Player Wins Research Articles

Subtraction games in more than one dimension

This paper concerns two-player alternating play combinatorial games (Conway 1976) in the normal-play convention, i.e. last move wins. Specifically, we study impartial vector subtraction games on tuples of nonnegative integers (Golomb 1966), with finite subtraction sets. In case of two move rulesets we find a complete solution, via a certain P-to-P principle (where P means that the previous player wins). Namely x∈P if and only if x+a+b∈P, where a and b are the two move options. Flammenkamp (1997) observed that, already in one dimension, rulesets with three moves can be hard to analyze, and still today his related conjecture remains open. Here, we solve instances of rulesets with three moves in two dimensions, and conjecture that they all have regular outcomes. Through several computer visualizations of outcomes of multi-move two-dimensional rulesets, we observe that they tend to partition the game board into periodic mosaics on very few regions/segments, which can depend on the number of moves in a ruleset. For example, we have found a five-move ruleset with an outcome segmentation into six semi-infinite slices. In this spirit, we develop a coloring automaton that generalizes the P-to-P principle. Given an initial set of colored positions, it quickly paints the P-positions in segments of the game board. Moreover, we prove that two-dimensional rulesets have row/column eventually periodic outcomes. We pose open problems on the generic hardness of two-dimensional rulesets; several regularity conjectures are provided, but we also conjecture that not all rulesets have regular outcomes.

Enhancing the Probability of Victor for Top Players via Knockout Tournament Fixture

A tournament fixture is an integral part of the tournament rules. It determines the random pairing of contestants, with several matches played per round. The selection of fixture type that optimizes the top player's winning probability significantly affects the financial aspects for organizers, individuals, and participants while also addressing the interests of millions of fans. In addressing this challenge, this study designed a balanced tournament fixture and employed a labeling system to represent each fixture, utilizing a recursive function. By assigning a strength rating to each player, their rankings were established, leading to varied probabilities of winning. It was decided to represent these abilities with randomly selected integers ranging from 1 to 21, with 1 denoting minimum strength and 21 denoting maximum strength. We explore hierarchical knockout tournament fixtures in competitions to develop optimal tournaments that enhance their attractiveness. In this study, we also performed calculations to determine the probability of each player winning in each round, thereby deducing which tournament fixture minimizes or maximizes the likelihood of the strongest player winning. In cases where the number of players is a power of 2, the first half comprises p/2 matches, where p is the total number of players. However, if the number of players is not a power of 2, k matches are played in the first round, with 𝑝 = 2r + 𝑘, where 0 ≤ k < 2r, followed by implementing a balanced tournament fixture. The findings underscore the effectiveness of employing a balanced tournament fixture to maximize the probability of winning in a single-elimination tournament. Keywords: Single Elimination, Binary Tree, Dummy Players, Election Procedures, Hierarchically.

CreativeStone: A Creativity Booster for Hearthstone Card Decks

Digital Collectible Card Games (DCCG) rely on human expertise to create competitive card decks. The most effective decks are shared and become popular among players through online communities. Players then keep enhancing those decks by replacing cards and testing those new deck variations in online arenas. This fine-tuning process is time-consuming and most of the time leads to small improvements in the players win rate. This paper presents CreativeStone, a creativity booster for Hearthstone card decks. Our creativity-guided approach uses a genetic algorithm and the Regent-Dependent Creativity (RDC) metric to identify the core cards of an existing deck, and then improves it towards a more valuable and novel deck by adding cards that are synergic to the core cards, but also different from the ones in the original deck. Our experimental results show that CreativeStone can boost even legendary decks, outperforming handcrafted ones by 21% in win rate.

