Probabilities in the Game of Monopoly®

Probabilities in the Game of Monopoly®

Table of Contents Long term probabilities for each square

Expected income per roll for each property

Expected income per roll for other squares

Payback times for purchases

Mortgage payback and loss times

Conclusions from all of this

The Markov matrix I recently saw an article in Scientific American (the April 1996 issue with additional information in the August 1996 and April 1997 issues) that discussed the probabilities of landing on the various squares in the game of Monopoly®. They used a simplified model of the game without considering the effects of the Chance and Community Chest cards or of the various ways of being sent to jail.

I was intrigued enough with this problem that I started working on trying to find the probabilities for landing on the different squares with all of the rules taken into account. I ran into some interesting problems but finally came up with the right answers, which you will find here along with some other useful derived data. Incidentally, I'm not much of a Monopoly® player myself, but I've always enjoyed interesting problems involving probability and statistics, of which this was one.

I first wrote a C program that simulates a single person rolling the dice and moving around the board a great number of times. It included all of the rules for going to jail and the Chance and Community Chest cards. Although this gave good aproximate answers, I decided that I wanted to write another program that would find the exact probabilities using a Markov matrix, which was the method described in a simplified form in the Scientific American article. I used an extended version of this program to generate this web page.

I discovered that it is really necessary to model two different strategies. When you are in jail, it is possible to get out immediately by paying $50 or by using a Get out of Jail Free card, but you can also wait until you roll doubles or pay on your third turn in jail. Early in the game it is often best to get out as soon as possible so as to have more opportunities to buy property. Later in the game, it is best to stay in jail as long as possible to avoid landing on an opponent's property. The choice of strategy changes the probabilities for all of the squares of the board because the more time you spend in jail, the less you will land on other squares. I computed probabilities for both cases and have included them here. I have compared the results from my simulation program and the Markov one and the results are very close, which leads me to believe that these results are reliable.

In the process of figuring all of this out I ran into an interesting difficulty. When trying to calculate the probabilities exactly using the Markov matrix, it is necessary to estimate the probability--for each square--that the last two rolls of the dice are doubles (since three doubles in a row sends you to jail). First I used an estimate of 1/36, but in practice it's different for each square and it's not that high for any square. I used my simulation program to find the empirical probability for each square and then used these values in my Markov matrix program. I simulated 32 billion rolls to make these estimates, so I believe they are reliable and any deviation from their exact values is extremely small. Interestingly, the probabilities of two previous rolls being doubles is slightly different on certain squares for the two jail strategies. Additionally, the average roll when landing on a utility is a bit lower or higher than 7 depending on the utility and the jail strategy, which affects the rent value.

Just as I finished putting together this web page, I realized that there is a more efficient way of making the probability calculations. It would have been better if I had created a larger Markov matrix with three entries for each square. The first would be for being on that square not having rolled doubles in the last roll. The second would be for having rolled doubles on the last roll but not the one before, and the third for having rolled doubles the last two times. This much larger matrix would insure that the exact probabilities would be generated and there would be no need for doing simulation at all. If I ever get the time and inclination I may redo this in that way. I don't expect it would change any of the probabilities by more than one or two in the third decimal place, but it would still be a better way of doing it.

Below are the two tables of probabilities, expressed as percentages, for landing on any of the squares of the game. I have separated the probabilities for visiting jail and being in jail. The number given for a particular square is the percent chance that a player will land on it after a single roll, in the long run. For example, on average, about 3.18% of the rolls will result in the player landing on the most probable non-jail square, Illinois Avenue. Of course, for a single roll starting on a particular square, the chances will be quite different, but in the long run it will average out. At the bottom of this page I have included a matrix containing the probabilities for landing on any square after one roll starting from each square on the board. It's very big and cumbersome but it's there if you want it.

The first column indicates the average probability for landing on each square when the player's strategy is to get out of jail immediately when he gets in. The third column is for a player who stays in jail as long as he can once there. The second and fourth columns hold the rank of the squares from most often to least often visited. Note the higher rank of the squares 2, 4, 6, 8, 10, and 12 in front of Jail caused by the increased likelihood of getting out of jail with doubles. In this table, and each of those following, I have split the jail square into two, "visiting jail" and "in jail", the latter of which is listed at the bottom of the tables.

Note that these numbers indicate the percent chance that you will "end up" on each square after a roll--not just land on. This takes into account being sent to another square because of a Chance card or for some other reason. For example, there is no possibility that you will end up on the Go To Jail square, because if you land on it, you immediately go to the Jail square and that one is counted. This is the reason the Chance and Community Chest probabilities are low.

Long Term Probabilities for Ending Up on Each of the Squares in Monopoly®

Square Probability % (Jail Short) Rank Probability % (Jail Long) Rank Go 3.0961 3 2.9143 3 Mediterranean Avenue 2.1314 36 2.0073 36 Community Chest 1.8849 37 1.7750 37 Baltic Avenue 2.1624 35 2.0369 35 Income Tax 2.3285 28 2.1934 27 Reading Railroad 2.9631 6 2.8010 8 Oriental Avenue 2.2621 32 2.1317 32 Chance 0.8650 40 0.8152 40 Vermont Avenue 2.3210 29 2.1874 28 Connecticut Avenue 2.3003 30 2.1680 30 Visiting Jail 2.2695 31 2.1392 31 St. Charles Place 2.7017 15 2.5560 15 Electric Company 2.6040 20 2.6140 13 States Avenue 2.3721 26 2.1741 29 Virginia Avenue 2.4649 24 2.4255 22 Pennsylvania Railroad 2.9200 8 2.6354 11 St. James Place 2.7924 12 2.6802 9 Community Chest 2.5945 21 2.2957 24 Tennessee Avenue 2.9356 7 2.8210 6 New York Avenue 3.0852 4 2.8118 7 Free Parking 2.8836 9 2.8253 5 Kentucky Avenue 2.8358 10 2.6143 12 Chance 1.0480 38 1.0448 38 Indiana Avenue 2.7357 13 2.5671 14 Illinois Avenue 3.1858 2 2.9929 2 B & O Railroad 3.0659 5 2.8930 4 Atlantic Avenue 2.7072 14 2.5370 16 Ventnor Avenue 2.6789 16 2.5191 18 Water Works 2.8074 11 2.6507 10 Marvin Gardens 2.5861 22 2.4381 21 Go To Jail 0.0000 41 0.0000 41 Pacific Avenue 2.6774 17 2.5236 17 North Carolina Avenue 2.6252 19 2.4721 20 Community Chest 2.3661 27 2.2276 26 Pennsylvania Avenue 2.5006 23 2.3531 23 Short Line 2.4326 25 2.2906 25 Chance 0.8669 39 0.8158 39 Park Place 2.1864 33 2.0595 33 Luxury Tax 2.1799 34 2.0521 34 Boardwalk 2.6260 18 2.4832 19 In Jail 3.9499 1 9.4569 1

I've used the above information to draw other conclusions about the game such as how much money you can expect to earn on average from each property, and more importantly, how many opponent's rolls it takes on average to earn back the money invested to buy property, houses, or hotels.

First, I have created two sets of tables containing the average income per opponent roll for each property, including railroads, and utilities. One set assumes preferred short jail stay and the other preferred long jail stay. The values for the railroads include the extra income from the two Chance cards that result in double railroad rent.

Expected Income Per Opponent Roll on all Properties Assuming Preferred Short Jail Stay

