Department of Decision Sciences, NUS Business School, National University of Singapore, Singapore, Singapore.
J Gambl Stud. 2009 Dec;25(4):503-21. doi: 10.1007/s10899-009-9145-9. Epub 2009 Jul 30.
In fixed-odds numbers games, the prizes and the odds of winning are known at the time of placement of the wager. Both players and operators are subject to the vagaries of luck in such games. Most game operators limit their liability exposure by imposing a sales limit on the bets received for each bet type, at the risk of losing the rejected bets to the underground operators. This raises a question--how should the game operator set the appropriate sales limit? We argue that the choice of the sales limit is intimately related to the ways players select numbers to bet on in the games. There are ample empirical evidences suggesting that players do not choose all numbers with equal probability, but have a tendency to bet on (small) numbers that are closely related to events around them (e.g., birth dates, addresses, etc.). To the best of our knowledge, this is the first paper to quantify this phenomenon and examine its relation to the classical Benford's law. We use this connection to develop a choice model, and propose a method to set the appropriate sales limit in these games.
在固定赔率的博彩游戏中，下注时就已经确定了奖品和获胜的赔率。在这种游戏中，玩家和运营商都受制于运气的变幻莫测。为了降低因拒绝接受投注而失去业务的风险，大多数博彩运营商都会对每种投注类型的投注额设定销售限制，从而限制自身的责任风险。这就引出了一个问题——博彩运营商应该如何设定合适的销售限制？我们认为，销售限制的选择与玩家在游戏中选择投注号码的方式密切相关。有大量的经验证据表明，玩家不会以均等的概率选择所有号码，而是倾向于投注（小）号码，这些号码与他们周围的事件密切相关（例如，出生日期、地址等）。据我们所知，这是第一篇量化这种现象并研究其与经典本福德定律关系的论文。我们利用这种联系建立了一个选择模型，并提出了一种在这些游戏中设置适当销售限制的方法。
