1.
Yes,
you can play Monopoly with a genetic algorithm
Niels Zeilemaker

2.
About me
• PhD in Parallel Computing @ TUDelft
• Data hacker at GDD
• Data scientist and/or data engineer
• Basically, drink coffee a lot while waiting for

3.
Monopoly
• Boardgame created in 1935
• For 2-6 players
• Buy houses/hotels –>
• Last man standing wins
• Pronounced in dutch as moonoopooly

4.
Terminology
• Players traverse the board by rolling two dice
• When landing on an unowned property, a
player can decide to buy it
• If a player owns all properties of a single color,
he can buy houses
• Visiting a property owned by another player
you will need to pay rent

5.
Rules
• A player passing Go receives $200
• All fines are paid into the free parking space
• When a player does not buy an unowned property an auction is
held
• Rolling doubles three times in a row results in goto jail
• If a player lands on Go he receives $400
• Rolling doubles will release a player from jail
• Paying $50 will release a player from jail

6.
Rules
• A player passing Go receives $200
• All fines are paid into the free parking space
• When a player does not buy an unowned property an auction is
held
• Rolling doubles three times in a row results in goto jail
• If a player lands on Go he receives $400
• Rolling doubles will release a player from jail
• Paying $50 will release a player from jail

7.
How much free time do you have?
• Interesting game,
• still doesn’t explain why you would attempt to “solve it”
• GDD Friday + = “Monopoly Simulations”
• He implemented a small python script which would roll dice + go
to jail
See: http://koaning.io/monopoly-simulations.html

8.
Probability distribution

9.
Datascientists writing code
• Initial script, 46 lines
• “Improved” script, 800 lines

10.
How much free time do you have?
• Implemented
• Board object
• Player object
• Deed object
• BankruptException ;)
• Unit-tested, coverage ~80%

11.
Player object
class Player(object):
def buy_position(self, deed, amount):
# after landing on a deed
def bid_position(self, deed, amount, current_bid):
# while in an auction
def anything_else(self):
# at the end of the turn
def raise_amount(self, amount):
# when we need to pay for something

12.
First players implemented
• BuyNothing
• BuyAll
• BuyFrom
• BuyBetween
0
50
100
150
200
250
300
350
400
450
Player BuyAll BuyFrom '10' BuyBetween '10-20'
Wins

13.
Which deeds to buy?
€ 0.00
€ 100,000.00
€ 200,000.00
€ 300,000.00
€ 400,000.00
€ 500,000.00
€ 600,000.00
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39
Money raised/invested
raised invested

14.
But, which will help you to win?
0
50
100
150
200
250
300
350
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39
Caused bankruptcy

15.
Next up, genetic algorithms
• Manually selecting which deeds to buy/how many houses to build
isn’t a lot of fun
• Enter, the GAPlayer

16.
Genetic algoritms?
• Search heuristic which mimics natural selection
• Convert search space into chromosome
• Eg 1,1,0,3,3, etc.
• Evaluate performance of chromosome using fitness function
• 1,1,0,3,3,… = 42
• 1,2,0,3,3,… = 42
I'm no expert on genetic algoritms, feel free to correct me

17.
Genetic algoritms?
• After each round (or population)
• Select top X chromosomes
• Append some mutations
• Generate offspring by combining those
• Stop after X generations

18.
Genetic algoritms?
Algorithm A: 1,0,0,0,0
Algorithm B: 0,0,2,2,2
Child C: 0,0,2,0,2
Child D: 1,0,0,2,2

19.
GAPlayer
• Chromosome:
• 0,6,0,5,0,1,2,0,3,2,0,5,1,5,4,1,1,0,0,1,0,0,0,0,0,1,1,0,1,0,0,0,1,0,0,1,0,4,0,4
• 0 = don’t buy
• 1 = buy
• 2..5 = build 1..4 houses
• 6 = build hotel
65
1
232

