From: Matthew Moss Date: 2009-01-23T06:26:00+09:00 Subject: [SUMMARY] Monopoly Walker (#188) Writing a simulator for a complete Monopoly game isn't overly complex, but it does require a lot of attention to detail in order to accurately reflect the game rules. Writing a simulator for just the movement portion of the game should be much simpler -- you can ignore property purchases and auctions, money tracking, rent, hotels, etc. What makes such a simulator non-trivial is the possibility of jumping around. If the only way to move around the board was via a dice rolls, the expected pattern to landing on properties would be even; that is, no one property would be more valuable than any other. However, when the Community Chest and Chance cards are added in, along with the Jail, the distribution is no longer even. When running the submission from _Daniel Moore_ for 10,000,000 iterations, the top ten properties show up as: Jail/Just Visiting - 5.0660% GO - 4.4057% Reading Railroad - 3.7458% Mediterranean - 3.4747% Income Tax - 3.3711% Baltic - 3.3506% Community Chest - 3.2478% Oriental - 2.8945% Illinois - 2.6351% New York - 2.5123% Now, four of those properties cannot be owned. The other six amount to almost 20% of property landings. And, interestingly, two of the highest properties are Mediterranean and Baltic, which form a monopoly. I'll note here that I believe Daniel's simulation to be a good start, but has some problems. I found one bug. It does not simulate the rolling of doubles to escape Jail, which would have an impact on the twelve properties that follow. Also, I'm not certain the handling of Community Chest and Chance cards is mathematically accurate, but may be reasonably close. Additionally, the human factor is completely removed here, which may be significant. In any case, while you may want to improve the script before preparing for your next game of Monopoly, we can certainly look at what Daniel has done. Let's begin with the overall simulation: class Board # ... def simulate(moves) @moves = moves position = 0 @moves.times do position += roll # Land on the properties and keep following the cards until we stay put while( position != (new_position = (@properties[position % BOARD_SIZE]).land) ) do position = new_position # Track the extra moves @moves += 1 end end end # ... end board = Board.new board.simulate((ARGV[0] || 100000).to_i) One parameter is pulled from the command line to be the number of simulation steps (i.e. dice rolls) to make, defaulting to 100,000 is no argument is provided. The board is created and `simulate` called. Inside, we loop, calculating the next position, finding the corresponding property, and calling `land` on that property. `land` will return new position, often itself, unless some condition causes the player to move elsewhere. If that happens (and so `position` will not equal `new_position`), we update `position` and increase `@moves`, just to keep track of how many moves were made overall (compared to how many rolls, the original parameter). When we look at `land`, we'll see the bookkeeping for tracking landing counts. There is a bug here, however: the calculation of `position`. In most cases, when you don't move beyond the roll, `land` will return the index into `@properties`: that is, `position % BOARD_SIZE`. Usually, this will be the same as `position`, except when passing Go (e.g. 46 ! = 6). In such a case, the move count will be incremented inappropriately, and `land` will be called once too often. To fix, change the loop to: @moves.times do position += roll position %= BOARD_SIZE # Land on the properties and keep following the cards until we stay put while( position != (new_position = (@properties[position]).land) ) do position = new_position # Track the extra moves @moves += 1 end end A seemingly minor bug, but this is why Baltic, Mediterranean, and Oriental showed up near the top of the distribution; they are the properties that would be hit more frequently when moving past Go. When this bug is fixed, the top ten distribution of properties is: Jail/Just Visiting - 5.4544% Illinois - 2.9668% GO - 2.9018% New York - 2.8461% B&O Railroad - 2.8458% Reading Railroad - 2.7957% Community Chest - 2.7122% Pennsylvania Railroad - 2.7024% Tennessee - 2.6937% Free Parking - 2.6587% Now we see Illinois Avenue, B&O Railroad and GO are closer to the top, which are the three most landed on properties according to most sources I've seen, including the Monopoly wiki. (Not sure why Jail is so high... and New York would drop in rank once in-Jail rolls are handled correctly). Let's now look a bit at the `Property` class, that which tracks how often a player lands on the property. class Property @@property_count = 0 attr_accessor :count def initialize(name, block) @count = 0 @name = name.gsub('_', ' ') @position = @@property_count @@property_count += 1 @move_block = block end # Record that the token landed on this cell # Return