Testing for dice control at craps
Abstract
Dice control involves "setting" the dice and then throwing them in a careful way, 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 $\theta\in[0,1]$, 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 $H_0:\theta = 0$ (no control) versus $H_1:\theta > 0$ (some control). We also want to test $H_0:\theta\le\theta_0$ versus $H_1:\theta>\theta_0$, where $\theta_0$ is the "break-even point." For the tests considered we estimate the power, either by normal approximation or by simulation.