How to Win Board Games
...Using Math
Dylan Field (@dylanjfield)
Ignite Sebastopol

NO ONE LIKES LOSING

MONOPOLY - METHOD
• Uses Markov Chains to calculate probability of landing on specific property groups
• Using probabilities, calculate average $ / turn
• Find best short term / long term properties

MARKOV CHAINS
• Contain Markov Property: Future outcomes are independent of past states
• Unlike card games - knowledge of past doesn’t help
• All that matters is current position and dice probabilities

Set of Cards
One House
Investment Return (Data from Truman Collins)

Three Houses
Hotel
Investment Return (Data from Truman Collins)

Undeveloped, Boardwalk + Park Place provide virtually no return.
Having all railroads is equivalent to having a property block with two
houses.
Utilities are terrible.

As more development occurs, three
properties consistently give good investment
return:
Boardwalk / Park Place
NY/St. James/Tennessee
Kentucky/Indiana/Illinois

BEST PROPERTIES OVERALL
• Orange and Red are excellent choices
• Easy to develop
• Fast Returns
• Blue is good if you have the money to develop it
• Railroads can be a decent purchase, but they are not as valuable in the end game

Monopoly is a Zero Sum Game
Be cautious of trades.

Capture continents for extra units

Attacker 2 3 6 6 3 2
Defender 2 6 6 2
Attacker Result: Lose Win

Baris Tan, 1997:
(1) “If you attack a territory with your armies, what is the probability that you will
capture this territory?”
(2) “If you engage in a war, how many armies should you expect to lose
depending on the number of armies your opponent has on that territory?”

Sharon Blatt, 2002 and Jason Osborne, 2003
(Question 1)
Rule of Thumb: Have 1.5x number of defending units

Baris Tan concluded that, if an
attack is successful, the number
of units lost is equal to slightly
less than the number of
defending units.
(Question 2)
There are battle simulators online!
Google “RISK Battle Odds Calculator”

Story-time: Applying these strategies
(A cautionary tale)
+ = big fight

The Golden Rule of Games (nothing to do with math!)
“No gloating if you win, no crying if you lose.”

IN CONCLUSION
Monopoly
• Buy the orange and red properties
• Be extremely cautious trading
Thank You!
Risk
Questions?
• Don’t attack if you have less than 1.5x defending units
• Expect to lose slightly less than number of defenders @dylanjfield
dylan@oreilly.com
Overall
• Be a good sport!