The Two-Dimensional Asymmetric Gambler's Ruin Problem with n Players and Simulations

In this article, the asymmetric n-player gambler's ruin problem is considered, when the players use equal initial fortunes of d dollars and d euros, 1 ≤ d ≤ n + 1. In each round an unfair coin is tossed to decide the currency. The expected ruin time and the individual ruin probabilities are computed. It is proved that the ruin time and which player is ruined are independent events. Finally, some special games are simulated. The simulation results verify the validity of the proposed formulas. As an innovation, the present study makes a combination of the n-player and multi dimensional games which can be viewed as a starting point for future studies.     

Teachers' Theory‐of‐mind Coaching and Children's Executive Function Predict the Training Effect of Sociodramatic Play on Children's Theory of Mind

Theory of mind (ToM), the ability to interpret one's own and others' mental states, is essential for social interaction; thus, it is important to promote the early development of ToM. The current study investigated (1) whether sociodramatic play (SDP) promotes the development of ToM in kindergarten children; (2) whether teachers' ToM coaching, as well as children's individual differences in language and executive function (EF), may influence how children benefit from SDP; and (3) whether SDP improves children's development in language and EF. Seventy‐one kindergarteners (M age = 60.2 months, SD = 5.7) divided into 12 groups were randomly assigned to three conditions: free play, SDP, or SDP + ToM coaching. Each condition included four weekly sessions, 45 min per session. Before and after the training, children's ToM, language and EF were measured. The results showed that after children's individual differences in ToM were considered, (1) SDP positively predicted children's post‐test ToM; (2) teachers' ToM‐related guidance during SDP and children's pretest EF positively predicted the training effect of SDP on children's ToM; (3) teachers' ToM‐related guidance during SDP, but not SDP alone, predicted children's post‐test language; and (4) neither SDP nor teachers' ToM‐related guidance during SDP predicted children's post‐test EF.     

Subtypes of Nonsocial Play and Psychosocial Adjustment in Malaysian Preschool Children

This study examined subtypes of nonsocial play and their relation to psychosocial adjustment in Malaysian preschool children (N = 141, 72 boys, M age = 4.65 years). Confirmatory factor analyses revealed that a three‐factor model that distinguished social reticence, solitary‐active play, and solitary‐passive play fit the data reasonably well, and also fit the data better than the alternative one‐ and two‐factor models. The distinction among the three subtypes of nonsocial play was found for both boys and girls. Controlling for children's age, gender, and parents' education, social reticence was related to teachers' ratings of anxious behavior, unsociability, and peer exclusion. Solitary‐active play was associated with parents' ratings of inattentiveness, child difficultness, and teachers' ratings of hyperactivity–distractibility. Solitary‐passive play was related to teachers' ratings of unsociability. The findings provide support for a multidimensional view of nonsocial play in Malaysian children.     

Two Competing Models of How People Learn in Games

Reinforcement learning and stochastic fictitious play are apparent rivals as models of human learning. They embody quite different assumptions about the processing of information and optimization. This paper compares their properties and finds that they are far more similar than were thought. In particular, the expected motion of stochastic fictitious play and reinforcement learning with experimentation can both be written as a perturbed form of the evolutionary replicator dynamics. Therefore they will in many cases have the same asymptotic behavior. In particular, local stability of mixed equilibria under stochastic fictitious play implies local stability under perturbed reinforcement learning. The main identifiable difference between the two models is speed: stochastic fictitious play gives rise to faster learning.     

The Maximum Throughput on a Golf Course

We develop stochastic models to help manage the pace of play on a conventional 18‐hole golf course. These models are for group play on each of the standard hole types: par‐3, par‐4, and par‐5. These models include the realistic feature that k−2 groups can be playing at the same time on a par‐k hole, but with precedence constraints. We also consider par‐3 holes with a “wave‐up” rule, which allows two groups to be playing simultaneously. We mathematically determine the maximum possible throughput on each hole under natural conditions. To do so, we analyze the associated fully loaded holes, in which new groups are always available to start when the opportunity arises. We characterize the stationary interval between the times successive groups clear the green on a fully loaded hole, showing how it depends on the stage playing times. The structure of that stationary interval evidently can be exploited to help manage the pace of play. The mean of that stationary interval is the reciprocal of the capacity. The bottleneck holes are the holes with the least capacity. The bottleneck capacity is then the capacity of the golf course as a whole.     

以游戏为中心的幼儿园课程：“课程游戏化”与“游戏

"“课程游戏化”与“游戏课程化”作为当前学前教育深化发展与幼儿园课程改革推进的代表性理论主张，二者同源、异构， 同趣、共建，是幼儿园课程与游戏有机融合、构建以游戏为中心的幼儿园课程的有益尝试与大胆探索。展望未来，可尝试从推 进幼儿园教育教学的三重重心转向、优化幼儿园课程体系的三度生长空间、搭建幼儿园内生发展的三维教研体系，切实推进构 建以游戏为中心的幼儿园课程与教育生活的实践进程。"