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Previous research suggests that intuitively appealing, yet uninformative unclaimed prize information is capable of biasing gambling-related judgments when people compare scratch cards that vary in the number of unclaimed prizes. However, it is unknown if the mere presence of unclaimed prize information alters a game's attractiveness. Using an online crowdsourcing platform, we recruited 402 U.S. residents to participate in an online study. In a within-subjects design, participants made four gambling-related judgments (likelihood of winning, excitement to play, urge to gamble, and hypothetical card purchasing) for scratch cards presented with and without unclaimed prize information. Compared to cards presented without unclaimed prize information, those with unclaimed prize information were judged as more likely to win, produced more excitement to play, a greater urge to gamble, and were chosen more often during a hypothetical purchasing task. Therefore, unclaimed prize information increases the appeal of scratch card games, and may be an important aspect of the scratch card gambling environment to consider from a harm reduction perspective. [ABSTRACT FROM AUTHOR]

Postmarketing safety surveillance studies address two actionable questions: (1) Is the test product riskier than a standard? (2) Is the risk associated with the test product within some tolerable margin by comparison to the standard? Established techniques, not commonly applied to the setting of such complementary one-sided hypotheses, lead to useful conclusions in practice. For two-group studies, a search over possible one-sided binomial test results yields sample sizes that guarantee that the confidence bounds exclude one or the other of the hypotheses. With continuous monitoring, simple curtailment reduces the sample size. Point and interval estimates follow from the binomial distribution of events at the end of the study or from component negative binomials for crossing a bound of simple curtailment with continuous monitoring and earlier stopping. An asymptotic derivation corresponds to the problem of constructing a confidence interval that is smaller than the distance between the parameter values for tolerable excess and the absence of excess risk. Studies with guaranteed rejection of one of the pair of complementary hypotheses are somewhat larger than corresponding studies of a single hypothesis under usual power requirements, but the increase may be tolerable in return for certainty that there will be an actionable conclusion. [ABSTRACT FROM AUTHOR]

For an integer b ⩾ 2 and a set S ⊂ { 0 , ... , b − 1 } , we define the Kempner set K (S , b) to be the set of all nonnegative integers whose base-b digital expansions contain only digits from S. These well-studied sparse sets provide a rich setting for additive number theory, and in this article we study various questions relating to the appearance of arithmetic progressions in these sets. In particular, for all b we determine exactly the maximal length of an arithmetic progression that omits a base-b digit. [ABSTRACT FROM AUTHOR]