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DOI: 10.4230/LIPIcs.FUN.2018.26
Uniform Distribution On Pachinko

Authors: Naoki Kitamura, Yuya Kawabata, and Taisuke Izumi

Published in: LIPIcs, Volume 100, 9th International Conference on Fun with Algorithms (FUN 2018)

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.
Cite as

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)

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@InProceedings{kitamura_et_al:LIPIcs.FUN.2018.26,
  author =	{Kitamura, Naoki and Kawabata, Yuya and Izumi, Taisuke},
  title =	{{Uniform Distribution On Pachinko}},
  booktitle =	{9th International Conference on Fun with Algorithms (FUN 2018)},
  pages =	{26:1--26:14},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-067-5},
  ISSN =	{1868-8969},
  year =	{2018},
  volume =	{100},
  editor =	{Ito, Hiro and Leonardi, Stefano and Pagli, Linda and Prencipe, Giuseppe},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.FUN.2018.26},
  URN =		{urn:nbn:de:0030-drops-88170},
  doi =		{10.4230/LIPIcs.FUN.2018.26},
  annote =	{Keywords: Pachinko, discrete mathematics}
}
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