Outcome Of Game Research Articles

Mathematical Principles in Texas Hold'em Poker

Texas Hold'em is a skill and strategy game that combines elements of probability, combinatorics, and game theory. This paper explores the mathematical principles behind the game, with a focus on applying probability theory to decision-making and strategy development. Analyzing the win rates of various hand rankings, the expected value of different playstyles, and the impact of player behavior on game outcomes. By applying combinatorial analysis, we calculate the probability of hand strength and assess the strategic significance of bluffing and betting patterns. Additionally, we study game theory concepts such as Nash equilibrium and apply them to poker strategy. The most significant section is game theory. The insights gained from this mathematical approach provide a comprehensive understanding of optimal play and how mathematical rigor enhances decision-making in Texas Hold'em. This research can help us calculate the probability of our hand based on its strength, thereby improving our sensitivity to probability-based problems

ClaG: A classification system for plays and games in toy libraries and libraries

The paper presents ClaG, a novel classification system for plays and games created for the Archivio Italiano del Gioco (AIG) [Italian Games Archive], Udine, Italy. The primary goal of the classification system is to serve as a practical tool for highlighting the characteristics of a game that are useful for the selection, research, identification, and delivery of a game, or a set of games, to a player or group of players using a game library or a library with a game collection. This objective guided all the decisions in its construction. The identification of the main relevant concepts was based on a twofold approach: a top-down strategy, by the identification of general concepts from specialized literature on play and game, and a bottom-up strategy, involving the recursive application and modification of these concepts to classify a set of 200 games (mainly table and board games). The paper elucidates the five fundamental concepts that underpin the construction of this classification: space, materials, setting, game outcome, and genre and provides a comprehensive overview of the classification system. To evaluate the classification system's effectiveness, it was presented twice to a panel of experts who appreciated it and offered suggestions for improvement. The results indicate that the resulting classes are very small, each containing only a few items. Finally, the paper discusses prospects for the future development and use of the classification system.

On predicting an NBA game outcome from half-time statistics

Predicting the outcome of an NBA game is a major concern for betting companies and individuals who are willing to bet. We attack this task by employing various advanced machine learning algorithms and techniques, utilizing simple half-time statistics from both teams. Data collected from 3 seasons, from 2020/21 up to 2022/23 were used to assess the predictive performance of the algorithms at two axes. For each season separately, apply the algorithms and estimate the outcomes of the games of the same season and secondly, apply the algorithms in one season and estimate the outcomes of the games in the next season. The results showed high levels of accuracy as measured by the area under the curve. The analysis was repeated after performing variable selection using a non-linear algorithm that selected the most important half-time statistics, while retaining the predictive performance at high levels of accuracy.

Educational outcomes of digital serious games in nursing education: a systematic review and meta-analysis of randomized controlled trials

BackgroundAdvancements in digital technologies and the coronavirus disease pandemic have rapidly shifted educational practices towards engaging digital methods, such as serious games, significantly influencing healthcare education. Digital serious games enhance nursing education by effectively overcoming limitations such as limited training time and inadequate resources, thereby improving knowledge and skills. Few high-quality systematic reviews and meta-analyses were focused exclusively on randomized controlled trials (RCTs) of digital serious games to determine their effects in nursing education.ObjectiveTo evaluate the effects of digital serious games on nursing education through a systematic review and meta-analysis using the Kirkpatrick model to evaluate learning and behavioral changes.MethodsA systematic review and meta-analysis of RCTs was performed. Six databases were searched for articles published before April 2024. Risk of bias was assessed using the Revised Cochrane Risk of Bias tool for randomized trials. A sensitivity analysis was performed. Outcome variables were categorized according to the Kirkpatrick model. Effect sizes were determined using Hedges’ g in a random-effects model. Subgroup analysis was performed.ResultsThe quality appraisal results revealed that all the studies exhibited a low risk of bias across these domains. Eleven studies were included in the systematic review, and eight studies, in the meta-analysis. The intervention group showed significant improvements in knowledge (Hedges’ g = 0.75, 95% confidence interval (CI) = [0.27, 1.22], p = .002, I² = 90.51%), confidence (Hedges’ g = 0.73, 95% CI = [0.23, 1.24], p = .005, I² = 82.71%), and performance (Hedges’ g = 0.49, 95% CI = [0.17, 0.80], p = .003, I² = 56.60%). Subgroup analysis showed a significant improvement in knowledge when the intervention period exceeded 2 weeks (Hedges’ g = 0.53, 95% CI = [0.32, 0.74], p < .001, I² = 25.41%).ConclusionThis study demonstrates that digital serious games significantly enhance knowledge, performance, and confidence of nursing students, offering a valuable alternative to traditional methods and equipping them with essential clinical competencies. However, the observed high heterogeneity and limitations like brief intervention durations necessitate caution in result interpretation and highlight the need for further research to explore long-term effects and behavioral changes in nursing education.

