LIPIcs.FUN.2018.26.pdf
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Uniform Distribution On Pachinko
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9th International Conference on Fun with Algorithms (FUN 2018)
Series: Leibniz International Proceedings in Informatics (LIPIcs)
Conference: International Conference on Fun with Algorithms (FUN) - License:
Creative Commons Attribution 3.0 Unported license
- Publication Date: 2018-06-04
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Naoki Kitamura, Yuya Kawabata, and Taisuke Izumi. Uniform Distribution On Pachinko. In 9th International Conference on Fun with Algorithms (FUN 2018). Leibniz International Proceedings in Informatics (LIPIcs), Volume 100, pp. 26:1-26:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2018)
https://doi.org/10.4230/LIPIcs.FUN.2018.26
https://doi.org/10.4230/LIPIcs.FUN.2018.26
Abstract
Pachinko is a japanese mechanical gambling game similar to pinball. Recently, Akitaya et al. proposed several mathematical models of Pachinko. A number of pins are spiked in a field. A ball drops from the top-side end of the playfield, and falls down. In the 50-50 model, if the ball hits a pin, it moves to the left or right of the pin with equal probability. An arrangement of pins generates a distribution of the drop probability over all columns. We consider the problem of generating uniform distributions. Akitaya et al. show that (1/2^{{a}})-uniform distribution is possible for {a} in {0,1,2,3,4} and conjectured that it is possible for any positive integer a. In this paper, we show that the conjecture is true by a constructive way.
Subject Classification
ACM Subject Classification
- Mathematics of computing → Combinatoric problems
Keywords
- Pachinko
- discrete mathematics
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References
- Pachinko - wikipedia. URL: https://en.wikipedia.org/wiki/Pachinko.
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Hugo A Akitaya, Erik D Demaine, Martin L Demaine, Adam Hesterberg, Ferran Hurtado, Jason S Ku, and Jayson Lynch. Pachinko. Computational Geometry: Theory and Applications, 68, 2018.
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Jin Akiyama and Mari-Jo P. Ruiz. Pachinko math.In A Day’s Adventure in Math Wonderland. World Scientific, 2008.