License: Creative Commons Attribution 3.0 Unported license (CC-BY 3.0)
When quoting this document, please refer to the following
DOI: 10.4230/LIPIcs.FUN.2018.26
URN: urn:nbn:de:0030-drops-88170
URL: https://drops.dagstuhl.de/opus/volltexte/2018/8817/
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Kitamura, Naoki ; Kawabata, Yuya ; Izumi, Taisuke

Uniform Distribution On Pachinko

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LIPIcs-FUN-2018-26.pdf (1 MB)


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.

BibTeX - Entry

@InProceedings{kitamura_et_al:LIPIcs:2018:8817,
  author =	{Naoki Kitamura and Yuya Kawabata and Taisuke Izumi},
  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 =	{Hiro Ito and Stefano Leonardi and Linda Pagli and Giuseppe Prencipe},
  publisher =	{Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{http://drops.dagstuhl.de/opus/volltexte/2018/8817},
  URN =		{urn:nbn:de:0030-drops-88170},
  doi =		{10.4230/LIPIcs.FUN.2018.26},
  annote =	{Keywords: Pachinko, discrete mathematics}
}

Keywords: Pachinko, discrete mathematics
Collection: 9th International Conference on Fun with Algorithms (FUN 2018)
Issue Date: 2018
Date of publication: 04.06.2018


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