arXiv:physics/0602165v1 [physics.soc-ph] 24 Feb 2006 Power-law distribution in Japanese racetrack betting Takashi Ichinomiya Nonlinear Studies and Computation, Research Institute for Electronic Science, Hokkaido University, Sapporo 060-0812, Japan. Abstract Gambling is one of the basic economic activities that humans indulge in. An inves- tigation of gambling activities provides deep insights into the economic actions of people and sheds lights on the study of econophysics. In this paper we present an analysis of the distribution of the final odds of the races organized by the Japan Racing Association. The distribution of the final odds P o (x) indicates a clear power law P o (x) ∝ 1/x, where x represents the final odds. This power law can be explained on the basis of the assumption that that every bettor bets his money on the horse that appears to be the strongest in a race. Key words: econophysics, the efficient market, scaling PACS: 02.50, 05.40, 89.75.-k 1 Introduction Since Pascal proposed the theory of probability, the phenomenon of gambling have given inspirations to many mathematicians, physicists and economists. For example, economists have studied gambling activities in order to examine the market efficiency. If bettors try to maximize their expected rewards, it would be equivalent for every race and every horse. In this case, the gambling market is efficient, and there is no assured way to gain money. Gabriel and Marsden studied market efficiency in British racetrack betting and found this gambling market to be inefficient[1]. Russo, Gandar and Zuber conducted a similar study on the National Football League betting market[2]. They found no clear indication of breakdown of efficiency. These results are re-examined Cain et al. and Ioannidis and Peel by different methods[3,4] Email address: miya@nsc.es.hokudai.ac.jp (Takashi Ichinomiya). Preprint submitted to Elsevier Science 2 February 2008