Threshold Protocol Game on Graphs with Magic Square-Generalization Labelings

Graphical games describe strategic interactions among a specified network of players. The threshold protocol game is a graphical game that models the adoption of a lesser-used product in a population when individuals benefit by using the same product. The threshold protocol game has historically been considered using infinite, simple graphs. In general, however, players might value some relationships more than others or may have different levels of influence in the graph. These traits are described by weights on graph edges or vertices, respectively. Relative comparisons on arbitrarily weighted graphs have been studied for a variety of graphical games. Alternatively, graph labelings are functions that assign values to the edges and vertices of graphs based on a particular set of rules. This work demonstrates that the outcome of the threshold protocol game can be characterized on a magic square-generalization labeled graph. There are a variety of graph labelings that generalize the concept of magic squares. In each, the labels on similar sets of graph elements sum to a constant. The constant sums of magic square-generalization labelings mean that each player experiences a constant level of influence without needing to specify the value of players relative to one another. The game outcome is compared across different types and features of labelings.

End Behavior of the Threshold Protocol Game on Complete and Bipartite Graphs

The threshold protocol game is a graphical game that models the adoption of an idea or product through a population. There are two states players may take in the game, and the goal of the game is to motivate the state that begins in the minority to spread to every player. Here, the threshold protocol game is defined, and existence results are studied on infinite graphs. Many generalizations are proposed and applied. This work explores the impact of graph topology on the outcome of the threshold protocol game and consequently considers finite graphs. By exploiting the well-known topologies of complete and complete bipartite graphs, the outcome of the threshold protocol game can be fully characterized on these graphs. These characterizations are ideal, as they are given in terms of the game parameters. More generally, initial conditions in terms of game parameters that cause the preferred game outcome to occur are identified. It is shown that the necessary conditions differ between non-bipartite and bipartite graphs because non-bipartite graphs contain odd cycles while bipartite graphs do not. These results motivate the primary result of this work, which is an exhaustive list of achievable game outcomes on bipartite graphs. While possible outcomes are identified, it is noted that a complete characterization of when game outcomes occur is not possible on general bipartite graphs.

What Can we Learn About Human Nature from Interacting with Strangers? Relationship Type Determines Behavior in the Dictator Game

Behavioral decision-making research has been exceptionally useful in the quest of the social sciences to understand human nature. A frequent assumption of this research is that using strangers as anonymous interaction partners allows for the clearest demonstration of basic human nature. But a diverse array of literature – from social and clinical psychology to ethology – suggests that a stranger is far from a “baseline partner.” We argue against the overreliance on strangers in economic games and that instead of one baseline partner, typical relationships should fall into basic types of partners, all eliciting different behaviors. Two high-powered experiments (Ns = 848 and 2400) in which participants played a hypothetical dictator game with one of sixteen partners (e.g., mother, friend, stranger) found particular clusters of interaction partners in which the possible partners were grouped into different and intuitively meaningful relationship types (i.e., loved ones, intimate partners, companions, contractual partners, infrahumanized others). The clusters suggest a typology of basic human relationships and predict behavior even when controlling for relationship distance. The findings help to calibrate the outcomes of past dictator games utilizing strangers and offer an interpretative context with a system of relationship types.

Development and Application of a Body Joint Angle Detection System for Free-Throw Shooting Prediction and Posture Correction

The success rate of free-throw shooting is often a critical factor in determining game outcomes. This study employs machine learning to develop a low-cost, hardware-free joint angle measurement system for free-throw shooting and applies it to the scientific training of free-throw shooting skills. With the system, the joint angle curves of players can be measured without the need for reflective markers, thereby reducing setup costs and facilitating the integration of scientific training. This study presents several innovative features. The experimental results indicate that the amount of training data required for modeling is 50% of that required by the J48 decision tree classifier, with an accuracy 1.2 times higher. Additionally, when a shot is missed, the system compares the disparity in joint angles and provides feedback for posture correction, allowing players to target specific problem areas for training, improve free-throw performance, and assist the team in winning games.

