Monopoly Walker (#188)


#1

Okay, this will be the last quiz I host for Ruby Q… I hope to
find a new quizmaster in the coming week.

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the original quiz message, if you can.

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Monopoly Walker

Your task this week is to simulate players walking about a Monopoly
board. You are not implementing the whole game; rather, you are to
simulate and track just the players’ movement. Throw dice, move
tokens. Keep track of the properties where players land and how often.

Your output should be a table showing the relative frequency each
property is landed upon. Now, if you only paid attention to the dice,
this should be pretty even across the board. To make it slightly more
interesting, you do need to pay attention to the “Go to Jail” space,
as well as the Chance and Community Chest cards.

For the cards, don’t worry about money tracking or anything like that;
again, we’re only interested in movement, and the few Chance and
Community Chest cards that affect movement should have an impact on
the relative landing frequency.

Some helpful links:

If there is version differences, use information from these pages
pertaining to the Standard (American edition) as of Sept 2008.


#2

On Fri, Jan 16, 2009 at 7:48 AM, Matthew M. removed_email_address@domain.invalid wrote:

Monopoly Walker

Your task this week is to simulate players walking about a Monopoly board.
You are not implementing the whole game; rather, you are to simulate and
track just the players’ movement. Throw dice, move tokens. Keep track of the
properties where players land and how often.

My solution is pretty straightforward, I have a Property class and a
Board class. The board holds an array of properties. The interesting
thing comes when some properties have a special move, like “Advance to
St. Charles Place”. I used some Procs to keep track of the extra move
behavior. The simulation part involves throwing the dice, then
following all moves until the token stays put (sometimes you can land
on Chance, go back three spaces, land on Community Chest, then advance
to GO).

The first argument to the program states the number of dice throws to
simulate, if none is given 100000 is used.

Ruby Q. #188

Monopoly Walker

Daniel M.

Get some dice action going on

class Fixnum
def d(sides)
sum = 0
self.times {sum += Kernel.rand(sides) + 1}
return sum
end
end

Cells keep track of their own hit count and any crazy bonus moves

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

Print out this cells name and count

def to_s
“(#{”%02d" % @position}) #{@name}#{spacing}- #{@count}"
end

Arbitrary spacing to format the output cleanly

def spacing
s = " "
(21 - @name.size).times do
s += " "
end
s
end
end

class Board
PROPERTY_NAMES = %w[GO Mediterranean Community_Chest Baltic
Income_Tax Reading_Railroad Oriental Chance Vermont Connecticut
Jail/Just_Visiting St._Charles_Place Electric_Company States
Virginia Pennsylvania_Railroad St._James_Place Community_Chest
Tennessee New_York
Free_Parking Kentucky Chance Indiana Illinois B&O_Railroad
Atlantic Ventnor Water_Works Marvin_Gardins
Go_To_Jail Pacific North_Carolina Community_Chest Pennsylvania
Short_Line_Railroad Chance Park_Place Luxury_Tax Boardwalk]

Some Board positions

GO_POSITION = 0
READING_POSITION = 5
JAIL_POSITION = 10
ST_CHARLES_POSITION = 11
ELECTRIC_COMPANY_POSITION = 12
ILLINOIS_POSITION = 24
WATER_WORKS_POSITION = 28
BOARDWALK_POSITION = 39

CHANCE_CARDS = 15
COMMUNITY_CHEST_CARDS = 16
BOARD_SIZE = 40

COMMUNITY_CHEST_EFFECT = Proc.new do |cur_pos|
# Simulate 16 card Community chest deck
case Kernel.rand(COMMUNITY_CHEST_CARDS)
when 0
GO_POSITION
when 1
JAIL_POSITION
else
# This card does not have an effect on position
cur_pos
end
end

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

Roll 2d6

def roll
2.d 6
end

def initialize
# Stay put Proc, used in most regular cells
stay_put = Proc.new {|cur_pos| cur_pos}

proc_for_name = {
  "Community_Chest" => COMMUNITY_CHEST_EFFECT,
  "Chance" => CHANCE_EFFECT,
  "Go_To_Jail" => Proc.new do |cur_pos|
    JAIL_POSITION
  end
}

@properties = PROPERTY_NAMES.map do |name|
  # Create the property and give it it's bonus move behavior proc
  Property.new(name, proc_for_name[name] || stay_put)
end

end

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

Displays the results of the simulation

Permanently alters the cells making them unsuitable for

further simulation.

def display
puts “Total hits in board order after #{@moves} turns:”
puts @properties
puts “------”

puts "Sorted by Relative Frequency: "
# Sort and display results
@properties.sort{|a, b| b.count <=> a.count }.each do |property|
  property.count = "%1.4f%" % (property.count * 100 / @moves.to_f)
  puts property
end
puts "------"

end
end

board = Board.new

board.simulate((ARGV[0] || 100000).to_i)
board.display


Sorted by Relative Frequency:
(10) Jail/Just Visiting - 5.0612%
(00) GO - 4.4737%
(05) Reading Railroad - 3.8067%
(01) Mediterranean - 3.5400%
(03) Baltic - 3.3674%
(04) Income Tax - 3.3528%
(02) Community Chest - 3.2069%
(06) Oriental - 2.7579%
(24) Illinois - 2.6526%
(19) New York - 2.5675%
(25) B&O Railroad - 2.5140%
(08) Vermont - 2.4062%
(17) Community Chest - 2.3746%
(21) Kentucky - 2.3462%
(18) Tennessee - 2.3341%
(16) St. James Place - 2.3292%
(20) Free Parking - 2.3227%
(22) Chance - 2.3154%
(11) St. Charles Place - 2.3130%
(09) Connecticut - 2.3090%
(15) Pennsylvania Railroad - 2.3057%
(28) Water Works - 2.3033%
(26) Atlantic - 2.2676%
(31) Pacific - 2.1947%
(39) Boardwalk - 2.1923%
(33) Community Chest - 2.1898%
(30) Go To Jail - 2.1817%
(12) Electric Company - 2.1525%
(23) Indiana - 2.1404%
(07) Chance - 2.1193%
(32) North Carolina - 2.1145%
(29) Marvin Gardins - 2.1023%
(27) Ventnor - 2.0861%
(34) Pennsylvania - 2.0610%
(14) Virginia - 2.0350%
(35) Short Line Railroad - 2.0026%
(13) States - 1.8964%
(36) Chance - 1.8778%
(38) Luxury Tax - 1.7376%
(37) Park Place - 1.6882%


#3

On Jan 22, 2009, at 3:26 PM, Matthew M. wrote:

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! :smiley:

Thanks Matthew. Great run.

James Edward G. II


#4

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 M. 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! :smiley:


#5

On Thu, Jan 22, 2009 at 3:26 PM, Matthew M. removed_email_address@domain.invalid wrote:

(Personally, I’d probably turn it into a mathematical formula.) But even

For the railroads, maybe use ruby’s truncation of integers…

(x + 5) / 10 * 10 + 5

…which is weird to simplify because of the truncation, of course.

For the Monopoly board layout, I’ve been a little confused trying to
come up with a mathematical pattern for it, starting with a folded
board and moving on to numbers and fractals. If there’s a pattern
there, I’m officially not and never even came close to be “rain man”
:slight_smile:

It may be an overlaid clockwise vs. counter-clockwise position setup
to make the moves more random, but I still don’t see it in this game.
Darn! I really wanted to master this quiz elegantly!

I’ll do this one on my own time, I think, and thank you, Matthew for
hosting the quiz. Especially this one, because it made me rethink my
own version of the Monopoly game.

Cheers,
Todd