We study triples of labeled dice in which the relation “is a better die than” is non-transitive. Focusing on such triples with an additional symmetry we call “balanced,” we prove that such triples of n-sided dice exist for all n ≥ 3. We then examine the sums of the labels of such dice, and use these results to construct an O(n) algorithm for verifying whether or not a triple of n-sided dice is ...

Five chronometric experiments examined the functional architecture of naming dice, digits, and number words. Speakers named pictured dice, Arabic digits, or written number words, while simultaneously trying to ignore congruent or incongruent dice, digit, or number word distractors presented at various stimulus onset asynchronies (SOAs). Stroop-like interference and facilitation effects were obt...

In order to promote the development of further research on “object finder”, this paper aims utilize existing mode and modern scientific technological progress. By combining with TRIZ innovation method, shortcomings original plans are analyzed, intending propose a new concept for object finder, which consists two components, i.e., “locator” “searcher”. Additionally, explores both “searcher” resp...

The precise and accurate segmentation of the vertebral column is essential in the diagnosis and treatment of various orthopedic, neurological, and oncological traumas and pathologies. Segmentation is especially challenging in the presence of pathology such as vertebral compression fractures. In this paper, we propose a method to produce segmentations for osteoporotic compression fractured verte...

In this paper we consider a non-cooperative two-person zero-sum matrix game, called dice game. In an (n, σ) dice game, two players can independently choose a dice from a collection of hypothetical dice having n faces and with a total of σ eyes distributed over these faces. They independently roll their dice and the player showing the highest number of eyes wins (in case of a tie, none of the pl...

We analyse a variety of ways that comparing dice values can be used to simulate battles in games, measuring the ‘win bias’, ‘tie percentage’, and ‘closeness’ of each variant, to provide game designers with quantitative measurements of how small rule changes can significantly affect game balance. Closeness, a metric we introduce, is related to the inverse of the second moment, and measures how c...