Square Single Property Own Whole Block One House Two Houses Three Houses Four Houses Hotel Mediterranean Avenue 0.0426 0.0853 0.2131 0.6394 1.9182 3.4102 5.3284 Baltic Avenue 0.0865 0.1730 0.4325 1.2974 3.8923 6.9197 9.7308 Oriental Avenue 0.1357 0.2715 0.6786 2.0359 6.1078 9.0486 12.4418 Vermont Avenue 0.1393 0.2785 0.6963 2.0889 6.2666 9.2839 12.7653 Connecticut Avenue 0.1840 0.3681 0.9201 2.3003 6.9010 10.3515 13.8020 St. Charles Place 0.2702 0.5403 1.3508 4.0525 12.1575 16.8854 20.2624 States Avenue 0.2372 0.4744 1.1860 3.5581 10.6744 14.8256 17.7907 Virginia Avenue 0.2958 0.5916 1.4789 4.4368 12.3245 17.2542 22.1840 St. James Place 0.3909 0.7819 1.9547 5.5848 15.3583 20.9431 26.5279 Tennessee Avenue 0.4110 0.8220 2.0549 5.8712 16.1457 22.0169 27.8880 New York Avenue 0.4936 0.9873 2.4681 6.7874 18.5110 24.6814 30.8517 Kentucky Avenue 0.5105 1.0209 2.5523 7.0896 19.8509 24.8137 29.7764 Indiana Avenue 0.4924 0.9848 2.4621 6.8392 19.1498 23.9373 28.7248 Illinois Avenue 0.6372 1.2743 3.1858 9.5573 23.8932 29.4683 35.0434 Atlantic Avenue 0.5956 1.1912 2.9779 8.9338 21.6576 26.3952 31.1328 Ventnor Avenue 0.5893 1.1787 2.9467 8.8402 21.4309 26.1189 30.8069 Marvin Gardens 0.6207 1.2413 3.1033 9.3098 21.9814 26.5070 31.0326 Pacific Avenue 0.6961 1.3922 3.4806 10.4417 24.0963 29.4511 34.1365 North Carolina Avenue 0.6825 1.3651 3.4127 10.2382 23.6266 28.8769 33.4710 Pennsylvania Avenue 0.7002 1.4004 3.7509 11.2528 25.0063 30.0075 35.0088 Park Place 0.7652 1.5305 3.8262 10.9320 24.0504 28.4232 32.7960 Boardwalk 1.3130 2.6260 5.2519 15.7558 36.7635 44.6414 52.5193

Square One Railroad Two Railroads Three Railroads Four Railroads Reading Railroad 0.8130 1.6261 3.2521 6.5043 Pennsylvania Railroad 0.8021 1.6041 3.2083 6.4165 B & O Railroad 0.8538 1.7076 3.4152 6.8304 Short Line 0.6082 1.2163 2.4326 4.8653

Square One Utility Two Utilities Electric Company 0.7189 1.7972 Water Works 0.7939 1.9849

Expected Income Per Opponent Roll on all Properties Assuming Preferred Long Jail Stay

Square Single Property Own Whole Block One House Two Houses Three Houses Four Houses Hotel Mediterranean Avenue 0.0401 0.0803 0.2007 0.6022 1.8066 3.2117 5.0183 Baltic Avenue 0.0815 0.1630 0.4074 1.2221 3.6664 6.5181 9.1661 Oriental Avenue 0.1279 0.2558 0.6395 1.9185 5.7556 8.5268 11.7243 Vermont Avenue 0.1312 0.2625 0.6562 1.9686 5.9058 8.7494 12.0304 Connecticut Avenue 0.1734 0.3469 0.8672 2.1680 6.5041 9.7561 13.0082 St. Charles Place 0.2556 0.5112 1.2780 3.8339 11.5018 15.9747 19.1697 States Avenue 0.2174 0.4348 1.0870 3.2611 9.7833 13.5879 16.3054 Virginia Avenue 0.2911 0.5821 1.4553 4.3660 12.1277 16.9788 21.8298 St. James Place 0.3752 0.7505 1.8761 5.3604 14.7411 20.1015 25.4619 Tennessee Avenue 0.3949 0.7899 1.9747 5.6421 15.5157 21.1578 26.7999 New York Avenue 0.4499 0.8998 2.2494 6.1859 16.8707 22.4942 28.1178 Kentucky Avenue 0.4706 0.9411 2.3528 6.5356 18.2998 22.8748 27.4497 Indiana Avenue 0.4621 0.9241 2.3104 6.4177 17.9696 22.4620 26.9544 Illinois Avenue 0.5986 1.1972 2.9929 8.9788 22.4470 27.6846 32.9223 Atlantic Avenue 0.5581 1.1163 2.7907 8.3721 20.2960 24.7357 29.1754 Ventnor Avenue 0.5542 1.1084 2.7710 8.3131 20.1530 24.5615 28.9700 Marvin Gardens 0.5852 1.1703 2.9258 8.7773 20.7241 24.9909 29.2576 Pacific Avenue 0.6561 1.3123 3.2807 9.8422 22.7127 27.7600 32.1764 North Carolina Avenue 0.6427 1.2855 3.2137 9.6412 22.2490 27.1933 31.5195 Pennsylvania Avenue 0.6589 1.3177 3.5296 10.5889 23.5308 28.2370 32.9431 Park Place 0.7208 1.4417 3.6042 10.2976 22.6547 26.7738 30.8928 Boardwalk 1.2416 2.4832 4.9664 14.8992 34.7647 42.2143 49.6639

Square One Railroad Two Railroads Three Railroads Four Railroads Reading Railroad 0.7682 1.5365 3.0730 6.1459 Pennsylvania Railroad 0.7268 1.4535 2.9070 5.8140 B & O Railroad 0.8103 1.6207 3.2413 6.4827 Short Line 0.5726 1.1453 2.2906 4.5811

Square One Utility Two Utilities Electric Company 0.6903 1.7258 Water Works 0.7507 1.8768

The following table details the expected income and expense from the non-property squares on the board. The value for passing or landing on Go was arrived at through simulation, whereas the others were computed exactly. The income associated with the Chance and Community Chest squares is somewhat high because I was unable to include the cards for property repairs since the cost is based on the number of buildings you own. I also left out the Community Chest card where you collect $50 from each player and the Chance card where you pay each player $50. These last two should even out in the long run. I have assumed that landing on the Income Tax square always results in a $200 payment.

Average Income per Roll from other Squares

Square Income per roll (Jail Short) Income per roll (Jail Long) Go 33.7807 31.8657 Community Chest 1.4669 1.3496 Income Tax -4.6571 -4.3869 Chance 0.8572 0.8250 Luxury Tax -1.6349 -1.5391 Total 29.8128 28.1144

The following two sets of tables give the average number of opponent rolls needed to regain the cost of the last improvement to the property or the cost of the property itself. These figures are quite useful for determining what improvements to make first. Two of the groups of figures in this table are a bit fuzzy. I have assumed that when one lands on a utility, the roll had the usual distribution probabilities, which isn't necessarily true, but it should be very close. Also, when I give the payback number of rolls for the railroads, I average the payoff of the other railroads that might be owned. For example, if you buy Pennsylvania Railroad and you already own another railroad, your payback is faster if that other railroad is B. and O. rather than Short Line. So, I have averaged out the contributions from the other owned railroad.

These numbers were calculated by taking the cost of whatever was bought and dividing it by the increased average rent from the table above. Note that the figures in this table are rounded to four decimal places, but the ones used to make the calculations for the following table are to full precision. In other words, if you try to calculate these numbers by using those in the table above, you won't get quite the same answer, and it will not be as accurate as what is here. Once again, I have included a set of tables for a preferred short jail stay and for a long one.

Expected Number of Opponent Rolls to Recoup Incremental Cost (Short Jail Stay)

Square Single Property Last Property on Block First House Second House Third House Fourth House Hotel Mediterranean Avenue 1407.5414 349.3427 390.9837 117.2951 39.0984 33.5129 26.0656 Baltic Avenue 693.6732 278.2678 192.6870 57.8061 19.2687 16.5160 17.7865 Oriental Avenue 736.7646 168.1402 122.7941 36.8382 12.2794 17.0023 14.7353 Vermont Avenue 718.0923 167.1483 119.6820 35.9046 11.9682 16.5714 14.3618 Connecticut Avenue 652.0786 186.6135 90.5665 36.2266 10.8680 14.4906 14.4906 St. Charles Place 518.2000 130.4354 123.3810 37.0143 12.3381 21.1510 29.6114 States Avenue 590.1964 134.5674 140.5229 42.1569 14.0523 24.0896 33.7255 Virginia Avenue 540.9301 145.5937 112.6938 33.8081 12.6780 20.2849 20.2849 St. James Place 460.4308 106.7308 85.2650 27.5471 10.2318 17.9056 17.9056 Tennessee Avenue 437.9757 105.4773 81.1066 26.2037 9.7328 17.0324 17.0324 New York Avenue 405.1640 111.7834 67.5273 23.1522 8.5298 16.2066 16.2066 Kentucky Avenue 430.9902 102.3026 97.9523 33.0589 11.7543 30.2253 30.2253 Indiana Avenue 446.7690 103.1675 101.5384 34.2692 12.1846 31.3319 31.3319 Illinois Avenue 376.6757 105.3934 78.4741 23.5422 10.4632 26.9054 26.9054 Atlantic Avenue 436.5461 108.2805 83.9512 25.1854 11.7889 31.6616 31.6616 Ventnor Avenue 441.1645 108.5624 84.8393 25.4518 11.9136 31.9965 31.9965 Marvin Gardens 451.1382 115.4050 80.5604 24.1681 11.8374 33.1448 33.1448 Pacific Avenue 430.9623 108.1099 95.7694 28.7308 14.6471 37.3501 42.6858 North Carolina Avenue 439.5314 108.6412 97.6736 29.3021 14.9383 38.0927 43.5345 Pennsylvania Avenue 457.0280 115.1488 85.0850 26.6600 14.5418 39.9900 39.9900 Park Place 457.3734 123.0895 87.1187 28.1461 15.2458 45.7373 45.7373 Boardwalk 304.6501 117.9523 76.1625 19.0406 9.5203 25.3875 25.3875