20.
Fitness function
• Implemented two approaches:
• Play vs BuyAll
• Use TrueSkill
• Not sure if either is correct ;)

21.
Fitness function, vs BuyAll
• Play 1000 matches against BuyAll
• Score = #times won
• Evaluate 10 generations
• Population size = 56
• Select 20% best perfoming
• Mutate 1% of the solutions
• Single generation takes 1 minute to evaluate

22.
Scores vs Generations
400
450
500
550
600
650
1 2 3 4 5 6 7 8 9 10
vs BuyAll

23.
But wait
• So, GaPlayer '[0, 6, 0, 5, 0, 1, 2, 0, 3, 2, 0, 5, 1, 5, 4, 1, 1, 0, 0, 1, 0, 0, 0,
0, 0, 1, 1, 0, 1, 0, 0, 0, 1, 0, 0, 1, 0, 4, 0, 4]‘ is a better strategy than
buying everything….
• But is it the best monopoly strategy?
BuyAll GaPlayer….

24.
TrueSkill
• A ranking system developed for Xbox player matching
• In my understanding
• Each player has a skill belief, eg a probability distribution
• When you win/lose from another we update the probabilities accordingly
• Let’s hope Vincent is in the room

25.
An example
• Before vs After
• Poke1 loses from Poke2

26.
Combining GA + Trueskill
• Have a global leaderbord
• Each new GA chromosome plays against 100 randomly selected
others
• Each game now is best of 10
• Leaderbord is sorted by value of curve descending

27.
Presenting
0,0,0,1,0,1,1,0,1,0,0,1,0,0,0,1,1,0,2,1,0,0,0,0,1,1,4,4,0,5,0,1,0,0,0,1,0,2,0,3
You will never beaten in monopoly again, maybe

28.
Runner ups
• 0,0,0,1,0,1,0,0,0,0,0,0,0,0,1,1,6,0,6,6,0,0,0,0,0,1,0,1,0,0,0,5,4,0,4,1,0,2,0,3
• 0,0,0,1,0,1,0,0,0,0,0,1,0,0,1,1,1,0,2,1,0,0,0,0,0,1,4,4,0,5,0,0,0,0,0,1,0,2,0,3
• 0,1,0,1,0,1,0,0,0,0,0,1,0,0,1,1,1,0,0,1,0,0,0,0,0,1,4,4,0,5,0,0,0,0,0,1,0,2,0,3
• 0,0,0,1,0,1,0,0,0,0,0,1,1,0,0,1,1,0,1,0,0,1,0,0,0,1,1,1,0,0,0,0,0,0,0,1,0,3,0,4
• 0,1,0,2,0,1,1,0,0,1,0,1,1,1,0,1,1,0,2,2,0,0,0,0,0,1,4,3,1,4,0,0,0,0,0,1,0,2,0,3
• 0,2,0,1,0,1,1,0,0,1,0,0,1,0,1,1,6,0,6,6,0,0,0,0,0,1,0,1,0,0,0,5,4,0,4,1,0,3,0,3
• 0,2,0,2,0,1,1,0,0,1,0,0,1,0,0,1,6,0,5,6,0,0,0,0,1,1,0,0,0,0,0,0,1,0,0,1,0,3,0,2
• 0,0,0,1,0,1,1,0,0,0,0,1,0,0,1,1,1,0,1,1,0,0,0,0,0,1,4,5,0,5,0,0,0,0,0,1,0,2,0,3
• 0,2,0,1,0,1,1,0,2,1,0,0,1,0,1,1,6,0,6,6,0,0,0,0,0,1,0,1,0,0,0,5,4,0,4,1,0,4,0,3

29.
So
• We get some probable “best” solutions
• But is monopoly rock paper scissors?
• We should be able to notice this by it not converging
• And, TrueSkill has some ”magic” numbers
• Blame vincent

30.
Future work/known issues
• We implemented a single behavior to
• Bid in an auction
• Buy/Sell houses
• When to start buying/selling houses
• We did not implement
• Trying to buy streets from other players
• Opensource the stuffs

31.
We’re hiring / Questions / Thank
you
Niels Zeilemaker