Modeling and prediction of tennis matches at Grand Slam tournaments

In this manuscript, different approaches for modeling and prediction of tennis matches in Grand Slam tournaments are proposed. The data used here contain information on 5,013 matches in men’s Grand Slam tournaments from the years 2011–2022. All regarded approaches are based on regression models, modeling the probability of the first-named player winning. Several potential covariates are considered including the players’ age, the ATP ranking and points, odds, elo rating as well as two additional age variables, which take into account that the optimal age of a tennis player is between 28 and 32 years. We compare the different regression model approaches with respect to three performance measures, namely classification rate, predictive Bernoulli likelihood, and Brier score in a 43-fold cross-validation-type approach for the matches of the years 2011 to 2021. The top five optimal models with highest average ranks are then selected. In order to predict and compare the results of the tournaments in 2022 with the actual results, a comparison over a continuously updating data set via a “rolling window” strategy is used. Also, again the previously mentioned performance measures are calculated. Additionally, we examine whether the assumption of non-linear effects or additional court- and player-specific abilities is reasonable.

Convexity of the triple helix of innovation game

Purpose This paper aims to determine the conditions for the core of the Triple Helix game to exist. The Triple Helix of university-industry-government relationships is a three-person cooperative game with transferable utility. Then, the core, the Shapley value and the nucleolus were used as indicators of the synergy within an innovation system. Whereas the Shapley value and the nucleolus always exist, the core may not. Design/methodology/approach The core of a three-person cooperative game with transferable utility exists only if and only if the game is convex. The paper applies the convexity condition to the Triple Helix game. Findings The Triple Helix game is convex if and only if there is output within the system; it is strictly convex if and only if all the three bilateral and the trilateral relationships have an output. Practical implications Convex games are competitive situations in which there are strong incentives towards the formation of large coalitions; therefore, innovation actors must cooperate to maximise their interests. Furthermore, a Triple Helix game may be split into subgames for comprehensive analyses and several Triple Helix games may be combined for a global study. Originality/value This paper extends the meaning of the Shapley value and the nucleolus for Triple Helix innovation actors: the Shapley value indicates the quantity a player wins because of the coalitions he involves in and the nucleolus the return for solidarity of an innovation actor.

Opponent choice in tournaments: winning and shirking

Abstract We propose an alternative design for tournaments that use a preliminary stage, followed by several rounds of single elimination play. The conventional “bracket” design of these tournaments suffers from several deficiencies. Specifically, various reasonable performance criteria for the tournament are not satisfied, there is an unnecessary element of luck in the matchups of players, and there are situations where players have an incentive to shirk. To address all these issues, we allow higher ranked players at the single elimination stage to choose their next opponent sequentially at each round. We allow each player’s ranking either to remain static, or to improve by beating a higher ranked player (Guyon, J. 2022. “Choose your opponent”: a new knockout design for hybrid tournaments. J. Sports Anal. 8: 9–29). Using data from 2215 men’s professional tennis tournaments from 1991 to 2017, we demonstrate the reasonableness of the results obtained. We also perform sensitivity analysis for the effect of increasing irregularity in the pairwise win probability matrix on three traditional performance measures. Finally, we consider strategic shirking behavior at both the individual and group levels, and show how our opponent choice design can mitigate such behavior. Overall, the opponent choice design provides higher probabilities that the best player wins and also that the two best players meet, and reduces shirking, compared to the conventional bracket design.

Realizability problem for constraint LTL

Constraint linear-time temporal logic (CLTL) is an extension of LTL that is interpreted on sequences of valuations of variables over an infinite domain. Atomic formulas can constrain valuations over a range of positions along a sequence, with the range being bounded by a parameter depending on the formula. The satisfiability and model checking problems for CLTL have been studied before. We consider the realizability problem for CLTL. The set of variables is partitioned into two parts, with each part controlled by a player. Players take turns to choose valuations for their variables, generating a sequence of valuations. The winning condition is specified by a CLTL formula — the first player wins if the sequence of valuations satisfies the specified formula. We prove that checking whether the first player has a winning strategy in the realizability game for a given CLTL formula is undecidable in general and identify decidable fragments.

