Like this presentation? Why not share!

# How to Win Board Games Using Math

## by Dylan Field, Student at Brown, Intern at O'Reilly Media on Jun 11, 2009

• 2,913 views

An in-depth look at Monopoly and Risk. (Given at Ignite Sebastopol)

An in-depth look at Monopoly and Risk. (Given at Ignite Sebastopol)

### Views

Total Views
2,913
Views on SlideShare
2,905
Embed Views
8

Likes
0
0
1

### 1 Embed8

 http://www.slideshare.net 8

### Categories

Uploaded via SlideShare as Apple Keynote

### Report content

11 of 1 previous next

• mdlm Love this presentation.

Excellent example of how math plus high-level concepts produce clear, valuable advice.

Thanks!
4 years ago
Are you sure you want to
• <br />
• <br />
• <br />
• <br />
• <br />
• <br />
• <br />
• <br />
• <br />
• <br />
• <br />
• <br />
• <br />
• <br />
• <br />
• <br />
• <br />
• <br />
• <br />
• <br />

## How to Win Board Games Using MathPresentation Transcript

• 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!