Skill Rating by Bayesian Inference

Systems Engineering often involves computer modelling the behaviour of proposed systems and their components. Where a component is human, fallibility must be modelled by a stochastic agent. The identification of a model of decision-making over quantifiable options is investigated using the game-domain of Chess. Bayesian methods are used to infer the distribution of players’ skill levels from the moves they play rather than from their competitive results. The approach is used on large sets of games by players across a broad FIDE Elo range, and is in principle applicable to any scenario where high-value decisions are being made under pressure.

Gentlemen, stop your engines!

For fifty years, computer chess has pursued an original goal of Artificial Intelligence, to produce a chess-engine to compete at the highest level. The goal has arguably been achieved, but that success has made it harder to answer questions about the relative playing strengths of man and machine. The proposal here is to approach such questions in a counter-intuitive way, handicapping or stopping-down chess engines so that they play less well. The intrinsic lack of man-machine games may be side-stepped by analysing existing games to place computer engines as accurately as possible on the FIDE ELO scale of human play. Move-sequences may also be assessed for likelihood if computer-assisted cheating is suspected.

Understanding distributions of chess performances

This paper presents evidence for several features of the population of chess players, and the distribution of their performances measured in terms of Elo ratings and by computer analysis of moves. Evidence that ratings have remained stable since the inception of the Elo system in the 1970’s is given in several forms: by showing that the population of strong players fits a simple logistic-curve model without inflation, by plotting players’ average error against the FIDE category of tournaments over time, and by skill parameters from a model that employs computer analysis keeping a nearly constant relation to Elo rating across that time. The distribution of the model’s Intrinsic Performance Ratings can hence be used to compare populations that have limited interaction, such as between players in a national chess federation and FIDE, and ascertain relative drift in their respective rating systems.

Skilloscopy: Bayesian modeling of decision makers' skill

This paper proposes and demonstrates an approach, Skilloscopy, to the assessment of decision makers. In an increasingly sophisticated, connected and information-rich world, decision making is becoming both more important and more difficult. At the same time, modelling decision-making on computers is becoming more feasible and of interest, partly because the information-input to those decisions is increasingly on record. The aims of Skilloscopy are to rate and rank decision makers in a domain relative to each other: the aims do not include an analysis of why a decision is wrong or suboptimal, nor the modelling of the underlying cognitive process of making the decisions. In the proposed method a decision-maker is characterised by a probability distribution of their competence in choosing among quantifiable alternatives. This probability distribution is derived by classic Bayesian inference from a combination of prior belief and the evidence of the decisions. Thus, decision-makers’ skills may be better compared, rated and ranked. The proposed method is applied and evaluated in the gamedomain of Chess. A large set of games by players across a broad range of the World Chess Federation (FIDE) Elo ratings has been used to infer the distribution of players’ rating directly from the moves they play rather than from game outcomes. Demonstration applications address questions frequently asked by the Chess community regarding the stability of the Elo rating scale, the comparison of players of different eras and/or leagues, and controversial incidents possibly involving fraud. The method of Skilloscopy may be applied in any decision domain where the value of the decision-options can be quantified.

Chess endgame news

This note defines what it means by the 'chess endgame' and looks at the frequency of sub-n-man and 'FinalGen' positions in games and studies and in the FIDE 2013 World Cup. It includes the exposition of the DTM-minimaxing line from one of the three DTM-deepest known (KQPKRBN) positions. It refines the definitions of 'longest game' and 'bionic game'. The games of the FIDE 2013 World Cup and the longest known decisive game are available here.

Chess Endgame News

This paper notes FIDE's 75-move rule (9.6b) and suggests some implications. It reviews two endgame-table initiatives associated with the 50-move rule. One is Huntington's mainly sub-6-man multi-valued DTM50 EGTs implemented in HASKELL. The other is Ronald de Man's WDL' and DTZ50' EGTs which introduce a 5-way evaluation of positions, and ascribe a depth to decisive positions which are not 50-move-rule wins or losses. There is also some first detail about the Lomonosov '7-man DTM EGT' team, and comments on reactions to 'Haworth's Law'.

Chess Endgame News

The DTZ metric indicates the minimaxed 'Depth To Zeroing of the ply-count' for decisive positions. Ronald de Man's DTZ50' metric is a variant of the DTZ metric as moderated by the FIDE 50-move draw-claim rule. DTZ50'-depths are given to '50-move-rule draws' as well as to unconditionally decisive positions. This note defines a two-dimensional taxonomy of positions implicitly defined by DTZ50'. 'Decisive' positions may have values of (wins/losses) v =1/-1 or v = 2/-2. A position's depth in the new DTZ50' metric may be greater than, equal to or less than its DTZ depth. The six parts of the taxonomy are examined in detail, and illustrated by some 40 positions and 16 lines. Positions, lines and the annotation of these lines are supplied in the ancillary data files.