Designing discrete-time control-based strategies for pursuit-evasion games on the plane

Two-player discrete-time pursuit-evasion games are proposed with control-based strategies on the plane, where each player's position is determined by the discrete-time version of the kinematic equation related to the moving structure of vehicles. In this regard, the first game is built in a one-target fashion where the high-speed pursuer tries to reach the running evader in optimal discrete time, whereas the second game is constructed from a two-target perspective where the evader becomes an attacker whose ultimate aim is to build a control-based strategy to capture the high-speed pursuer who follows the shortest tracking policy within his target region. Each player's winning and losing strategies are designed under certain playability conditions. Later, the main results are generalized for players sharing various discrete-time speeds during the game. The motivation of the study is to investigate the losing and winning strategies of the evader against the high-speed pursuer, who tries to capture his opponent in optimal discrete time on the plane. Numerical experiments are performed on four different unmanned aerial vehicles (UAVs) flying at the same altitude with various airspeeds and turning radii, where several capture scenarios and control-based strategies for each UAV are constructed according to the main results.

Mirror games against an open book player

Mirror games were invented by Garg and Schneider (ITCS 2019). Alice and Bob take turns (with Alice playing first) in declaring numbers from the set {1,2,…,2n}. If a player picks a number that was previously played, that player loses the game and the other player wins. If all numbers are declared without repetition, the result is a draw. Bob has a simple mirror strategy that assures he won't lose the game and requires no memory. On the other hand, Garg and Schneider showed that every deterministic Alice requires memory of size that is proportional to n in order to secure a draw.Regarding probabilistic strategies, previous work showed that assuming Alice has access to a secret random perfect matching over {1,2,…,2n} allows her to achieve a draw in the game w.p. at least 1−1n and using only polylog bits of memory.We show that the requirement for secret bits is crucial: for an ‘open book’ Alice with no secrets (Bob knows her memory but not future coin flips) and memory of at most n/4c bits for any c≥2, there is a Bob that wins w.p. close to 1−2−c/2.

Tournament Fixing Parameterized by Feedback Vertex Set Number Is FPT

A knockout (or single-elimination) tournament is a format of a competition that is very popular in practice (particularly in sports, elections and decision making), and which has been extensively and intensively studied from a theoretical point of view for more than a decade. Particular attention has been devoted to the Tournament Fixing problem, where, roughly speaking, the objective is to determine whether we can conduct the knockout tournament in a way that makes our favorite player win. Here, part of the input is a tournament graph D that encodes the winner of each possible match. A sequence of papers has studied the parameterized complexity of Tournament Fixing with respect to the feedback arc set number (fas) of D Given that this parameter yielded tractability, it has been asked explicitly and repeatedly whether Tournament Fixing is FPT also with respect to the feedback vertex set number (fvs) of D. We answer this question positively. In fact, although fvs can be arbitrarily smaller than fas, we attain the same dependency on the parameter in the time complexity. So, additionally, our work subsumes the best known algorithm for Tournament Fixing with respect to as.

Initially contestable property rights and Coase: Evidence from the lab

This article investigates how the existence of initially contestable property rights affects the efficiency of the Coase theorem. We design a two-stage experiment that incorporates a stage where property rights are initially allocated to participants followed by a stage that allows bargaining between participants. In stage one, participants endogenously choose rent-seeking effort (and thus the probability) to initially obtain property rights before entering an unstructured bargaining game. We find the presence of costly rent seeking to obtain the property rights makes it significantly less likely that the efficient outcome is reached. We introduce bargaining costs and find that allowing for symmetric bargaining costs has no impact on the likelihood of the efficient outcome being reached, whereas asymmetric bargaining costs – costs that differ if the player wins or loses the initial property rights – substantially reduces the likelihood of reaching an efficient outcome. Our analysis is applicable to contexts with initially contestable and tradable nature resource rights.

A methodology for solving bimatrix games under 2-tuple linguistic environment

In a game problem, when the situation is formulated as the gain of one equals the loss of other, the game is called zero-sum. But actually, one player's win is not always the other's loss. Such a game is referred to as non-zero sum or bimatrix game. The work provided in this research is primarily elaborated on linguistic bimatrix games under 2-tuple linguistic environment. This class of bimatrix games consists of payoffs having entries as linguistic 2-tuples, that are based on a finite subscript-symmetric additive linguistic set defined in the domain , where g is a positive integer. In this direction, a novel linguistic equilibrium concept is defined to solve such games, and a methodology based on a nonlinear linguistic programme is proposed to compute mixed Nash equilibrium. The proposed methodology is sufficient to evaluate the Nash equilibrium and the maximum expected payoffs corresponding to each player simultaneously in a single programme. The necessary and sufficient conditions for the existence of Nash equilibrium and a computation procedure are also provided. Finally, some hypothetical working examples are given to show the practical applicability of the defined methodology. The proposed methodology is also applied to solve two-player constant sum linguistic games.