Square First Railroad Second Railroad Third Railroad Fourth Railroad Reading Railroad 245.9926 84.0075 31.8937 12.8532 Pennsylvania Railroad 249.3562 84.6574 32.0431 12.8895 B & O Railroad 234.2459 81.6762 31.3501 12.7198 Short Line 328.8612 98.0735 34.9375 13.5677

Square First Utility Second Utility Electric Company 208.6603 50.1991 Water Works 188.9292 48.9687

Expected Number of Opponent Rolls to Recoup Incremental Cost (Long Jail Stay)

Square Single Property Last Property on Block First House Second House Third House Fourth House Hotel Mediterranean Avenue 1494.5282 370.8991 415.1467 124.5440 41.5147 35.5840 27.6764 Baltic Avenue 736.4116 295.4227 204.5588 61.3676 20.4559 17.5336 18.8823 Oriental Avenue 781.8495 178.4163 130.3083 39.0925 13.0308 18.0427 15.6370 Vermont Avenue 761.9564 177.3596 126.9927 38.0978 12.6993 17.5836 15.2391 Connecticut Avenue 691.8736 198.0109 96.0936 38.4374 11.5312 15.3750 15.3750 St. Charles Place 547.7404 137.3005 130.4144 39.1243 13.0414 22.3568 31.2995 States Avenue 643.9566 142.6429 153.3230 45.9969 15.3323 26.2839 36.7975 Virginia Avenue 549.7065 151.6400 114.5222 34.3567 12.8837 20.6140 20.6140 St. James Place 479.7082 112.8324 88.8348 28.7005 10.6602 18.6553 18.6553 Tennessee Avenue 455.7593 111.4549 84.3999 27.2677 10.1280 17.7240 17.7240 New York Avenue 444.5587 119.7646 74.0931 25.4034 9.3591 17.7823 17.7823 Kentucky Avenue 467.5215 109.9014 106.2549 35.8610 12.7506 32.7872 32.7872 Indiana Avenue 476.1134 110.3696 108.2076 36.5201 12.9849 33.3898 33.3898 Illinois Avenue 400.9446 112.6859 83.5301 25.0590 11.1373 28.6389 28.6389 Atlantic Avenue 465.8340 115.2667 89.5835 26.8750 12.5798 33.7858 33.7858 Ventnor Avenue 469.1373 115.4679 90.2187 27.0656 12.6690 34.0253 34.0253 Marvin Gardens 478.5081 122.6644 85.4479 25.6344 12.5556 35.1557 35.1557 Pacific Avenue 457.2156 114.7708 101.6035 30.4810 15.5394 39.6253 45.2861 North Carolina Avenue 466.7445 115.3620 103.7210 31.1163 15.8632 40.4512 46.2299 Pennsylvania Avenue 485.6852 122.2951 90.4201 28.3316 15.4536 42.4975 42.4975 Park Place 485.5496 130.4382 92.4856 29.8800 16.1850 48.5550 48.5550 Boardwalk 322.1658 124.8429 80.5414 20.1354 10.0677 26.8471 26.8471

Square First Railroad Second Railroad Third Railroad Fourth Railroad Reading Railroad 260.3346 89.2966 33.9793 13.7128 Pennsylvania Railroad 275.1957 92.1411 34.6302 13.8707 B & O Railroad 246.8124 86.5847 33.3434 13.5564 Short Line 349.2577 104.5080 37.2832 14.4902

Square First Utility Second Utility Electric Company 217.2844 52.5958 Water Works 199.8068 51.5053

It's also useful to know what the payback times are involving mortgages. For example, if you own all of the red properties and have no houses on them, you may want to know which one to mortgage so that you lose the least income while it's mortgaged. Below there are two sets of tables -- for both short and long jail stay strategies -- containing the expected number of opponent rolls it takes on average to lose the mortgage value of each property due to lost rent and the expected number of opponent rolls it takes to pay back the cost of unmortgaging each property. I have included values for all of the different possible ownership situations. The calculations were performed in the same way as in the tables above.

Expected Number of Opponent Rolls to Lose or Recoup Mortgages (Short Jail Stay)

Square Mortgage Single Property Mortgage Property on Full Block Unmortgage Single Property Unmortgage Property on Full Block Mediterranean Avenue 703.7707 351.8853 774.1478 387.0739 Baltic Avenue 346.8366 173.4183 381.5203 190.7601 Oriental Avenue 368.3823 184.1911 405.2205 202.6103 Vermont Avenue 359.0461 179.5231 394.9508 197.4754 Connecticut Avenue 326.0393 163.0197 358.6433 179.3216 St. Charles Place 259.1000 129.5500 285.0100 142.5050 States Avenue 295.0982 147.5491 324.6080 162.3040 Virginia Avenue 270.4650 135.2325 297.5115 148.7558 St. James Place 230.2154 115.1077 253.2370 126.6185 Tennessee Avenue 218.9878 109.4939 240.8866 120.4433 New York Avenue 202.5820 101.2910 222.8402 111.4201 Kentucky Avenue 215.4951 107.7476 237.0446 118.5223 Indiana Avenue 223.3845 111.6923 245.7230 122.8615 Illinois Avenue 188.3378 94.1689 207.1716 103.5858 Atlantic Avenue 218.2731 109.1365 240.1004 120.0502 Ventnor Avenue 220.5823 110.2911 242.6405 121.3202 Marvin Gardens 225.5691 112.7845 248.1260 124.0630 Pacific Avenue 215.4811 107.7406 237.0292 118.5146 North Carolina Avenue 219.7657 109.8829 241.7423 120.8711 Pennsylvania Avenue 228.5140 114.2570 251.3654 125.6827 Park Place 228.6867 114.3434 250.9020 125.4510 Boardwalk 152.3250 76.1625 167.5576 83.7788

Square Mortgage Single Railroad Mortgage One of Two Railroads Mortgage One of Three Railroads Mortgage One of Four Railroads Unmortgage Single Railroad Unmortgage One of Two Railroads Unmortgage One of Three Railroads Unmortgage One of Four Railroads Reading Railroad 122.9963 61.4982 30.7491 15.3745 135.2960 67.6480 33.8240 16.9120 Pennsylvania Railroad 124.6781 62.3390 31.1695 15.5848 137.1459 68.5729 34.2865 17.1432 B & O Railroad 117.1230 58.5615 29.2807 14.6404 128.8353 64.4176 32.2088 16.1044 Short Line 164.4306 82.2153 41.1076 20.5538 180.8737 90.4368 45.2184 22.6092

Square Mortgage Single Utility Mortgage One of Two Utilities Unmortgage Single Utility Unmortgage One of Two Utilities Electric Company 104.3301 41.7321 114.0676 45.6271 Water Works 94.4646 37.7858 103.2813 41.3125

Expected Number of Opponent Rolls to Lose or Recoup Mortgages (Long Jail Stay)

Square Mortgage Single Property Mortgage Property on Full Block Unmortgage Single Property Unmortgage Property on Full Block Mediterranean Avenue 747.2641 373.6320 821.9905 410.9953 Baltic Avenue 368.2058 184.1029 405.0264 202.5132 Oriental Avenue 390.9248 195.4624 430.0172 215.0086 Vermont Avenue 380.9782 190.4891 419.0760 209.5380 Connecticut Avenue 345.9368 172.9684 380.5305 190.2652 St. Charles Place 273.8702 136.9351 301.2572 150.6286 States Avenue 321.9783 160.9891 354.1761 177.0881 Virginia Avenue 274.8533 137.4266 302.3386 151.1693 St. James Place 239.8541 119.9270 263.8395 131.9198 Tennessee Avenue 227.8797 113.9398 250.6676 125.3338 New York Avenue 222.2793 111.1397 244.5073 122.2536 Kentucky Avenue 233.7608 116.8804 257.1368 128.5684 Indiana Avenue 238.0567 119.0284 261.8624 130.9312 Illinois Avenue 200.4723 100.2361 220.5195 110.2598 Atlantic Avenue 232.9170 116.4585 256.2087 128.1043 Ventnor Avenue 234.5687 117.2843 258.0255 129.0128 Marvin Gardens 239.2540 119.6270 263.1795 131.5897 Pacific Avenue 228.6078 114.3039 251.4686 125.7343 North Carolina Avenue 233.3722 116.6861 256.7095 128.3547 Pennsylvania Avenue 242.8426 121.4213 267.1269 133.5634 Park Place 242.7748 121.3874 266.3586 133.1793 Boardwalk 161.0829 80.5414 177.1912 88.5956

