documented. For example, see Probabilities in the Game of Monopoly® This reveals that Jail, Go, and New York are the most visited squares in the game.

The addition of the cards «Go To Stock Exchange» and a «Go To Jail» card will certainly change these probabilities. Will the Orange properties no longer be the most visited? By how much will the probability of landing on the the Yellow properties be increased?

[tl;dr] The Question

Has anyone written a computer program to compute the probabilities of landing on the various squares when the add-on is used?

  • Can't wait for StackExchange add-on :D – Aulis Ronkainen Jul 27 at 14:34
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Linked in Probabilities in the Game of Monopoly® by Truman Collins, are C source code files written to calculate the probabilities of normal Monopoly. We can just roll up our sleeves and tweak the program ourselves to see what kind of changes we get.

Choices

There are two separate programs linked: one that calculates the probabilities based on simulated die rolls, and one that uses a Markov matrix to calculate the exact probabilities. Collins says the data on the webpage were generated using a "extended" version of the Markov code, and then goes on to describe how even that process may be improved. However, to start off I decided to use the simpler (but less accurate) roll-up-the-probabilities code to see how far it gets us. I told it to simulate 10 million rolls. The code also outputs probabilities for two strategies: paying $50 to get out of jail immediately, and staying in jail until you get doubles or escape naturally. Below are only the probabilities for the "short jail" strategy.

Changes

I decided to split the difference between the two versions listed in the question, and add three Community Chest and three Chance cards that go to the Stock Exchange square, and also add the one Chance card the can send the player to jail. I chose for that card to always send the player to jail, rather than try and add in the complexity of simulating if the player had stocks.

Results

                            W/SE  Rank Normal Rank Difference RankChange
Go                          2.919 7    3.105  3    94.01%     -4
Mediterranean Avenue        2.13  34   2.137  36   99.67%      2
Community Chest             1.577 37   1.888  37   83.53%      0
Baltic Avenue               2.143 33   2.16   35   99.21%      2
Income Tax                  2.273 26   2.322  28   97.89%      2
Reading Railroad            2.781 12   2.958  6    94.02%     -6
Oriental Avenue             2.205 30   2.267  32   97.27%      2
Chance                      0.668 40   0.857  40   77.95%      0
Vermont Avenue              2.233 29   2.322  28   96.17%     -1
Connecticut Avenue          2.188 31   2.302  30   95.05%     -1
Visiting Jail               2.159 32   2.272  31   95.03%     -1
St. Charles Place           2.5   22   2.71   14   92.25%     -8
Electric Company            2.442 23   2.596  20   94.07%     -3
States Avenue               2.274 25   2.372  26   95.87%      1
Virginia Avenue             2.373 24   2.462  24   96.39%      0
Pennsylvania Railroad       2.77  13   2.92   8    94.86%     -5
St. James Place             2.711 15   2.799  12   96.86%     -3
Community Chest             2.129 35   2.596  20   82.01%     -15
Tennessee Avenue            2.842 10   2.935  7    96.83%     -3
New York Avenue             2.947 6    3.088  4    95.43%     -2
Free Parking/Stock Exchange 5.1   1    2.875  9    177.39%     8
Kentucky Avenue             2.704 17   2.83   10   95.55%     -7
Chance                      0.815 38   1.048  38   77.77%      0
Indiana Avenue              2.702 18   2.745  13   98.43%     -5
Illinois Avenue             3.109 3    3.176  2    97.89%     -1
B & O Railroad              3.08  4    3.073  5    100.23%     1
Atlantic Avenue             2.877 9    2.702  15   106.48%     6
Ventnor Avenue              2.916 8    2.683  16   108.68%     8
Water Works                 2.955 5    2.816  11   104.94%     6
Marvin Gardens              2.746 14   2.581  22   106.39%     8
Go To Jail                  0     41   0      41   0           0
Pacific Avenue              2.8   11   2.679  17   104.52%     6
North Carolina Avenue       2.711 15   2.624  18   103.32%     3
Community Chest             2.024 36   2.366  27   85.55%     -9
Pennsylvania Avenue         2.6   19   2.5    23   104%        4
Short Line                  2.535 21   2.438  25   103.98%     4
Chance                      0.721 39   0.861  39   83.74%      0
Park Place                  2.264 27   2.182  34   103.76%     7
Luxury Tax                  2.236 28   2.189  33   102.15%     5
Boardwalk                   2.556 20   2.617  19   97.67%     -1
In Jail                     4.284 2    3.948  1    108.51%    -1

The addition of six cards that take you to the Stock Exchange square almost double the odds of landing on it. Due to the effect of it warping you across the board, in general the properties before the SE square have a slight reduction in probability, and the squares after it experience a slight increase. The Chance and Community Chest squares have the most dramatically lowered chance due to the increased chance of drawing a card that moves you away (from about 81% to 85%).

For rankings, the Stock Exchange square becomes the first or second most landed on square, depending on if you decide to stay in jail or leave right away. Illinois Avenue and the B & O Railroad continue to stay around the top, and the squares following them (Atlantic, Ventnor, and the Water Works) have some of the most notable increases in rank. New York drops down to sixth, after the Water Works. Go drops down to seventh, since the cards that warp you to the Stock Exchange put you the furthest away from GO possible.

If playing with this Monopoly Add-on, I'd probably invest in the Yellow.

  • A terrific answer, involving a lot of work, in less than 3 hours. I'm going to invest a lot of time in comparing the results to those for regular Monopoly. Thanks... – Robert Miller Jul 22 at 23:11

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