Finding the Best Dueler

Consider a set of n players. We suppose that each game involves two players, that there is some unknown player who wins each game it plays with a probability greater than 1/2, and that our objective is to determine this best player. Under the requirement that the policy employed guarantees a correct choice with a probability of at least some specified value, we look for a policy that has a relatively small expected number of games played before decision. We consider this problem both under the assumption that the best player wins each game with a probability of at least some specified value p0>1/2, and under a Bayesian assumption that the probability that player i wins a game against player j is vivi+vj, where v1,…,vn are the unknown values of n independent and identically distributed exponential random variables. In the former case, we propose a policy where chosen pairs play a match that ends when one of them has had a specified number of wins more than the other; in the latter case, we propose a Thompson sampling type rule.

Estimating the Implied Probabilities in the Tennis Betting Market: A New Normalization Procedure: Comment

Abstract: In this note, we comment on a recent paper in the journal that proposes a new normalization procedure when converting tennis betting odds to the implied probabilities of each player winning. The new procedure is especially germane for matches in which there is a heavy favorite and where there is concern that traditional conversion methods understate the true probability of the favorite winning. However, in this comment, we argue that the new adjustment, while an interesting contribution, suffers from at least three limitations that make the procedure relatively costly while not materially improving predictions of match outcomes.

On a dart game of Niedermaier

We analyze a game introduced by Andy Niedermaier, where m players take turns throwing a dart at a dartboard. A player is eliminated unless his dart lands closer to the center than all previously thrown darts, in which case he goes to the back of the line, until only one player remains. Using generating functions, we determine the distribution of the number of throws in the game, and we obtain a recursive formula to compute the probability that each player wins.

THEORETICAL ASPECTS OF RESEARCHING OF THE TOPIC OF WAR IN TOYS AND PLAY ACTIVITIES OF PRESCHOOL CHILDREN

The actuality of the study is determined by the need for reaction of teachers and scientists to the phenomena that children reflect in the game – military actions. The professional inadequacy of the methodology for organizing military-themed games encourages scientific research to provide adequate support to teachers and practitioners in wartime. The purpose of the article is to determine the features of military toys, toy weapons usage investigating the theme of war in preschool children’s play activities by analyzing and summarizing the views of child psychologists, psychotherapists, kindergarten teachers and scientists. The following methods were used for the study: analysis, generalization, synthesis. The idea of leisure militarization penetrated not only the games of preschool children, but also children of middle and high school age. The main mechanics were to seize territories and increase military power: men’s and technical. If the role of an adult does not have a purposeful positive impact, then such games will be identified by spontaneity, conflict, consolidation of psychological attitudes, the stronger player wins, and moral norms in such games are not valid.
 The results of scientific research are accumulated in the following features: children's games on the theme of war and toy weapons usage have a deep historical origin from the stable stereotypical views on the upbringing of boys and girls; the theme of war and the plots of military events penetrate all kinds of children's games: creative and with rules, while their interpenetration and mutual enrichment is noticeable; games and toys can be the subject of ideological and military reflection and influence of different political and historical periods; such games can reflect the experienced traumatic events, and be necessary means of preventive and psychotherapeutic treatment, etc. It is noted that the organization of children's military-themed games ensures preschoolers’ value orientations formation: patriotism, respect for a person and his life, the value of protecting the Motherland, interest in military’s heroic deeds etc.

