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Keywords

craps; dice control; statistical modeling; hypothesis testing; sample-proportion test; sample-mean test; likelihood ratio test; power

Disciplines

Applied Statistics | Statistical Methodology | Statistical Models

Document Type

Original Research Article

Abstract

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 ∈ [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 H0 : θ = 0 (no control) versus H1 : θ > 0 (some control). We also want to test H0 : θ ≤ θ0 versus H1 : θ > θ0, where θ0 is the “break-even point.” For the tests considered we estimate the power, either by normal approximation or by simulation.

Funding Sources

None

Competing Interests

None

Permissions

None

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