A simulation study of Texas hold 'em poker: what Taylor Swift understands and James Bond doesn't

Recent years have seen a large increase in the popularity of Texas hold ’em poker. It is now the most commonly played variant of the game, both in casinos and through online platforms. In this paper, we present a simulation study for games of Texas hold ’em with between two and 23 players. From these simulations, we estimate the probabilities of each player having been dealt the winning hand. These probabilities are calculated conditional on both partial information (that is, the player only having knowledge of his/her cards) and also on fuller information (that is, the true probabilities of each player winning given knowledge of the cards dealt to each player). Where possible, our estimates are compared to exact analytic results and are shown to have converged to three significant figures. With these results, we assess the poker strategies described in two recent pieces of popular culture. In comparing the ideas expressed in Taylor Swift’s song, New Romantics, and the betting patterns employed by James Bond in the 2006 film, Casino Royale, we conclude that Ms Swift demonstrates a greater understanding of the true probabilities of winning a game of Texas hold ’em poker. doi:10.1017/S144618111800015

Two FEM-BEM methods for the numerical solution of 2D transient elastodynamics problems in unbounded domains

We consider wave propagation problems in 2D unbounded isotropic homogeneous elastic media, with rigid boundary conditions. For their solution, we propose and compare two alternative numerical approaches, both obtained by coupling the differential equation with the associated space-time boundary integral equation. The latter is defined on an artificial boundary, chosen to surround the (bounded) exterior computational domain of interest. The integral equation defines a boundary condition which is non-reflecting for incoming and also for outgoing waves. In both approaches, the differential equations are discretized by applying a finite element method combined with the Crank Nicolson time marching scheme, while the discretization of the integral equation is obtained by coupling a time convolution quadrature with a space collocation boundary element method. The construction of the two approaches is described and discussed. Some numerical tests are also presented

Next generation water efficiency: looking over the horizon

After major investment during the Millennium drought, many Australian cities have become more resilient by diversifying their water supplies with desalination, water recycling, rain tanks, and importantly, increased water efficiency through both programs and regulations. The achievements in efficiency such as reduced per capita demand and success of large-scale demand management programs, are internationally recognised. However, with both Sydney and Melbourne heading towards mega-city status by mid-century, further increases in efficiency must be considered. This paper explores the technologies, behavioural interfaces and programs that could aid Australia’s next generation of water efficiency

CVEM-BEM Coupling with Decoupled Orders for 2D Exterior Poisson Problems

For the solution of 2D exterior Dirichlet Poisson problems, we propose the coupling of a Curved Virtual Element Method (CVEM) with a Boundary Element Method (BEM), by using decoupled approximation orders. We provide optimal convergence error estimates, in the energy and in the weaker L-2-norm, in which the CVEM and BEM contributions to the error are separated. This allows for taking advantage of the high order flexibility of the CVEM to retrieve an accurate discrete solution by using a low order BEM. The numerical results confirm the a priori estimates and show the effectiveness of the proposed approach

The bathroom of the future - prospects for information and control

Across sectors, innovative data collection at a device level and command and control appliances, are providing an opportunity for improved resource efficiencies, facilities management and user experiences. The applications of intelligent technologies and localised networks are growing rapidly. This discussion paper demonstrates the value and potential applications of smart water management technologies specifically focused on commercial bathroom products. The work was commissioned by the GWA Bathrooms and Kitchens Group. The paper has been developed using available knowledge, with a literature scan of fixture driven innovations, innovations in collecting and using data from fixtures and other monitoring devices

Terra e rendite nei secoli XII-XIII: Normandia, Inghliterra, Terrasanta.

Land and revenue in the Twelfth and Thirteenth Century: Normandy, England, the Holy Land Thanks to the documentation made available by the “Patrologia Latina” database, the author has managed to reconstruct the legal-institutional profile of the concessions ad firmam and their socio-economic contexts from the twelfth to the thirteenth centuries in Normandy, England, and the Holy Land. These agrarian contracts have usually escaped scholarly attention and are intriguing for their connection with the contractus censualis and the census reservativus, a legal institution present throughout the modern age and which played an important role in the revolutionaryn. M e d i t e r r a n e a R i c e r c h e s t o r i c h e Anno VII - Aprile 201

Strategies for Imputation of High-Resolution Environmental Data in Clinical Randomized Controlled Trials.

Time series data collected in clinical trials can have varying degrees of missingness, adding challenges during statistical analyses. An additional layer of complexity is introduced for missing data in randomized controlled trials (RCT), where researchers must remain blinded between intervention and control groups. Such restriction severely limits the applicability of conventional imputation methods that would utilize other participants' data for improved performance. This paper explores and compares various methods to impute high-resolution temperature logger data in RCT settings. In addition to the conventional non-parametric approaches, we propose a spline regression (SR) approach that captures the dynamics of indoor temperature by time of day that is unique to each participant. We investigate how the inclusion of external temperature and energy use can improve the model performance. Results show that SR imputation results in 16% smaller root mean squared error (RMSE) compared to conventional imputation methods, with the gap widening to 22% when more than half of data is missing. The SR method is particularly useful in cases where missingness occurs simultaneously for multiple participants, such as concurrent battery failures. We demonstrate how proper modelling of periodic dynamics can lead to significantly improved imputation performance, even with limited data