Models and Rating Systems for Head-to-Head Competition

One of the most important tasks in sports analytics is the development of binary response models for head-to-head game outcomes to estimate team and player strength. We discuss commonly used probability models for game outcomes, including the Bradley–Terry and Thurstone–Mosteller models, as well as extensions to ties as a third outcome and to the inclusion of a home-field advantage. We consider dynamic extensions to these models to account for the evolution of competitor strengths over time. Full likelihood-based analyses of these time-varying models can be simplified into rating systems, such as the Elo and Glicko rating systems. We present other modern rating systems, including popular methods for online gaming, and novel systems that have been implemented for online chess and Go. The discussion of the analytic methods are accompanied by examples of where these approaches have been implemented for various gaming organizations, as well as a detailed application to National Basketball Association game outcomes.

Optimal private payoff manipulation against commitment in extensive-form games

Stackelberg equilibrium describes the optimal strategies of a player, when she (the leader) first credibly commits to a strategy. Her opponent (the follower) will best respond to her commitment. To compute the optimal commitment, a leader must learn enough follower's payoff information. The follower can then potentially provide fake information, to induce a different final game outcome that benefits him more than when he truthfully behaves.We study such follower's manipulation in extensive-form games. For all four settings considered, we characterize all the inducible game outcomes. We show the polynomial-time tractability of finding the optimal payoff function to misreport. We compare the follower's optimal attainable utilities among different settings, with the true game fixed. In particular, one comparison shows that the follower gets no less when the leader's strategy space expands from pure strategies to behavioral strategies. Our work completely resolves this follower's optimal manipulation problem on extensive-form game trees.

Three‐body confrontation differential game for an aggressive attacker

AbstractIn this work, we study the three‐body confrontation differential game, in which an Attacker attempts to capture a Target while a Defender guards the latter. We decompose the three‐body game into two subgames based on the game of kind theory: the included angle game and the distance ratio game. By integrating the Apollonius circle with these subgames, we define the semipermeable surface and infer the optimal guidance strategies for the three players on this surface. Unlike existing methods, our method effectively addresses the coupling relationship between the target, defender, and attacker, resulting in greater applicability. Based on the derived semipermeable surface, the conditions for the three players to win the game are also presented. These winning conditions are comprehensively considered from both lines of sight, including the angle and the ratio between the Attacker–Target distance and the Attacker–Defender distance, thereby providing a game solution through an analysis of the players' dynamics. From the perspective of viewing angle ratio, our method bridges the gap in the viewing angle game outcomes compared to existing methods. To demonstrate the effectiveness of our method, we provide simulation examples that illustrate the three‐body confrontation game in various scenarios.

No Player Left Behind: Evolving Dungeons and Dragons Combat to Optimize Difficulty and Player Contributions

Creating well-balanced combat encounters can be a difficult task for Game Managers (GMs) in tabletop games such as Dungeons and Dragons (DnD). This work uses a simulation environment to generate new sets of DnD encounters that can be optimized for both difficulty and balance among player contributions. Encounters are evaluated using simulated games that can either be run probabilistically (using dice rolls) or with deterministic expected outcomes. While the expected approach allows game outcomes to be simulated substantially faster and is a good estimate of difficulty, it is a less reliable measure of balance. A genetic algorithm was used to generate encounters that meet the desired difficulty and where all players are needed for success.

