A simple simulation of the board game "Monopoly"
HistoryNOTE: this paragraph is an excerptSlightly 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 ProgramBeing 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.I had to add a few things so that it more accurately simulated an actual Monopoly game. This meant that I had to actually go to Jail when I landed on the GO TO JAIL spot. After running this again, the results seemed more like an actual game. Naturally, I'd have to add the spice of the Chance and Community Chest cards. There are 16 of each type. 9 Chance cards made you move somewhere, the other 6 had to do with money and the last one a Get out of jail free card. A measly 2 Community Chest cards made you move somewhere, the other 13 had to do with money and the last one a Get out of jail free card. I figured I'd not worry about the 2 skip out of Jail free cards since if you had them, you would still need to move to the Jail before you could use them, and secondly, since I had to shuffle the 2 decks when I exhausted them, it really wasn't a big deal if the card was not part of the shuffle process a few times. The sole exception being if I got both cards, and kept them for the remainder of the game without ever using them. 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 ResultsFirst, 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 Reading Railroad < RR > = 3 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)=7This 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 Reading Railroad < RR > = 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 Reading Railroad < RR > = 2 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 Reading Railroad < RR > = 1 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)=4Already 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 = 32To 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 Reading Railroad < RR > = 28 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 Reading Railroad < RR > = 36 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 Reading Railroad < RR > = 27 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)=16Now 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 Reading Railroad < RR > = 14982 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 Reading Railroad < RR > = 149584 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 Reading Railroad < RR > = 823714 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 Reading Railroad < RR > = 29390919 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
ConclusionsBased 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
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