Yahtzee®: The Solution

Woodward, Phil

doi:10.1080/09332480.2003.10554833

Cited by 11 publications

(8 citation statements)

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“…Another example was an NSF-funded project which posed some specific Yahtzee problems, with solutions, to interest high school students in advanced mathematics (Cornell 2006). The Chance paper "Yahtzee: The Solution" used a computer to exhaustively calculate the 10 12 possible outcomes to the game (Woodward 2003). After reviewing such resources, on the one hand, I concluded that the theoretical calculations available did not achieve the level of difficulty we could attain in the class.…”

Section: The Gamementioning

confidence: 99%

A Comprehensive Probability Project for the Upper Division One-Semester Probability Course Using Yahtzee

Wilson

Lawman

Murphy

et al. 2011

Journal of Statistics Education

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This article describes a probability project used in an upper division, one-semester probability course with third-semester calculus and linear algebra prerequisites. The student learning outcome focused on developing the skills necessary for approaching projectsized math/stat application problems. These skills include appropriately defining terms, making necessary simplifying assumptions, budgeting time, determining when to search literature, and checking theoretical calculations with simulation. It was assumed students would learn the technical material in the process. The result exceeded expectations. This article is written to summarize the project, provide a complete solution 1 Journal of Statistics Education, Volume 19, Number 1 (2011) (including R code with simulations and theoretical solutions), and describe the methods which facilitated the positive outcome, with the hope that it might be adapted by others.

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Section: The Gamementioning

confidence: 99%

A Comprehensive Probability Project for the Upper Division One-Semester Probability Course Using Yahtzee

Wilson

Lawman

Murphy

et al. 2011

Journal of Statistics Education

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“…The previous work indeed treats solitaire Yahtzee in this way. We quickly present the technique used by Glenn [1], Holderied [3], Verhoeff [2], and Woodward [4] to compute the optimal strategy. Some important differences in the work of the four will be noted in a subsequent section.…”

Section: A Solitaire Yahtzee Position Graphmentioning

confidence: 99%

“…Woodward did not make use of the fact that, in each component, it does not matter how one arrives at the second roll [4]: he treats the positions after the sequences of moves as different positions, even though the optimal strategy does not depend on how the roll [3 3 3 3 6] was obtained. As a result, it took him "many computing days" to compute the optimal strategy.…”

Section: B Refinements Of the Position Graphmentioning

confidence: 99%

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Computer Strategies for Solitaire Yahtzee

Glenn¹

2007

2007 IEEE Symposium on Computational Intelligence and Games

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Abstract-Solitaire Yahtzee has been solved completely. However, the optimal strategy is not one a human could practically use, and for computer play it requires either a very large database or significant CPU time. We present some refinements to the techniques used to solve solitaire Yahtzee and give a method for analyzing other solitaire strategies and give some examples of this analysis for some non-optimal strategies, including some produced by evolutionary algorithms.

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“…Optimal solitaire strategies -again in the sense of maximizing the expected scorewere independently developed by Tom Verhoeff [12] and James Glenn [6] around 1999, but never formally published. To this end, further authors developed optimal strategies for the solitaire game [11], [13]. Obviously, Yahtzee is much more involved than Ten times 18, and so is the analysis of the game.…”

Section: Introductionmentioning

confidence: 99%

Ten Times Eighteen

Böcker

2015

Journal of Information Processing

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Abstract:We consider the following simple game: We are given a table with ten slots indexed one to ten. In each of the ten rounds of the game, three dice are rolled and the numbers are added. We then put this number into any free slot. For each slot, we multiply the slot index with the number in this slot, and add up the products. The goal of the game is to maximize this score. In more detail, we play the game many times, and try to maximize the sum of scores or, equivalently, the expected score. We present a strategy to optimally play this game with respect to the expected score. We then modify our strategy so that we need only polynomial time and space. Finally, we show that knowing all ten rolls in advance, results in a relatively small increase in score. Although the game has a random component and requires a non-trivial strategy to be solved optimally, this strategy needs only polynomial time and space.

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Yahtzee®: The Solution

Cited by 11 publications

References 0 publications

A Comprehensive Probability Project for the Upper Division One-Semester Probability Course Using Yahtzee

A Comprehensive Probability Project for the Upper Division One-Semester Probability Course Using Yahtzee

Computer Strategies for Solitaire Yahtzee

Ten Times Eighteen

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