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Uniform Distribution On Pachinko

Authors Naoki Kitamura, Yuya Kawabata, Taisuke Izumi

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LIPIcs.FUN.2018.26.pdf
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ACM Subject Classification
  • Mathematics of computing → Combinatoric problems
Keywords
  • Pachinko
  • discrete mathematics

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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.

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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

Author Details

Naoki Kitamura
  • Nagoya Institute of Technology, Syowa-ku, Gokiso-cho, Nagoya, Aichi, 466-8555, Japan
Yuya Kawabata
  • Nagoya Institute of Technology, Syowa-ku, Gokiso-cho, Nagoya, Aichi, 466-8555, Japan
Taisuke Izumi
  • Nagoya Institute of Technology, Syowa-ku, Gokiso-cho, Nagoya, Aichi, 466-8555, Japan

References

  1. Pachinko - wikipedia. URL: https://en.wikipedia.org/wiki/Pachinko.
  2. 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. Google Scholar
  3. Jin Akiyama and Mari-Jo P. Ruiz. Pachinko math.In A Day’s Adventure in Math Wonderland. World Scientific, 2008. Google Scholar
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