Square Mortgage Single Railroad Mortgage One of Two Railroads Mortgage One of Three Railroads Mortgage One of Four Railroads Unmortgage Single Railroad Unmortgage One of Two Railroads Unmortgage One of Three Railroads Unmortgage One of Four Railroads Reading Railroad 130.1673 65.0836 32.5418 16.2709 143.1840 71.5920 35.7960 17.8980 Pennsylvania Railroad 137.5978 68.7989 34.3995 17.1997 151.3576 75.6788 37.8394 18.9197 B & O Railroad 123.4062 61.7031 30.8515 15.4258 135.7468 67.8734 33.9367 16.9684 Short Line 174.6288 87.3144 43.6572 21.8286 192.0917 96.0459 48.0229 24.0115

Square Mortgage Single Utility Mortgage One of Two Utilities Unmortgage Single Utility Unmortgage One of Two Utilities Electric Company 108.6422 43.4569 118.7821 47.5128 Water Works 99.9034 39.9614 109.2277 43.6911

So, now that we have all of this data, how can it be used to play better Monopoly®? It should be possible to add up all of the expected income values for all of the properties in a partially completed game and get an estimate of who is likely to win in the end. Of course, this ignores lots of factors in a particular game such as cash on hand, bargaining, and luck. The capricious nature of short-term probability insures that you never know what will happen in the next few rounds.

It's also possible to make some general observations about the properties. The railroads are excellent investments, particularly when owned together, although in absolute income terms they don't keep up with heavily built on properties later in the game. The best return on investment to be found is from putting a third house on New York Avenue. In fact, the third house has the fastest payoff of any building on almost all of the properties. The square most landed on other than Jail is Illinois Avenue, and in fact a hotel there will bring the most income other than a hotel on Boardwalk. By far the worst individual investment is to buy Medeterranean Avenue without first owning Baltic. That's not to say that you shouldn't buy it, but it's not going to make you much money without quite a bit of construction. The properties between the Jail square and the Go To Jail square are landed on the most, because of the jump caused by landing on Go To Jail. The Orange ones have the biggest bang for the buck as far as building goes.

One more thing is worth pointing out if it's not obvious. The numbers given here are all long term averages. They are useful as guidelines, but particular circumstances must be considered in practice. For example, if you have the opportunity to put a house on either Illinois Avenue or Marvin Gardens, in general you should put it on Illinois Avenue. If one of your opponent's tokens is currently on Indiana Avenue, however, then he's got about a 14% chance of landing on Marvin Gardens on the next roll but no chance of landing on Illinois Avenue. Considering this, it's better to put the new house on Marvin Gardens in this particular situation.

Here are the two Markov matrices, which are quite large. The point of these tables is to show how likely you are to land on any square of the board starting from any other square. For example, the figures in the Baltic Avenue row are the probabilities that you will land on each one of those squares with one roll of the dice starting on Baltic Avenue. Similarly, the column associated with Baltic Avenue contains the probabilities that you will land on Baltic in one roll starting from any other square (those appearing in the left-most column). Note that these numbers take into account the probability that the two previous rolls before this one were doubles. Because this table is so large, I've duplicated the row and column headings a couple of times for readability.

Individual Square Probabilities for Preferred Short Term Jail Stay (as Percentages)

