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# How to Win Board Games Using Math

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

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### How to Win Board Games Using Math

1. 1. How to Win Board Games ...Using Math Dylan Field (@dylanjﬁeld) Ignite Sebastopol
2. 2. NO ONE LIKES LOSING
3. 3. 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
4. 4. 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
5. 5. Set of Cards One House Investment Return (Data from Truman Collins)
6. 6. Three Houses Hotel Investment Return (Data from Truman Collins)
7. 7. Undeveloped, Boardwalk + Park Place provide virtually no return. Having all railroads is equivalent to having a property block with two houses. Utilities are terrible.
8. 8. As more development occurs, three properties consistently give good investment return: Boardwalk / Park Place NY/St. James/Tennessee Kentucky/Indiana/Illinois
9. 9. 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
10. 10. Monopoly is a Zero Sum Game Be cautious of trades.
11. 11. Capture continents for extra units
12. 12. Attacker 2 3 6 6 3 2 Defender 2 6 6 2 Attacker Result: Lose Win
13. 13. 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?”
14. 14. Sharon Blatt, 2002 and Jason Osborne, 2003 (Question 1) Rule of Thumb: Have 1.5x number of defending units
15. 15. 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”
16. 16. Story-time: Applying these strategies (A cautionary tale) + = big fight
17. 17. The Golden Rule of Games (nothing to do with math!) “No gloating if you win, no crying if you lose.”
18. 18. 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!