2026-07-30T06:25:14Z https://drops.dagstuhl.de/oai

oai:drops-oai.dagstuhl.de:8817 2024-03-06T10:42:43Z ddc:004 open_access

Uniform Distribution On Pachinko Kitamura, Naoki Kawabata, Yuya Izumi, Taisuke Pachinko discrete mathematics 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. Schloss Dagstuhl – Leibniz-Zentrum für Informatik Naoki Kitamura and Yuya Kawabata and Taisuke Izumi 2018 Is Part Of LIPIcs, Volume 100, 9th International Conference on Fun with Algorithms (FUN 2018) InProceedings Text doc-type:ResearchArticle publishedVersion application/pdf doi:10.4230/LIPIcs.FUN.2018.26 urn:nbn:de:0030-drops-88170 https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.FUN.2018.26 eng https://creativecommons.org/licenses/by/3.0/legalcode