Square Go Mediterranean Avenue Community Chest Baltic Avenue Income Tax Reading Railroad Oriental Avenue Chance Vermont Avenue Connecticut Avenue Visiting Jail St. Charles Place Electric Company States Avenue Virginia Avenue Pennsylvania Railroad St. James Place Community Chest Tennessee Avenue New York Avenue Free Parking Kentucky Avenue Chance Indiana Avenue Illinois Avenue B & O Railroad Atlantic Avenue Ventnor Avenue Water Works Marvin Gardens Go To Jail Pacific Avenue North Carolina Avenue Community Chest Pennsylvania Avenue Short Line Chance Park Place Luxury Tax Boardwalk In Jail Go 1.212 0.000 2.384 5.556 9.322 12.153 13.836 6.250 13.836 11.111 8.280 Go 6.597 3.766 0.000 0.000 2.083 0.000 0.000 0.000 0.000 0.000 Go 0.000 0.000 0.000 1.042 0.000 0.000 0.000 0.000 0.000 0.000 Go 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 1.042 1.531 Go Mediterranean Avenue 0.863 0.000 0.000 2.695 6.418 9.113 11.111 5.177 16.667 13.806 11.111 Mediterranean Avenue 9.113 6.418 2.695 0.000 1.726 0.000 0.000 0.000 0.000 0.000 Mediterranean Avenue 0.000 0.000 0.000 0.863 0.000 0.000 0.000 0.000 0.000 0.000 Mediterranean Avenue 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.863 1.361 Mediterranean Avenue Community Chest 0.694 0.000 0.000 0.000 3.423 6.250 8.284 4.167 13.840 16.667 13.840 Community Chest 11.806 8.979 5.556 2.729 1.389 0.000 0.000 0.000 0.000 0.000 Community Chest 0.000 0.000 0.000 0.694 0.000 0.000 0.000 0.000 0.000 0.000 Community Chest 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.694 0.990 Community Chest Baltic Avenue 0.516 0.000 0.000 0.000 0.516 3.214 5.556 3.095 11.111 13.809 16.667 Baltic Avenue 14.325 11.627 8.254 5.556 3.730 0.000 0.000 0.000 0.000 0.000 Baltic Avenue 0.000 0.000 0.000 0.516 0.000 0.000 0.000 0.000 0.000 0.000 Baltic Avenue 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.516 0.993 Baltic Avenue Income Tax 0.347 0.000 0.000 0.000 0.347 0.347 2.720 2.083 8.275 11.111 13.831 Income Tax 17.014 14.178 11.111 8.275 6.250 2.720 0.000 0.000 0.000 0.000 Income Tax 0.000 0.000 0.000 0.347 0.000 0.000 0.000 0.000 0.000 0.000 Income Tax 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.347 0.695 Income Tax Reading Railroad 0.338 0.000 0.000 0.000 0.169 0.169 0.000 1.014 5.556 8.261 11.111 Reading Railroad 13.985 16.836 13.816 11.111 8.599 5.556 2.367 0.000 0.000 0.000 Reading Railroad 0.000 0.000 0.000 0.169 0.000 0.000 0.000 0.000 0.000 0.000 Reading Railroad 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.169 0.773 Reading Railroad Oriental Avenue 0.347 0.000 0.000 0.000 0.000 0.000 0.000 0.000 2.721 5.556 8.277 Oriental Avenue 11.111 13.833 16.667 13.833 11.111 8.277 4.861 2.721 0.000 0.000 Oriental Avenue 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 Oriental Avenue 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.685 Oriental Avenue Chance 0.516 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 2.703 5.556 Chance 8.259 11.111 13.814 16.667 13.814 11.111 7.226 5.556 2.703 0.000 Chance 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 Chance 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.965 Chance Vermont Avenue 0.694 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 2.723 Vermont Avenue 5.556 8.278 11.111 13.834 16.667 13.834 9.722 8.278 5.556 2.723 Vermont Avenue 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 Vermont Avenue 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 1.026 Vermont Avenue Connecticut Avenue 0.864 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 Connecticut Avenue 2.711 5.556 8.267 11.111 13.822 16.667 12.094 11.111 8.267 5.556 Connecticut Avenue 2.711 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 Connecticut Avenue 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 1.264 Connecticut Avenue Visiting Jail 1.211 0.000 0.000 0.000 0.000 0.170 0.000 0.000 0.000 0.000 0.000 Visiting Jail 0.170 2.715 5.556 8.271 11.111 13.826 14.583 13.826 11.281 8.271 Visiting Jail 5.556 1.018 0.000 0.170 0.339 0.000 0.000 0.170 0.000 0.000 Visiting Jail 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.170 1.586 Visiting Jail Go Mediterranean Avenue Community Chest Baltic Avenue Income Tax Reading Railroad Oriental Avenue Chance Vermont Avenue Connecticut Avenue Visiting Jail St. Charles Place Electric Company States Avenue Virginia Avenue Pennsylvania Railroad St. James Place Community Chest Tennessee Avenue New York Avenue Free Parking Kentucky Avenue Chance Indiana Avenue Illinois Avenue B & O Railroad Atlantic Avenue Ventnor Avenue Water Works Marvin Gardens Go To Jail Pacific Avenue North Carolina Avenue Community Chest Pennsylvania Avenue Short Line Chance Park Place Luxury Tax Boardwalk In Jail St. Charles Place 1.211 0.000 0.000 0.000 0.000 0.347 0.000 0.000 0.000 0.000 0.000 St. Charles Place 0.347 0.000 2.711 5.556 8.267 11.111 12.095 16.667 14.170 11.111 St. Charles Place 8.267 2.083 2.711 0.347 0.694 0.000 0.000 0.347 0.000 0.000 St. Charles Place 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.347 1.610 St. Charles Place Electric Company 1.211 0.000 0.000 0.000 0.000 0.517 0.000 0.000 0.000 0.000 0.000 Electric Company 0.517 0.000 0.000 2.714 5.556 8.270 9.722 13.825 17.184 13.825 Electric Company 11.111 3.101 5.556 3.231 1.034 0.000 0.000 0.517 0.000 0.000 Electric Company 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.517 1.593 Electric Company States Avenue 1.211 0.000 0.000 0.000 0.000 0.694 0.000 0.000 0.000 0.000 0.000 States Avenue 0.694 0.000 0.000 0.000 2.717 5.556 7.238 11.111 14.522 16.667 States Avenue 13.828 4.167 8.272 6.250 4.106 0.000 0.000 0.694 0.000 0.000 States Avenue 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.694 1.578 States Avenue Virginia Avenue 1.211 0.000 0.000 0.000 0.000 0.864 0.000 0.000 0.000 0.000 0.000 Virginia Avenue 0.864 0.000 0.000 0.000 0.000 2.716 4.861 8.271 11.975 13.827 Virginia Avenue 16.667 5.185 11.111 9.135 7.284 2.716 0.000 0.864 0.000 0.000 Virginia Avenue 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.864 1.585 Virginia Avenue Pennsylvania Railroad 1.212 0.000 0.000 0.000 0.000 1.042 0.000 0.000 0.000 0.000 0.000 Pennsylvania Railroad 1.042 0.000 0.000 0.000 0.000 0.000 2.381 5.556 9.319 11.111 Pennsylvania Railroad 13.833 6.250 13.833 12.153 10.361 5.556 2.722 1.042 0.000 0.000 Pennsylvania Railroad 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 1.042 1.548 Pennsylvania Railroad St. James Place 0.864 0.000 0.000 0.000 0.000 0.864 0.000 0.000 0.000 0.000 0.000 St. James Place 0.864 0.000 0.000 0.000 0.000 0.000 0.000 2.718 6.420 8.273 St. James Place 11.111 5.186 16.667 14.693 12.840 8.273 5.556 3.582 0.000 0.000 St. James Place 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.864 1.225 St. James Place Community Chest 0.694 0.000 0.000 0.000 0.000 0.694 0.000 0.000 0.000 0.000 0.000 Community Chest 0.694 0.000 0.000 0.000 0.000 0.000 0.000 0.000 3.424 5.556 Community Chest 8.285 4.167 13.840 17.361 15.229 11.111 8.285 6.250 2.729 0.000 Community Chest 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.694 0.986 Community Chest Tennessee Avenue 0.517 0.000 0.000 0.000 0.000 0.517 0.000 0.000 0.000 0.000 0.000 Tennessee Avenue 0.517 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.517 2.718 Tennessee Avenue 5.556 3.102 11.111 14.346 17.701 13.829 11.111 8.790 5.556 0.000 Tennessee Avenue 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.517 3.595 Tennessee Avenue New York Avenue 0.347 0.000 0.000 0.000 0.000 0.347 0.000 0.000 0.000 0.000 0.000 New York Avenue 0.347 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.347 0.000 New York Avenue 2.730 2.083 8.286 11.458 14.536 16.667 13.842 11.458 8.286 0.000 New York Avenue 2.730 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.347 6.187 New York Avenue Free Parking 0.170 0.000 0.000 0.000 0.000 0.170 0.000 0.000 0.000 0.000 0.000 Free Parking 0.170 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.170 0.000 Free Parking 0.000 1.017 5.556 8.438 11.450 13.824 16.667 13.994 11.111 0.000 Free Parking 5.556 2.713 0.000 0.000 0.000 0.000 0.000 0.000 0.170 8.827 Free Parking Go Mediterranean Avenue