Collective Action for Sustainable Farmer Water Management: The Case of the KILIMO NA MAJI Serious Game

Background Farmers in water scarce landscapes adapt in response to the erratic weather conditions. Adaptation through irrigation, depend on water access, while impacting on downstream water availability. Competition for scarce water commons among multiple users defines a collective action problem. Farmer land-, and water-use decisions are based on both economic rationality of cost-benefit expectations, and relational rationality of reconciling conflicting opinions of important person(s) in a farmer’s social world, such as other water users, government, or spirits. Serious games that represent this duality of choices can help both players and interested others to analyze how social relations influence farmer decision-making. Intervention Here we describe the generic design and early experiences with specific use of the KILIMO NA MAJI game. The game is designed to analyse effect of social relations as farmers individually and/or collectively explore alternative options for crop production in scarce water commons. Methods We designed and applied the game in the Mt. Kenya region; a semi-arid region, ranging across a gradient of upstream water abundance to downstream water scarcity. The design of the game was informed by literature, and information from local stakeholders. We analyzed data from the pilot game sessions to assess quality and effectiveness of the game using Likert scale and a ‘solution space’ which defines a bandwidth around the mean where tradeoffs between farm-income and water-use can be partially managed. Results Playing the game with local stakeholders showed that social relations that participants had with traders, agro-export companies and other important persons determined where their game outcomes were positioned within the solution space. Conclusion Playing KILIMO NA MAJI can help assess influence of social relations and support collective exploration of alternatives to crops production in water scarce landscapes.

Penerapan Algoritma Backpropagation dalam Memprediksi Kemenangan dalam Bermain Mobile Legends

Victory in Mobile Legends is influenced by various factors, such as player skills, strategy, and character selection. To predict game outcomes, the backpropagation algorithm is applied to process historical gameplay data and create an accurate predictive model. This study aims to apply the backpropagation algorithm to predict victory based on player attributes, including team role, experience level, and past performance. The research method involves training and testing the model using data from multiple gameplay sessions with varied outcomes. Findings show that the backpropagation algorithm can predict game results with high accuracy, especially when the data includes a more comprehensive range of attributes. The implications of this study suggest that a backpropagation-based predictive model can help players understand their chances of winning and optimize their gameplay strategies. Furthermore, future developments in this algorithm could provide benefits for similar applications in other digital gaming fields.

Analysis of GPS and collision metrics during ball in play to identify positional key performance indicators and their prediction on game outcome in professional rugby union.

Analysis of GPS and collision metrics during ball in play to identify positional key performance indicators and their prediction on game outcome in professional rugby union.

W-system: A system to understand words in Wordle

Abstract Wordle is a popular puzzle game where players share their daily scores on Twitter. Based on this data, we developed a W-system to analyze and predict Wordle game outcomes, providing insights for further game development. The number of reported results varies daily. To explain this variation, we first cleaned the data reported on Twitter and performed autocorrelation and ADF tests, revealing that the series was not stationary. After performing first-order differencing, we confirmed stationarity. Using the AIC criterion, we determined that the ARIMA (1, 1, 0) model was optimal. We performed residual and LB tests, and then predicted the number of reports for the next 60 days, identifying a decreasing trend. Additionally, we investigated whether any attributes of the words affected the percentage of scores reported in Hard Mode using a random forest model. We found that certain vowels, such as A and E, made words easier, while I and O made words harder. To predict the distribution of reported results for a given future solution word, we designed a 24-5-7 fully connected neural network. The input layer consists of a 24-dimensional vector representing letter occurrences, the hidden layer has five neurons, and the output layer is a 7-dimensional vector representing the distribution of scores. We trained the model using MSE error and the Adam optimizer, achieving a final test set loss of 7.22, indicating good generalization ability. For example, for the word EERIE on March 1, 2023, the model predicted distribution with reasonable confidence, accounting for associated uncertainties. We also developed a model to classify solution words by difficulty. We identified eight attributes of words and used the Analytic Hierarchy Process (AHP) to assign weights to each feature. Applying the k-means clustering algorithm, we classified 355 words into three categories: easy, medium, and hard. Using our model, the word EERIE was classified as medium difficulty. We validated our model by plotting a two-dimensional clustering scatter plot using the two features with the highest weights, showing good separation among the three categories, and indicating the accuracy of our classification model.

Quantification Analysis of Sports Momentum Based on a Multi-Index Approach and TOPSIS

This study quantifies the concept of momentum in sports, inspired by Novak Djokovic's unexpected loss in 2023, and evaluates its impact on game outcomes. Utilizing a structured multi-index approach, we categorized performance into fourteen primary and three secondary indexes. The TOPSIS model enhanced by entropy weighting, along with the Delphi model, was applied for weight assessments of these indexes. Our analysis, incorporating the Mann-Kendall trend test and Spearman correlation coefficient, revealed a significant correlation of 0.51 between momentum and match results, underscoring its pivotal role. The results contribute to a deeper understanding of momentum, enabling coaches to refine strategies and optimize performance based on dynamic changes in momentum. This study provides a comprehensive framework for quantifying momentum, with potential applications extending beyond tennis to other sports where strategic momentum management could influence outcomes.