Depth to mate and the 50-move rule

The most popular endgame tables (EGTs) documenting ‘DTM’ Depth to Mate in chess endgames are those of Eugene Nalimov but these do not recognise the FIDE 50-move rule ‘50mr’. This paper marks the creation by the first author of EGTs for sub-6-man (s6m) chess and beyond which give DTM as affected by the ply count pc. The results are put into the context of previous work recognising the 50mr and are compared with the original unmoderated DTM results. The work is also notable for being the first EGT generation work to use the functional programming language HASKELL.

A comparative review of skill assessment: performance, prediction and profiling

The assessment of chess players is an increasingly attractive opportunity and an unfortunate necessity. The chess community needs to limit potential reputational damage by inhibiting cheating and unjustified accusations of cheating: there has been a recent rise in both. A number of counter-intuitive discoveries have been made by benchmarking the intrinsic merit of players’ moves: these call for further investigation. Is Capablanca actually, objectively the most accurate World Champion? Has ELO rating inflation not taken place? Stimulated by FIDE/ACP, we revisit the fundamentals of the subject to advance a framework suitable for improved standards of computational experiment and more precise results. Other domains look to chess as the demonstrator of good practice, including the rating of professionals making high-value decisions under pressure, personnel evaluation by Multichoice Assessment and the organization of crowd-sourcing in citizen science projects. The ‘3P’ themes of performance, prediction and profiling pervade all these domains.

AFM analysis of bleaching effects on dental enamel microtopography

The purpose of this in vitro study was to test a new methodology to evaluate the effects of 35% hydrogen peroxide agent on the microtopography of sound enamel using an atomic force microscope (AFM). The buccal sound surfaces of three extracted human lower incisors were used, without polishing the surfaces to maintain them with natural morphology. These unpolished surfaces were subjected to bleaching procedure with 35% hydrogen peroxide that consisted of 4 applications of the bleaching agent on enamel surfaces for 10 min each application. Surface images were obtained in a 15 mu m x 15 mu m area using an AFM. The roughness (Ra and RMS) and the power spectral density (PSD) were obtained before and after the bleaching treatment. As results we could inquire that the PSD analyses were very suitable to identifying the morphological changes on the surfaces, while the Ra and RMS parameters were insufficient to represent the morphological alterations promoted by bleaching procedure on enamel. The morphological wavelength in the range of visible light spectrum(380-750 nm) was analyzed, showing a considerable increase of the PSD with the bleaching treatment. (C) 2009 Elsevier B. V. All rights reserved.

Stability of periodic travelling shallow-water waves determined by Newton`s equation

We study the existence and stability of periodic travelling-wave solutions for generalized Benjamin-Bona-Mahony and Camassa-Holm equations. To prove orbital stability, we use the abstract results of Grillakis-Shatah-Strauss and the Floquet theory for periodic eigenvalue problems.

Ostracoda from Lee Point on Shoal Bay, Northern Australia: part 3, podocopina (cytheracea)

The littoral environments present in Shoal Bay, Northern Territory (Australia) show a high diversity of ostracods cytheráceos (51 genera and 97 species). Probably this diversity is due to three factors: (1) marine environments warm and well oxygenated leading to a high level of biological productivity, (2) shallow marine environments favorable for the accumulation of material conchífero post mortem, and (3) a location central in the way of dispersal on the continental shelf between the regions of the Pacific and Southeast Asia. A particular feature of this fauna Cytherscea is that some genres, such as Alocopocythere, can be traced back to the Cretaceous when it first appeared in the shallow waters of the Tethys. In this overlay component of the ancient ostracods are the dominant fauna in partnerships of the modern Indo / Pacific, such as gender Keiji. While the Cytheracea ostracods are the dominant groups, especially the Cypridacea marine Bairdiacea and Plstycopina, are well represented and are quite different (fide Whatley et al., 1995, 1996). We describe here a new genre, Paraxestoleberis, and 15 new species: Dentibyíhere multituberosa, Dampiercythere papillolineata, Neocyíheromorpha papilloporosa, Loxoconcha catasíeros, Semicyrherura gamma, Callistocyíhere cookei, Loxocorniculum koolpionyahensis, Keúia interim, K. profundosculpia, K. parademissa, Quasibradleya leepoiníensis, Actinocyíhereis gippsi, Henryhowella sinespinosa, Poníicocyíhereis spatulospinosa and Paraxestoleberis posteroacuminata. Due to the limited material obtained, 16 species are kept in open nomenclature: Bythoceratina sp. Corallicyíhere sp. Venericythere sp. Tanella sp. Loxocorniculum sp. 1 L. sp. 2, Gambiella sp. Javanella sp. Paradoxostoma sp. Neomonoceratina sp., Bradley (sl) sp. Echinocytbereis (sl) sp. Plaíycyíhereis? sp. Alocopocyíhere sp. Xestoleberis sp. and Paraxestoleberis sp. The remaining 66 species have been described previously in other areas.

Economic impact of advanced pediatric cancer on families

Despite emerging evidence of substantial financial distress in families of children with complex illness, little is known about economic hardship in families of children with advanced cancer.