Community Chest Baltic Avenue Income Tax Reading Railroad Oriental Avenue Chance Vermont Avenue Connecticut Avenue Visiting Jail St. Charles Place Electric Company States Avenue Virginia Avenue Pennsylvania Railroad St. James Place Community Chest Tennessee Avenue New York Avenue Free Parking Kentucky Avenue Chance Indiana Avenue Illinois Avenue B & O Railroad Atlantic Avenue Ventnor Avenue Water Works Marvin Gardens Go To Jail Pacific Avenue North Carolina Avenue Community Chest Pennsylvania Avenue Short Line Chance Park Place Luxury Tax Boardwalk In Jail Kentucky Avenue 0.170 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 Kentucky Avenue 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 Kentucky Avenue 0.000 0.000 2.724 5.556 8.280 11.111 13.836 16.667 13.836 0.000 Kentucky Avenue 8.280 5.556 2.384 0.000 0.000 0.000 0.000 0.000 0.000 11.602 Kentucky Avenue Chance 0.347 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 Chance 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 Chance 0.000 0.000 0.000 2.706 5.556 8.262 11.111 13.817 16.667 0.000 Chance 11.111 8.262 4.861 2.706 0.000 0.000 0.000 0.000 0.000 14.593 Chance Indiana Avenue 0.517 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 Indiana Avenue 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 Indiana Avenue 0.000 0.000 0.000 0.000 2.720 5.556 8.276 11.111 13.831 0.000 Indiana Avenue 13.831 11.111 7.241 5.556 2.720 0.000 0.000 0.000 0.000 17.531 Indiana Avenue Illinois Avenue 0.874 0.000 0.000 0.000 0.000 0.508 0.000 0.000 0.000 0.000 0.000 Illinois Avenue 0.169 0.169 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 Illinois Avenue 0.000 0.000 0.000 0.169 0.000 2.709 5.556 8.265 11.111 0.000 Illinois Avenue 16.667 13.820 9.870 8.265 5.556 1.016 0.000 0.000 0.169 15.107 Illinois Avenue B & O Railroad 1.233 0.000 0.000 0.000 0.000 1.042 0.000 0.000 0.000 0.000 0.000 B & O Railroad 0.347 0.347 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 B & O Railroad 0.000 0.000 0.000 0.347 0.000 0.000 2.717 5.556 8.273 0.000 B & O Railroad 13.829 16.667 12.404 11.111 8.273 2.083 2.717 0.000 0.347 12.706 B & O Railroad Atlantic Avenue 1.591 0.000 0.000 0.000 0.000 1.550 0.000 0.000 0.000 0.000 0.000 Atlantic Avenue 0.517 0.517 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 Atlantic Avenue 0.000 0.000 0.000 0.517 0.000 0.000 0.000 2.711 5.556 0.000 Atlantic Avenue 11.111 13.822 15.035 13.822 11.111 3.100 5.556 2.711 0.517 10.259 Atlantic Avenue Ventnor Avenue 1.602 0.000 0.000 0.000 0.000 2.083 0.000 0.000 0.000 0.000 0.000 Ventnor Avenue 0.694 0.694 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 Ventnor Avenue 0.000 0.000 0.000 0.694 0.000 0.000 0.000 0.000 2.714 0.000 Ventnor Avenue 8.269 11.111 12.704 16.667 13.825 4.167 8.269 5.556 3.408 7.541 Ventnor Avenue Water Works 4.323 0.000 0.000 0.000 0.000 2.592 0.000 0.000 0.000 0.000 0.000 Water Works 0.864 0.864 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 Water Works 0.000 0.000 0.000 0.864 0.000 0.000 0.000 0.000 0.000 0.000 Water Works 5.556 8.266 10.478 13.822 16.667 5.183 11.111 8.266 6.419 4.724 Water Works Marvin Gardens 7.179 2.710 0.000 0.000 0.000 3.125 0.000 0.000 0.000 0.000 0.000 Marvin Gardens 1.042 1.042 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 Marvin Gardens 0.000 0.000 0.000 1.042 0.000 0.000 0.000 0.000 0.000 0.000 Marvin Gardens 2.710 5.556 8.144 11.111 13.821 6.250 13.821 11.111 9.307 2.031 Marvin Gardens Go To Jail 9.776 5.556 2.431 0.000 0.000 2.604 0.000 0.000 0.000 0.000 0.000 Go To Jail 0.868 0.868 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 Go To Jail 0.000 0.000 0.000 0.868 0.000 0.000 0.000 0.000 0.000 0.000 Go To Jail 0.000 2.778 5.621 8.333 11.111 5.208 16.667 13.889 11.979 1.443 Go To Jail Go Mediterranean Avenue Community Chest Baltic Avenue Income Tax Reading Railroad Oriental Avenue Chance Vermont Avenue Connecticut Avenue Visiting Jail St. Charles Place Electric Company States Avenue Virginia Avenue Pennsylvania Railroad St. James Place Community Chest Tennessee Avenue New York Avenue Free Parking Kentucky Avenue Chance Indiana Avenue Illinois Avenue B & O Railroad Atlantic Avenue Ventnor Avenue Water Works Marvin Gardens Go To Jail Pacific Avenue North Carolina Avenue Community Chest Pennsylvania Avenue Short Line Chance Park Place Luxury Tax Boardwalk In Jail Pacific Avenue 12.365 8.265 4.861 2.709 0.000 2.083 0.000 0.000 0.000 0.000 0.000 Pacific Avenue 0.694 0.694 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 Pacific Avenue 0.000 0.000 0.000 0.694 0.000 0.000 0.000 0.000 0.000 0.000 Pacific Avenue 0.000 0.000 2.978 5.556 8.265 4.167 13.820 16.667 14.515 1.667 Pacific Avenue North Carolina Avenue 14.904 11.111 7.246 5.556 2.726 1.553 0.000 0.000 0.000 0.000 0.000 North Carolina Avenue 0.518 0.518 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 North Carolina Avenue 0.000 0.000 0.000 0.518 0.000 0.000 0.000 0.000 0.000 0.000 North Carolina Avenue 0.000 0.000 0.453 2.726 5.556 3.105 11.111 13.837 17.184 1.381 North Carolina Avenue Community Chest 17.730 13.817 9.722 8.261 5.556 3.747 0.000 0.000 0.000 0.000 0.000 Community Chest 0.347 0.347 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 Community Chest 0.000 0.000 0.000 0.347 0.000 0.000 0.000 0.000 0.000 0.000 Community Chest 0.000 0.000 0.304 0.000 2.705 2.083 8.261 11.111 14.164 1.498 Community Chest Pennsylvania Avenue 14.885 16.667 12.109 11.111 8.284 6.067 2.728 0.000 0.000 0.000 0.000 Pennsylvania Avenue 0.171 0.171 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 Pennsylvania Avenue 0.000 0.000 0.000 0.171 0.000 0.000 0.000 0.000 0.000 0.000 Pennsylvania Avenue 0.000 0.000 0.149 0.000 0.000 1.023 5.556 8.284 11.282 1.345 Pennsylvania Avenue Short Line 12.322 13.813 14.583 13.813 11.280 8.426 5.556 1.013 0.000 0.000 0.000 Short Line 0.169 0.169 0.000 0.000 0.338 0.000 0.000 0.000 0.000 0.000 Short Line 0.000 0.000 0.000 0.169 0.000 0.000 0.000 0.000 0.000 0.000 Short Line 0.000 0.000 0.000 0.000 0.000 0.000 2.702 5.556 8.426 1.667 Short Line Chance 9.487 11.111 12.102 16.667 14.179 11.458 8.276 2.083 2.720 0.000 0.000 Chance 0.347 0.347 0.000 0.000 0.694 0.000 0.000 0.000 0.000 0.000 Chance 0.000 0.000 0.000 0.347 0.000 0.000 0.000 0.000 0.000 0.000 Chance 0.000 0.000 0.000 0.000 0.000 0.000 0.000 2.720 5.903 1.557 Chance Park Place 6.766 8.249 9.722 13.805 17.182 14.321 11.111 3.094 5.556 2.694 0.000 Park Place 0.516 0.516 0.000 0.000 1.031 0.000 0.000 0.000 0.000 0.000 Park Place 0.000 0.000 0.000 0.516 0.000 0.000 0.000 0.000 0.000 0.000 Park Place 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 3.209 1.714 Park Place Luxury Tax 3.939 5.556 7.247 11.111 14.532 17.361 13.838 4.167 8.282 5.556 2.727 Luxury Tax 0.694 0.694 0.000 0.000 1.389 0.000 0.000 0.000 0.000 0.000 Luxury Tax 0.000 0.000 0.000 0.694 0.000 0.000 0.000 0.000 0.000 0.000 Luxury Tax 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.694 1.519 Luxury Tax Boardwalk 1.210 2.698 4.861 8.254 11.974 14.673 16.667 5.179 11.111 8.254 5.556 Boardwalk 3.562 0.863 0.000 0.000 1.726 0.000 0.000 0.000 0.000 0.000 Boardwalk 0.000 0.000 0.000 0.863 0.000 0.000 0.000 0.000 0.000 0.000 Boardwalk 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.863 1.686 Boardwalk In Jail 1.215 0.000 0.000 0.000 0.000 0.174 0.000 0.000 0.000 0.000 0.000 In Jail 0.174 2.778 5.556 8.333 11.111 13.889 14.583 13.889 11.285 8.333 In Jail 5.556 1.042 0.000 0.174 0.347 0.000 0.000 0.174 0.000 0.000 In Jail 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.174 1.215 In Jail Go Mediterranean Avenue Community Chest Baltic Avenue Income Tax Reading Railroad Oriental Avenue Chance Vermont Avenue Connecticut Avenue Visiting Jail St. Charles Place Electric Company States Avenue Virginia Avenue Pennsylvania Railroad St. James Place Community Chest Tennessee Avenue New York Avenue Free Parking Kentucky Avenue Chance Indiana Avenue Illinois Avenue B & O Railroad Atlantic Avenue Ventnor Avenue Water Works Marvin Gardens Go To Jail Pacific Avenue North Carolina Avenue Community Chest Pennsylvania Avenue Short Line Chance Park Place Luxury Tax Boardwalk In Jail