any bonus move (new location) def land @count += 1 # Sometimes cells have a bonus move, this returns # the new location, could be the same if no bonus move. @move_block.call(@position) end #... end The basics of this class is pretty simple: a `@count` data member is initialized to zero at creation, and incremented once for each call to `land`. `attr_accessor` provides a way to get the count later. `@name` is also initialized at creation. `@move_block` is also assigned at creation; this is a code block that, given a position, will return another position. The idea here is that some spots on the board (such as Chance, Community Chest, and Go to Jail) will immediately move the player somewhere else. Calling this block (provided elsewhere) will return the new position. In most cases, where the player does not move, the `stay_put` block is used; given the current position, it returns that same position -- the player will stay in one place. stay_put = Proc.new {|cur_pos| cur_pos} My main concern with the `Property` class is the duplication of effort found in `@@property_count`. The idea is to have each newly created property receive a unique index, stored in `@position`. However, this information is already provided externally by the `PROPERTY_NAMES` constant array, which dictates the order in which properties are created. Whenever you have two data "masters", you run the risk that they disagree. My revision would be to lose `@@property_count` and pass an extra parameter into the initializer. class Property #... def initialize(pos, name, block) @count = 0 @position = pos @name = name.gsub('_', ' ') @move_block = block end #... end Also, I would like to change `attr_accessor` to `attr_reader`, but the `count` field is written to later in the code. However, it is reused for a purpose other than the count; it would be better to provide a separate data member, appropriately named, rather than overlap use of `count`. Or, better yet, calculate the frequency on the fly, since it's a simple calculation that doesn't need to be stored. The last thing I'll look at here is one of the code blocks used to handle special movement around the board. There are a few of them, but let's look at the block for handling Chance cards. (The other blocks are reasonably similar.) CHANCE_EFFECT = Proc.new do |cur_pos| case Kernel.rand(CHANCE_CARDS) when 0 GO_POSITION when 1 ILLINOIS_POSITION when 2 # Nearest Utility if (cur_pos >= WATER_WORKS_POSITION) || (cur_pos < ELECTRIC_COMPANY_POSITION) ELECTRIC_COMPANY_POSITION else WATER_WORKS_POSITION end when 3..4 # Nearest Railroad case cur_pos when 5..14 15 when 15..24 25 when 25..34 35 else READING_POSITION end when 5 ST_CHARLES_POSITION when 6 # Go back three spaces cur_pos - 3 when 7 JAIL_POSITION when 8 READING_POSITION when 9 BOARDWALK_POSITION else # This card does not have an effect on position cur_pos end end Each time the block is called, a "card" is chosen at rand, and the player's new position is returned. In many cases (i.e. the `else` statement), the current position is returned; that is, there is no addition movement beyond the where the player is located. In most other cases, constants (e.g. ILLINOIS_POSITION) are used to provide the new location. The `case` statement is a decent, straightforward mechanism for sorting this out. (I can imagine other ways to do this, but I leave those as an exercise for the reader. Ha.) What I will mention here are how those constants are initialized, and also the use of some hardcoded numbers. For the latter, the approach that worked for the "nearest utility" case would be suitable for the railroads. (Personally, I'd probably turn it into a mathematical formula.) But even assuming we turn the hardcoded numbers into constants, how are those defined? GO_POSITION = 0 ILLINOIS_POSITION = 24 BOARDWALK_POSITION = 39 Now, normally, this would be the place to put the literal integers; however, as mentioned before, this is another "master" in generating board position numbers. All this information is present in the array `PROPERTY_NAMES`. To make use of that master array, rather than providing redundant information, I would do this: GO_POSITION = PROPERTY_NAMES.index("GO") ILLINOIS_POSITION = PROPERTY_NAMES.index("Illinois") BOARDWALK_POSITION = PROPERTY_NAMES.index("Boardwalk") Likewise, BOARD_SIZE = PROPERTY_NAMES.size instead of: BOARD_SIZE = 40 Note, while the property names are being repeated here, it is (in a way) not redundant information, since it is not acting as an authority for property names (as the literal integers were). Also note, with the flexibility of Ruby, this could be made even less redundant and more compact, but that's not something I'm going to get into here. Thanks for the submission, Daniel! It was good fun to see your approach. And thanks for everyone during my stint as quizmaster. I look forward to seeing more great quizzes in the future from quizmaster, version 3.0! :D