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Uniform Distribution for Pachinko
Theoretical Computer Science ( IF 0.718 ) Pub Date : 2020-05-22 , DOI: 10.1016/j.tcs.2020.05.032
Naoki Kitamura; Yuya Kawabata; Taisuke Izumi

Pachinko is a Japanese mechanical gambling game similar to pinball. Recently, several mathematical models of Pachinko have been proposed. A number of pins are spiked in a field. A ball drops from the top of the playfield and the ball falls down. In the 50-50 model, if the ball hits a pin, it moves to the left or right passage of the pin with an equal probability. An arrangement of pins generates a distribution of the drop probability for all of the columns. This problem was considered by generating uniform distributions. Previous studies have demonstrated that the (1/2a)-uniform distribution is possible for a∈{0,1,2,3,4} and is conjectured so that it is possible for any positive integer a. This study describes the constructive proof for this conjecture. This study also formalizes a natural decision problem yielded by this model while investigating its computational complexity. More precisely, given any drop-probability distribution A and any partial drop-probability distribution B, this study uses non-deterministic polynomial-time (NP) hardness to determine if there exists a pin arrangement that transforms A into B.
更新日期:2020-05-22

 

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