Individual Square Probabilities for Preferred Long Term Jail Stay (as Percentages)

Square Go Mediterranean Avenue Community Chest Baltic Avenue Income Tax Reading Railroad Oriental Avenue Chance Vermont Avenue Connecticut Avenue Visiting Jail St. Charles Place Electric Company States Avenue Virginia Avenue Pennsylvania Railroad St. James Place Community Chest Tennessee Avenue New York Avenue Free Parking Kentucky Avenue Chance Indiana Avenue Illinois Avenue B & O Railroad Atlantic Avenue Ventnor Avenue Water Works Marvin Gardens Go To Jail Pacific Avenue North Carolina Avenue Community Chest Pennsylvania Avenue Short Line Chance Park Place Luxury Tax Boardwalk In Jail Go 1.212 0.000 2.383 5.556 9.321 12.153 13.835 6.250 13.835 11.111 8.279 Go 6.597 3.765 0.000 0.000 2.083 0.000 0.000 0.000 0.000 0.000 Go 0.000 0.000 0.000 1.042 0.000 0.000 0.000 0.000 0.000 0.000 Go 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 1.042 1.538 Go Mediterranean Avenue 0.863 0.000 0.000 2.695 6.418 9.113 11.111 5.177 16.667 13.806 11.111 Mediterranean Avenue 9.113 6.418 2.695 0.000 1.726 0.000 0.000 0.000 0.000 0.000 Mediterranean Avenue 0.000 0.000 0.000 0.863 0.000 0.000 0.000 0.000 0.000 0.000 Mediterranean Avenue 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.863 1.361 Mediterranean Avenue Community Chest 0.694 0.000 0.000 0.000 3.423 6.250 8.284 4.167 13.840 16.667 13.840 Community Chest 11.806 8.979 5.556 2.729 1.389 0.000 0.000 0.000 0.000 0.000 Community Chest 0.000 0.000 0.000 0.694 0.000 0.000 0.000 0.000 0.000 0.000 Community Chest 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.694 0.990 Community Chest Baltic Avenue 0.516 0.000 0.000 0.000 0.516 3.214 5.556 3.095 11.111 13.809 16.667 Baltic Avenue 14.325 11.627 8.253 5.556 3.730 0.000 0.000 0.000 0.000 0.000 Baltic Avenue 0.000 0.000 0.000 0.516 0.000 0.000 0.000 0.000 0.000 0.000 Baltic Avenue 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.516 0.995 Baltic Avenue Income Tax 0.347 0.000 0.000 0.000 0.347 0.347 2.720 2.083 8.275 11.111 13.831 Income Tax 17.014 14.178 11.111 8.275 6.250 2.720 0.000 0.000 0.000 0.000 Income Tax 0.000 0.000 0.000 0.347 0.000 0.000 0.000 0.000 0.000 0.000 Income Tax 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.347 0.695 Income Tax Reading Railroad 0.338 0.000 0.000 0.000 0.169 0.169 0.000 1.014 5.556 8.259 11.111 Reading Railroad 13.984 16.836 13.815 11.111 8.597 5.556 2.366 0.000 0.000 0.000 Reading Railroad 0.000 0.000 0.000 0.169 0.000 0.000 0.000 0.000 0.000 0.000 Reading Railroad 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.169 0.781 Reading Railroad Oriental Avenue 0.347 0.000 0.000 0.000 0.000 0.000 0.000 0.000 2.721 5.556 8.277 Oriental Avenue 11.111 13.832 16.667 13.832 11.111 8.277 4.861 2.721 0.000 0.000 Oriental Avenue 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 Oriental Avenue 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.686 Oriental Avenue Chance 0.516 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 2.702 5.556 Chance 8.258 11.111 13.813 16.667 13.813 11.111 7.226 5.556 2.702 0.000 Chance 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 Chance 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.969 Chance Vermont Avenue 0.694 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 2.722 Vermont Avenue 5.556 8.278 11.111 13.833 16.667 13.833 9.722 8.278 5.556 2.722 Vermont Avenue 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 Vermont Avenue 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 1.027 Vermont Avenue Connecticut Avenue 0.864 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 Connecticut Avenue 2.710 5.556 8.266 11.111 13.821 16.667 12.094 11.111 8.266 5.556 Connecticut Avenue 2.710 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 Connecticut Avenue 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 1.269 Connecticut Avenue Visiting Jail 1.211 0.000 0.000 0.000 0.000 0.170 0.000 0.000 0.000 0.000 0.000 Visiting Jail 0.170 2.715 5.556 8.271 11.111 13.826 14.583 13.826 11.281 8.271 Visiting Jail 5.556 1.018 0.000 0.170 0.339 0.000 0.000 0.170 0.000 0.000 Visiting Jail 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.170 1.588 Visiting Jail Go Mediterranean Avenue Community Chest Baltic Avenue Income Tax Reading Railroad Oriental Avenue Chance Vermont Avenue Connecticut Avenue Visiting Jail St. Charles Place Electric Company States Avenue Virginia Avenue Pennsylvania Railroad St. James Place Community Chest Tennessee Avenue New York Avenue Free Parking Kentucky Avenue Chance Indiana Avenue Illinois Avenue B & O Railroad Atlantic Avenue Ventnor Avenue Water Works Marvin Gardens Go To Jail Pacific Avenue North Carolina Avenue Community Chest Pennsylvania Avenue Short Line Chance Park Place Luxury Tax Boardwalk In Jail St. Charles Place 1.211 0.000 0.000 0.000 0.000 0.347 0.000 0.000 0.000 0.000 0.000 St. Charles Place 0.347 0.000 2.710 5.556 8.265 11.111 12.093 16.667 14.168 11.111 St. Charles Place 8.265 2.083 2.710 0.347 0.694 0.000 0.000 0.347 0.000 0.000 St. Charles Place 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.347 1.621 St. Charles Place Electric Company 1.212 0.000 0.000 0.000 0.000 0.517 0.000 0.000 0.000 0.000 0.000 Electric Company 0.517 0.000 0.000 2.718 5.556 8.273 9.722 13.829 17.184 13.829 Electric Company 11.111 3.103 5.556 3.235 1.034 0.000 0.000 0.517 0.000 0.000 Electric Company 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.517 1.571 Electric Company States Avenue 1.211 0.000 0.000 0.000 0.000 0.694 0.000 0.000 0.000 0.000 0.000 States Avenue 0.694 0.000 0.000 0.000 2.714 5.556 7.236 11.111 14.520 16.667 States Avenue 13.825 4.167 8.270 6.250 4.103 0.000 0.000 0.694 0.000 0.000 States Avenue 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.694 1.592 States Avenue Virginia Avenue 1.211 0.000 0.000 0.000 0.000 0.864 0.000 0.000 0.000 0.000 0.000 Virginia Avenue 0.864 0.000 0.000 0.000 0.000 2.713 4.861 8.269 11.975 13.824 Virginia Avenue 16.667 5.184 11.111 9.133 7.284 2.713 0.000 0.864 0.000 0.000 Virginia Avenue 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.864 1.598 Virginia Avenue Pennsylvania Railroad 1.212 0.000 0.000 0.000 0.000 1.042 0.000 0.000 0.000 0.000 0.000 Pennsylvania Railroad 1.042 0.000 0.000 0.000 0.000 0.000 2.379 5.556 9.316 11.111 Pennsylvania Railroad 13.830 6.250 13.830 12.153 10.358 5.556 2.719 1.042 0.000 0.000 Pennsylvania Railroad 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 1.042 1.566 Pennsylvania Railroad St. James Place 0.864 0.000 0.000 0.000 0.000 0.864 0.000 0.000 0.000 0.000 0.000 St. James Place 0.864 0.000 0.000 0.000 0.000 0.000 0.000 2.709 6.419 8.265 St. James Place 11.111 5.183 16.667 14.684 12.839 8.265 5.556 3.573 0.000 0.000 St. James Place 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.864 1.274 St. James Place Community Chest 0.694 0.000 0.000 0.000 0.000 0.694 0.000 0.000 0.000 0.000 0.000 Community Chest 0.694 0.000 0.000 0.000 0.000 0.000 0.000 0.000 3.420 5.556 Community Chest 8.281 4.167 13.837 17.361 15.226 11.111 8.281 6.250 2.726 0.000 Community Chest 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.694 1.008 Community Chest Tennessee Avenue 0.516 0.000 0.000 0.000 0.000 0.516 0.000 0.000 0.000 0.000 0.000 Tennessee Avenue 0.516 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.516 2.706 Tennessee Avenue 5.556 3.098 11.111 14.334 17.699 13.817 11.111 8.778 5.556 0.000 Tennessee Avenue 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.516 3.652 Tennessee Avenue New York Avenue 0.347 0.000 0.000 0.000 0.000 0.347 0.000 0.000 0.000 0.000 0.000 New York Avenue 0.347 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.347 0.000 New York Avenue 2.727 2.083 8.283 11.458 14.533 16.667 13.839 11.458 8.283 0.000 New York Avenue 2.727 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.347 6.205 New York Avenue Free Parking 0.169 0.000 0.000 0.000 0.000 0.169 0.000 0.000 0.000 0.000 0.000 Free Parking 0.169 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.169 0.000 Free Parking 0.000 1.012 5.556 8.422 11.448 13.809 16.667 13.978 11.111 0.000 Free Parking 5.556 2.698 0.000 0.000 0.000 0.000 0.000 0.000 0.169 8.901 Free Parking Go