Related papers: Achieving the Highest Possible Elo Rating

In this report, we inspect the application of an evolutionary approach to the game of Rack'O, which is a card game revolving around the notion of decision making. We first apply the evolutionary technique for obtaining a set of rules over…

In a classical chess round-robin tournament, each of $n$ players wins, draws, or loses a game against each of the other $n-1$ players. A win rewards a player with 1 points, a draw with 1/2 point, and a loss with 0 points. We are interested…

Owning up to the authors' occasional mixed performances when playing darts we follow up on the ingenious work to determine the optimal aim to score high by Tibshirani et. al [JRS A 174, 213 (2011)] and expand on maximal expected reward…

We introduce an evolutionary game with feedback between perception and reality, which we call the reality game. It is a game of chance in which the probabilities for different objective outcomes (e.g., heads or tails in a coin toss) depend…

Fighting Fantasy is a popular recreational fantasy gaming system worldwide. Combat in this system progresses through a stochastic game involving a series of rounds, each of which may be won or lost. Each round, a limited resource (`luck')…

This paper presents a new exponential lower bound for the two most popular deterministic variants of the strategy improvement algorithms for solving parity, mean payoff, discounted payoff and simple stochastic games. The first variant…

This paper looks into the gain or loss from rolling a fair die multiple times and choosing the highest or lowest number as the outcome over rolling the die just once. Specifically, this paper gives a general formula for the expected value…

The games of prediction with expert advice are considered in this paper. We present some modification of Kalai and Vempala algorithm of following the perturbed leader for the case of unrestrictedly large one-step gains. We show that in…

Flip a coin repeatedly, and stop whenever you want. Your payoff is the proportion of heads, and you wish to maximize this payoff in expectation. This so-called Chow-Robbins game is amenable to computer analysis, but while simple-minded…

We consider games that have (k,t)-robust equilibria when played with a mediator, where an equilibrium is (k,t)-robust if it tolerates deviations by coalitions of size up to k and deviations by up to $t$ players with unknown utilities. We…

This paper presents a game-theoretic strategy for racing, where the autonomous ego agent seeks to block a racing opponent that aims to overtake the ego agent. After a library of trajectory candidates and an associated reward matrix are…

Delay games are two-player games of infinite duration in which one player may delay her moves to obtain a lookahead on her opponent's moves. For $\omega$-regular winning conditions it is known that such games can be solved in…

Evaluating the reasoning capabilities of Large Language Models is increasingly challenging as models improve. Human curation of hard questions is highly expensive, especially in recent benchmarks using PhD-level domain knowledge to…

Rating systems play a vital role in the exponential growth of service-oriented markets. As highly rated online services usually receive substantial revenue in the markets, malicious sellers seek to boost their service evaluation by…

We study the performance of Fictitious Play, when used as a heuristic for finding an approximate Nash equilibrium of a 2-player game. We exhibit a class of 2-player games having payoffs in the range [0,1] that show that Fictitious Play…

Follow the regularized leader FTRL is the premier algorithm for online optimization. However, despite decades of research on its convergence in constrained optimization -- and potential games in particular -- its behavior remained hitherto…

In the standard setting of approachability there are two players and a target set. The players play repeatedly a known vector-valued game where the first player wants to have the average vector-valued payoff converge to the target set which…

In RL, given a prompt, we sample a group of completions from a model and score them. Two questions follow: which completions should gain probability mass, and how should the parameters move to realize that change? Standard policy-gradient…

We design and analyze minimax-optimal algorithms for online linear optimization games where the player's choice is unconstrained. The player strives to minimize regret, the difference between his loss and the loss of a post-hoc benchmark…

Experience replay enables reinforcement learning agents to memorize and reuse past experiences, just as humans replay memories for the situation at hand. Contemporary off-policy algorithms either replay past experiences uniformly or utilize…