Illusions of control: A quasi-experiment comparing skill-based and traditional slotmachines.

Electronic gaming machines (EGMs) are a significant source of gambling spend due to their widespread use. Skill-based gambling machines (SGMs) represent an innovative adaptation, merging EGMs' chance-based rewards with video game-like skills. This study aimed to explore the appeal and behavioural consequences of playing SGMs in comparison to traditional reel-based EGMs, particularly focusing on illusions of control, betting behaviour, and the subjective experience of gamblers. Participants (N = 1,260) were recruited online and engaged in an online task simulating either an SGM or a reel-based EGM, with outcomes represented to influence their survey compensation. The study examined the effect of SGMs relative to EGMs on bet size, persistence, enjoyment, illusionsofcontrol, game immersion, and the influence of demographic and gambling problem severity. SGMs particularly appealed to younger adults, regular EGM players, and people with more gambling problems. Despite identical payout structures, people assigned to play SGM showed greater illusions of control, believing in the influence of skill on game outcomes and that practice could improveresults. However, there was no significant difference in overall betting intensity between SGM and EGM players, although specific demographic groups showed faster betting speeds in SGMs. SGMs, despite not inherently encouraging higher betting intensity, attract vulnerable groups and create illusions of control, posing new regulatory challenges. The visual and interactive features of SGMs, while appealing, might contribute to these perceptions, indicating a need for careful regulation and further research on their long-term impacts on gambling behaviour and harm.

Rational Expectations Models with Higher-Order Beliefs

Abstract We develop a method of solving rational expectations models with dispersed information and dynamic strategic complementarities. In these types of models, the equilibrium outcome hinges on an infinite number of higher-order expectations which require an increasing number of state variables to keep track of. Despite this complication, we prove that the equilibrium outcome always admits a finite-state representation when the signals follow finite ARMA processes. We also show that such a finite-state result may not hold with endogenous information aggregation. We further illustrate how to use the method to derive comparative statics, characterize equilibrium outcomes in HANK-type network games, reconcile with empirical evidence on expectations, and integrate incomplete information with bounded rationality in general equilibrium.

Abuzaharen's Challenge: Building Sustainability Competencies through Science-Fiction Narratives and Game-based Learning

This paper presents a case study of the evolution of science-fiction themed game-based learning across two Masters units in a higher education course on sustainable development. The authors created three sustainability games to be played by classes in live workshop settings – a card matching game about urban challenges, a hackathon-style sustainability innovation challenge, and a systemic change analysis game - to build students’ capacity to think about systems, sustainability values, and strategies to advance positive change. The story of a bumbling, but well-intentioned, alien protagonist, Abuzaharen, serves as a dynamic backdrop to the games, which see students ‘transported’ to an alternative reality to complete time-bound challenges in a rigorous yet engaging manner in order to find their way ‘home’ to Earth. This paper documents how each game’s narrative, storytelling, design, and play evolved through multiple iterations over four years, drawing on critical reflection, evidence of engagement and student feedback. The paper also reflects on the affordances of generative artificial intelligence (GenAI) for game-based learning designers. One of the games has integrated GenAI to make Abuzaharen a real-time character in the delivery of the game, including judging student’s innovation pitches and generating live narrative content about game outcomes. The GenAI alien agent subsequently appears in ‘regular’ learning content as a course tutor. Qualitative feedback and educator observations suggest the games increased active class participation, built peer connections, fostered skills in problem-solving, promoted collaboration, and modelled creativity. The games also challenge existing narratives about negative impacts of GenAI on tertiary education by illustrating productive and creative uses of GenAI for students and educators. This paper argues that immersive, narrative-driven approaches, coupled with the strategic use of GenAI, can significantly enrich higher education for sustainability and other educational experiences by scaffolding selected competencies and applying complex concepts to real-world challenges in a light-hearted way. It concludes with practice-led insights and directions for future exploration of interest to sustainability educators, designers of interactive learning, and those experimenting with GenAI in narrative-based games.