相关论文: Victory Probability in the Fire Emblem Arena

Explainable reinforcement learning allows artificial agents to explain their behavior in a human-like manner aiming at non-expert end-users. An efficient alternative of creating explanations is to use an introspection-based method that…

India's most popular sport is cricket and is played across all over the nation in different formats like T20, ODI, and Test. The Indian Premier League (IPL) is a national cricket match where players are drawn from regional teams of India,…

An open problem posed by the first author is the complexity to decide whether a sequence of nonnegative integer numbers can be the final score of a football tournament. In this paper we propose polynomial time approximate and exponential…

We study the computational complexity of the popular board game backgammon. We show that deciding whether a player can win from a given board configuration is NP-Hard, PSPACE-Hard, and EXPTIME-Hard under different settings of known and…

Can a probabilistic gambler get arbitrarily rich when all deterministic gamblers fail? We study this problem in the context of algorithmic randomness, introducing a new notion -- almost everywhere computable randomness. A binary sequence…

An efficient finite element method (FEM) for calculating eigenvalues and eigenfunctions of quantum billiard systems is presented. We consider the FEM based on triangular $C_1$ continuity quartic interpolation. Various shapes of quantum…

We consider turn-based game arenas for which we investigate uniformity properties of strategies. These properties involve bundles of plays, that arise from some semantical motive. Typically, we can represent constraints on allowed…

A random forest is a popular tool for estimating probabilities in machine learning classification tasks. However, the means by which this is accomplished is unprincipled: one simply counts the fraction of trees in a forest that vote for a…

In the study of complex systems, evaluating physical observables often requires sampling representative configurations via Monte Carlo techniques. These methods rely on repeated evaluations of the system's energy and force fields, which can…

Multi-round competitions often double or triple the points awarded in the final round, calling it a bonus, to maximize spectators' excitement. In a two-player competition with $n$ rounds, we aim to derive the optimal bonus size to maximize…

One of the main goals in the study of quantum nonlocality is to determine the maximum violation achieved by quantum correlations in a Bell scenario. However, given a Bell inequality, there is no general algorithm to perform this task. As an…

The pairwise winning indices, computed in the Stochastic Multicriteria Acceptability Analysis, give the probability with which an alternative is preferred to another taking into account all the instances of the assumed preference model…

In this work, we extended a stochastic model for football leagues based on the team's potential [R. da Silva et al. Comput. Phys. Commun. \textbf{184} 661--670 (2013)] for making predictions instead of only performing a successful…

In arena-style evaluation of large language models (LLMs), two LLMs respond to a user query, and the user chooses the winning response or deems the "battle" a draw, resulting in an adjustment to the ratings of both models. The prevailing…

A popular challenge on the social media app TikTok is to place the output of a random number generator in ascending order without arriving at a contradiction. Most players rely on intuition to construct their sequences and debate has…

In this paper, we study the distribution of the number of internal equilibria of a multi-player two-strategy random evolutionary game. Using techniques from the random polynomial theory, we obtain a closed formula for the probability that…

We construct a non-locality game that can be won with certainty by a quantum strategy using log n shared EPR-pairs, while any classical strategy has winning probability at most 1/2+O(log n/sqrt{n}). This improves upon a recent result of…

Consider a P\'olya urn where a drawn ball of colour $i$ is replaced together with a fixed number $m_i$ of balls of the same colour. We give a simple proof that if, for example, there are two colours and the urn starts with more balls of…

We present a simple game model where agents with different memory lengths compete for finite resources. We show by simulation and analytically that an instability exists at a critical memory length, and as a result, different memory lengths…

Reinforcement learning for the optimization of quantum circuits uses an agent whose goal is to maximize the value of a reward function that decides what is correct and what is wrong during the exploration of the search space. It is an open…