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Optimal Yatzy Strategy
KTH, School of Computer Science and Communication (CSC).
KTH, School of Computer Science and Communication (CSC).
2013 (English)Independent thesis Basic level (degree of Bachelor), 10 credits / 15 HE creditsStudent thesis
Abstract [en]

Yatzy is a famous dice game that is played with a scorecard and five dice.

By rolling the dice the player’s goal is to achieve a combination of dice and

place the score in one of 15 categories. At the end of the game when all

categories are filled the points for every category are summarized. We

have developed an algorithm that makes up the optimal strategy of the

game by calculating the expected value for each state of the game,

recursing backwards from the last roll of the game to the first. The

implementation was unsuccessful, as the algorithm was too inefficient to

run in an acceptable amount of time. Instead, a part of the algorithm was

run, starting the game with 10 randomly chosen categories filled with 0

points and collecting the average scores for the remaining categories using

1 million simulations.

The result was 167.60 points, which sets a lower boundary to the expected

value for the complete game.

Abstract [sv]

Yatzy är ett känt tärningssspel som spelas med ett poängblock och fem

tärningar. Genom att rulla tärningarna önskar spelaren uppnå en

tärningskombination och placera poängen i någon av 15 kategorier. I slutet

av spelet när alla kategorier är fyllda summeras alla kategorier ihop. Vi har

utvecklat en algoritm som utgör spelets optimala strategi genom att

beräkna väntevärdet för varje tillstånd i spelet och rekursera från spelets

sista kast till det första. Implementationen misslyckades, då algoritmen

var för ineffektiv för att köras inom rimlig tid. Istället kördes en del av

algoritmen, där spelet börjar med 10 slumpvis valda kategorier fyllda med

0 poäng och snittpoängen för de resterande kategorierna samlades genom

1 miljon simulationer.

Resultatet var 167.60 poäng, vilket fungerar som undre gräns för spelets

totala väntevärde.

Place, publisher, year, edition, pages
Kandidatexjobb CSC, K13065
National Category
Computer Science
URN: urn:nbn:se:kth:diva-136688OAI: diva2:676659
Educational program
Master of Science in Engineering - Computer Science and Technology
Available from: 2013-12-13 Created: 2013-12-06 Last updated: 2013-12-13Bibliographically approved

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