Complexity Limitations on One-turn Quantum Refereed Games

This paper studies complexity theoretic aspects of quantum refereed games, which are abstract games between two competing players that send quantum states to a referee, who performs an efficiently implementable joint measurement on the two states to determine which of the player wins. The complexity class QRG(1) contains those decision problems for which one of the players can always win with high probability on yes-instances and the other player can always win with high probability on no-instances, regardless of the opposing player’s strategy. This class trivially contains QMA ∪co-QMA and is known to be contained in PSPACE. We prove stronger containments on two restricted variants of this class. Specifically, if one of the players is limited to sending a classical (probabilistic) state rather than a quantum state, the resulting complexity class CQRG(1) is contained in ∃⋅PP (the nondeterministic polynomial-time operator applied to PP); while if both players send quantum states but the referee is forced to measure one of the states first, and incorporates the classical outcome of this measurement into a measurement of the second state, the resulting class MQRG(1) is contained in P ⋅PP (the unbounded-error probabilistic polynomial-time operator applied to PP).

Implementation of a Tic-Tac-Toe game Using Python Environment for gaming application

In this paper, we present the implementation of ta tic-tac toe game using the python environment for any gaming application problem. Two players compete in the game of Tic-Tac-Toe, which is played on a 3 by 3 grid. Each participant is given a unique symbol (X or O) to represent the slot they are responsible for filling. The player who first covers a horizontal, vertical, or diagonal row of the board with solely their symbols wins the game. This work, which was written in Python using Pygame on a Jupyter Notebook, suggests a winning Tic-Tac-Toe strategy. This algorithm is made to act like a player while the computer maximises the odds of success by acting in accordance with the model's intelligence. The purpose of this work is to develop a Tic-Tac-Toe strategy in which the game will continue until one player wins and will conclude in a draw if no player selected the optimal spots that may have increased their chances of winning. The work presented here is the mini-project work of the 2nd sem students of electronics & communication engineering department of dayananda sagar college of engg., bangalore.

Application of the Polar Coordinate Technique in the Study of Technical-Tactical Scoring Actions in Taekwondo.

The objective of this study was to design, validate and update an observation tool to analyse the technical-tactical actions by which taekwondo players win points. An ad hoc observational tool was developed for subsequent use in HOISAN software by viewing seven finals (14 viewings) in the Rome 2019 Grand Prix, collecting data (1,382 technical/tactical actions) from both winners and losers (women, n = 3; men, n = 4). An observational methodology based on a nomothetic, follow-up and multidimensional (N/F/M) observational design was used. In the statistical analysis, to check the validity of the generalizability analysis, the Category/Observer (C/O) and Observer/Category (O/C) models were employed, and to determine reliability between observations (intra- and interobserver), the Pearson, Spearman, Kendall's tau-b and Cohen's kappa correlation coefficients were applied. One point were awarded for every penalty given against the opponent. Two points were obtained for a circular technique to the trunk protector (in winners) or by scoring a point for a punch plus a penalty against the opponent, three points in melee actions, anticipatory actions with the left side (winners), or after a punch action, and circular technique (losers). Four and five points were only obtained by winners, in a direct attack with the right leg, turning (five points) or simultaneous (four points). The results of this study provide information on the most effective technical-tactical actions in taekwondo for scoring points in a contest.

Design of Checkers Game Using Alpha-Beta Pruning Algorithm

Checkers is a board game that is played by two people which has a purpose to defeat the opponent by eating all the opponent's pieces or making the opponent unable to make a move. The sophistication of technology at this modern time makes the checkers game can be used on a computer even with a smartphone. The application of artificial intelligence in checkers games makes the game playable anywhere and anytime. Alpha Beta Pruning is an optimization technique from the Minimax Algorithm that can reduce the number of branch/node extensions to get better and faster step search results. In this study, a checkers game based on artificial intelligence will be developed using the alpha-beta pruning method. This research is expected to explain in detail how artificial intelligence works in a game. Alpha-beta pruning was chosen because it can search for the best steps quickly and precisely. This study tested 10 respondents to play this game. The results show that the player's win rate was 60% at the easy level, 40% at the medium level, and 20% at the hard level. Besides that, the level of interest in this game was 80% being entertained and 20% feeling ordinary.