Dice control involves "setting" the dice and then throwing them carefully, in the hope of influencing the outcomes and gaining an advantage at craps. How does one test for this ability? To specify the alternative hypothesis, we need a statistical model of dice control. Two have been suggested in the gambling literature, namely the Smith-Scott model and the Wong-Shackleford model. Both models are parameterized by $θ\in[0,1]$, which measures the shooter's level of control. We propose and compare four test statistics: (a) the sample proportion of 7s; (b) the sample proportion of pass-line wins; (c) the sample mean of hand-length observations; and (d) the likelihood ratio statistic for a hand-length sample. We want to test $H_0:θ= 0$ (no control) versus $H_1:θ> 0$ (some control). We also want to test $H_0:θ\leθ_0$ versus $H_1:θ>θ_0$, where $θ_0$ is the "break-even point." For the tests considered we estimate the power, either by normal approximation or by simulation.

翻译：骰子控制指通过特定方式'设定'骰子并谨慎投掷，以期影响结果并在双骰赌博中获得优势。如何检验这种能力？为明确备择假设，需要建立骰子控制的统计模型。赌博文献中已提出两种模型：Smith-Scott模型与Wong-Shackleford模型。两种模型均以$θ∈[0,1]$为参数，用于衡量投掷者的控制水平。本文提出并比较四种检验统计量：(a) 样本中7点出现的比例；(b) 样本中过关投注获胜的比例；(c) 手牌长度观测值的样本均值；(d) 基于手牌长度样本的似然比统计量。我们需要检验$H_0:θ=0$（无控制）与$H_1:θ>0$（存在控制），同时检验$H_0:θ≤θ_0$与$H_1:θ>θ_0$，其中$θ_0$为'盈亏平衡点'。针对所研究的检验方法，我们通过正态近似或模拟仿真对检验功效进行了估计。