Mediterranean Avenue Community Chest Baltic Avenue Income Tax Reading Railroad Oriental Avenue Chance Vermont Avenue Connecticut Avenue Visiting Jail St. Charles Place Electric Company States Avenue Virginia Avenue Pennsylvania Railroad St. James Place Community Chest Tennessee Avenue New York Avenue Free Parking Kentucky Avenue Chance Indiana Avenue Illinois Avenue B & O Railroad Atlantic Avenue Ventnor Avenue Water Works Marvin Gardens Go To Jail Pacific Avenue North Carolina Avenue Community Chest Pennsylvania Avenue Short Line Chance Park Place Luxury Tax Boardwalk In Jail Kentucky Avenue 0.170 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 Kentucky Avenue 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 Kentucky Avenue 0.000 0.000 2.723 5.556 8.279 11.111 13.834 16.667 13.834 0.000 Kentucky Avenue 8.279 5.556 2.383 0.000 0.000 0.000 0.000 0.000 0.000 11.610 Kentucky Avenue Chance 0.347 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 Chance 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 Chance 0.000 0.000 0.000 2.689 5.556 8.244 11.111 13.800 16.667 0.000 Chance 11.111 8.244 4.861 2.689 0.000 0.000 0.000 0.000 0.000 14.680 Chance Indiana Avenue 0.517 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 Indiana Avenue 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 Indiana Avenue 0.000 0.000 0.000 0.000 2.720 5.556 8.276 11.111 13.831 0.000 Indiana Avenue 13.831 11.111 7.241 5.556 2.720 0.000 0.000 0.000 0.000 17.531 Indiana Avenue Illinois Avenue 0.873 0.000 0.000 0.000 0.000 0.504 0.000 0.000 0.000 0.000 0.000 Illinois Avenue 0.168 0.168 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 Illinois Avenue 0.000 0.000 0.000 0.168 0.000 2.686 5.556 8.241 11.111 0.000 Illinois Avenue 16.667 13.797 9.869 8.241 5.556 1.007 0.000 0.000 0.168 15.222 Illinois Avenue B & O Railroad 1.233 0.000 0.000 0.000 0.000 1.042 0.000 0.000 0.000 0.000 0.000 B & O Railroad 0.347 0.347 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 B & O Railroad 0.000 0.000 0.000 0.347 0.000 0.000 2.716 5.556 8.271 0.000 B & O Railroad 13.827 16.667 12.402 11.111 8.271 2.083 2.716 0.000 0.347 12.716 B & O Railroad Atlantic Avenue 1.589 0.000 0.000 0.000 0.000 1.546 0.000 0.000 0.000 0.000 0.000 Atlantic Avenue 0.515 0.515 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 Atlantic Avenue 0.000 0.000 0.000 0.515 0.000 0.000 0.000 2.690 5.556 0.000 Atlantic Avenue 11.111 13.801 15.034 13.801 11.111 3.092 5.556 2.690 0.515 10.361 Atlantic Avenue Ventnor Avenue 1.602 0.000 0.000 0.000 0.000 2.083 0.000 0.000 0.000 0.000 0.000 Ventnor Avenue 0.694 0.694 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 Ventnor Avenue 0.000 0.000 0.000 0.694 0.000 0.000 0.000 0.000 2.714 0.000 Ventnor Avenue 8.270 11.111 12.705 16.667 13.826 4.167 8.270 5.556 3.409 7.538 Ventnor Avenue Water Works 4.306 0.000 0.000 0.000 0.000 2.589 0.000 0.000 0.000 0.000 0.000 Water Works 0.863 0.863 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 Water Works 0.000 0.000 0.000 0.863 0.000 0.000 0.000 0.000 0.000 0.000 Water Works 5.556 8.250 10.477 13.806 16.667 5.177 11.111 8.250 6.418 4.804 Water Works Marvin Gardens 7.179 2.711 0.000 0.000 0.000 3.125 0.000 0.000 0.000 0.000 0.000 Marvin Gardens 1.042 1.042 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 Marvin Gardens 0.000 0.000 0.000 1.042 0.000 0.000 0.000 0.000 0.000 0.000 Marvin Gardens 2.711 5.556 8.145 11.111 13.822 6.250 13.822 11.111 9.308 2.024 Marvin Gardens Go To Jail 9.776 5.556 2.431 0.000 0.000 2.604 0.000 0.000 0.000 0.000 0.000 Go To Jail 0.868 0.868 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 Go To Jail 0.000 0.000 0.000 0.868 0.000 0.000 0.000 0.000 0.000 0.000 Go To Jail 0.000 2.778 5.621 8.333 11.111 5.208 16.667 13.889 11.979 1.443 Go To Jail Go Mediterranean Avenue Community Chest Baltic Avenue Income Tax Reading Railroad Oriental Avenue Chance Vermont Avenue Connecticut Avenue Visiting Jail St. Charles Place Electric Company States Avenue Virginia Avenue Pennsylvania Railroad St. James Place Community Chest Tennessee Avenue New York Avenue Free Parking Kentucky Avenue Chance Indiana Avenue Illinois Avenue B & O Railroad Atlantic Avenue Ventnor Avenue Water Works Marvin Gardens Go To Jail Pacific Avenue North Carolina Avenue Community Chest Pennsylvania Avenue Short Line Chance Park Place Luxury Tax Boardwalk In Jail Pacific Avenue 12.366 8.266 4.861 2.710 0.000 2.083 0.000 0.000 0.000 0.000 0.000 Pacific Avenue 0.694 0.694 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 Pacific Avenue 0.000 0.000 0.000 0.694 0.000 0.000 0.000 0.000 0.000 0.000 Pacific Avenue 0.000 0.000 2.979 5.556 8.266 4.167 13.821 16.667 14.516 1.660 Pacific Avenue North Carolina Avenue 14.897 11.111 7.241 5.556 2.719 1.552 0.000 0.000 0.000 0.000 0.000 North Carolina Avenue 0.517 0.517 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 North Carolina Avenue 0.000 0.000 0.000 0.517 0.000 0.000 0.000 0.000 0.000 0.000 North Carolina Avenue 0.000 0.000 0.453 2.719 5.556 3.103 11.111 13.830 17.184 1.417 North Carolina Avenue Community Chest 17.730 13.818 9.722 8.262 5.556 3.748 0.000 0.000 0.000 0.000 0.000 Community Chest 0.347 0.347 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 Community Chest 0.000 0.000 0.000 0.347 0.000 0.000 0.000 0.000 0.000 0.000 Community Chest 0.000 0.000 0.304 0.000 2.707 2.083 8.262 11.111 14.165 1.490 Community Chest Pennsylvania Avenue 14.884 16.667 12.108 11.111 8.282 6.067 2.727 0.000 0.000 0.000 0.000 Pennsylvania Avenue 0.170 0.170 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 Pennsylvania Avenue 0.000 0.000 0.000 0.170 0.000 0.000 0.000 0.000 0.000 0.000 Pennsylvania Avenue 0.000 0.000 0.149 0.000 0.000 1.023 5.556 8.282 11.282 1.352 Pennsylvania Avenue Short Line 12.322 13.814 14.583 13.814 11.280 8.427 5.556 1.013 0.000 0.000 0.000 Short Line 0.169 0.169 0.000 0.000 0.338 0.000 0.000 0.000 0.000 0.000 Short Line 0.000 0.000 0.000 0.169 0.000 0.000 0.000 0.000 0.000 0.000 Short Line 0.000 0.000 0.000 0.000 0.000 0.000 2.703 5.556 8.427 1.661 Short Line Chance 9.488 11.111 12.103 16.667 14.179 11.458 8.276 2.083 2.721 0.000 0.000 Chance 0.347 0.347 0.000 0.000 0.694 0.000 0.000 0.000 0.000 0.000 Chance 0.000 0.000 0.000 0.347 0.000 0.000 0.000 0.000 0.000 0.000 Chance 0.000 0.000 0.000 0.000 0.000 0.000 0.000 2.721 5.903 1.554 Chance Park Place 6.766 8.250 9.722 13.806 17.182 14.321 11.111 3.094 5.556 2.694 0.000 Park Place 0.516 0.516 0.000 0.000 1.031 0.000 0.000 0.000 0.000 0.000 Park Place 0.000 0.000 0.000 0.516 0.000 0.000 0.000 0.000 0.000 0.000 Park Place 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 3.210 1.710 Park Place Luxury Tax 3.939 5.556 7.247 11.111 14.533 17.361 13.838 4.167 8.283 5.556 2.727 Luxury Tax 0.694 0.694 0.000 0.000 1.389 0.000 0.000 0.000 0.000 0.000 Luxury Tax 0.000 0.000 0.000 0.694 0.000 0.000 0.000 0.000 0.000 0.000 Luxury Tax 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.694 1.515 Luxury Tax Boardwalk 1.210 2.698 4.861 8.254 11.974 14.672 16.667 5.178 11.111 8.254 5.556 Boardwalk 3.561 0.863 0.000 0.000 1.726 0.000 0.000 0.000 0.000 0.000 Boardwalk 0.000 0.000 0.000 0.863 0.000 0.000 0.000 0.000 0.000 0.000 Boardwalk 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.863 1.689 Boardwalk In Jail 0.460 0.000 0.000 0.000 0.000 0.174 0.000 0.000 0.000 0.000 0.000 In Jail 0.174 2.778 1.526 4.304 3.053 5.830 4.006 5.830 3.226 4.304 In Jail 1.526 1.042 0.000 0.174 0.347 0.000 0.000 0.174 0.000 0.000 In Jail 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.174 60.899 In Jail Go Mediterranean Avenue Community Chest Baltic Avenue Income Tax Reading Railroad Oriental Avenue Chance Vermont Avenue Connecticut Avenue Visiting Jail St. Charles Place Electric Company States Avenue Virginia Avenue Pennsylvania Railroad St. James Place Community Chest Tennessee Avenue New York Avenue Free Parking Kentucky Avenue Chance Indiana Avenue Illinois Avenue B & O Railroad Atlantic Avenue Ventnor Avenue Water Works Marvin Gardens Go To Jail Pacific Avenue North Carolina Avenue Community Chest Pennsylvania Avenue Short Line Chance Park Place Luxury Tax Boardwalk In Jail

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