arXiv subjects

Shiva Maharaj

Publications and source records attributed to Shiva Maharaj.

6 recordsLinked to original sources

arXiv2024

Kramnik vs Nakamura: A Chess Scandal

We provide a statistical analysis of the recent controversy between Vladimir Kramnik (ex chess world champion) and Hikaru Nakamura. Hikaru Nakamura is a chess prodigy and a five-time United States chess champion. Kramnik called into question Nakamura's 45.5 out of 46 win streak in an online blitz contest at chess.com. We assess the weight of evidence using a priori assessment of Viswanathan Anand and the streak evidence. Based on this evidence, we show that Nakamura has a 99.6 percent chance of not cheating. We study the statistical fallacies prevalent in both their analyses. On the one hand Kramnik bases his argument on the probability of such a streak is very small. This falls precisely into the Prosecutor's Fallacy. On the other hand, Nakamura tries to refute the argument using a cherry-picking argument. This violates the likelihood principle. We conclude with a discussion of the relevant statistical literature on the topic of fraud detection and the analysis of streaks in sports data.

stat.AP↗

arXiv2023

The Value of Chess Squares

We propose a neural network-based approach to calculate the value of a chess square-piece combination. Our model takes a triplet (Color, Piece, Square) as an input and calculates a value that measures the advantage/disadvantage of having this piece on this square. Our methods build on recent advances in chess AI, and can accurately assess the worth of positions in a game of chess. The conventional approach assigns fixed values to pieces $(\symking=\infty, \symqueen=9, \symrook=5, \symbishop=3, \symknight=3, \sympawn=1)$. We enhance this analysis by introducing marginal valuations. We use deep Q-learning to estimate the parameters of our model. We demonstrate our method by examining the positioning of Knights and Bishops, and also provide valuable insights into the valuation of pawns. Finally, we conclude by suggesting potential avenues for future research.

cs.AI↗

arXiv2022

On the Probability of Magnus Carlsen reaching 2900

How likely is it that Magnus Carlsen will achieve an Elo rating of $2900$? This has been a goal of Magnus and is of great current interest to the chess community. Our paper uses probabilistic methods to address this question. The probabilistic properties of Elo's rating system have long been studied, and we provide an application of such methods. By applying a Brownian motion model of Stern as a simple tool we provide answers. Our research also has fundamental bearing on the choice of the $K$-factor used in Elo's system for GrandMaster (GM) chess play. Finally, we conclude with a discussion of policy issues involved with the choice of $K$-factor.

stat.AP↗

arXiv2022

Gambits: Theory and Evidence

Gambits are central to human decision-making. Our goal is to provide a theory of Gambits. A Gambit is a combination of psychological and technical factors designed to disrupt predictable play. Chess provides an environment to study gambits and behavioral game theory. Our theory is based on the Bellman optimality path for sequential decision-making. This allows us to calculate the $Q$-values of a Gambit where material (usually a pawn) is sacrificed for dynamic play. On the empirical side, we study the effectiveness of a number of popular chess Gambits. This is a natural setting as chess Gambits require a sequential assessment of a set of moves (a.k.a. policy) after the Gambit has been accepted. Our analysis uses Stockfish 14.1 to calculate the optimal Bellman $Q$ values, which fundamentally measures if a position is winning or losing. To test whether Bellman's equation holds in play, we estimate the transition probabilities to the next board state via a database of expert human play. This then allows us to test whether the \emph{Gambiteer} is following the optimal path in his decision-making. Our methodology is applied to the popular Stafford and reverse Stafford (a.k.a. Boden-Kieretsky-Morphy) Gambit and other common ones including the Smith-Morra, Goring, Danish and Halloween Gambits. We build on research in human decision-making by proving an irrational skewness preference within agents in chess. We conclude with directions for future research.

econ.TH↗

arXiv2021

Chess AI: Competing Paradigms for Machine Intelligence

Endgame studies have long served as a tool for testing human creativity and intelligence. We find that they can serve as a tool for testing machine ability as well. Two of the leading chess engines, Stockfish and Leela Chess Zero (LCZero), employ significantly different methods during play. We use Plaskett's Puzzle, a famous endgame study from the late 1970s, to compare the two engines. Our experiments show that Stockfish outperforms LCZero on the puzzle. We examine the algorithmic differences between the engines and use our observations as a basis for carefully interpreting the test results. Drawing inspiration from how humans solve chess problems, we ask whether machines can possess a form of imagination. On the theoretical side, we describe how Bellman's equation may be applied to optimize the probability of winning. To conclude, we discuss the implications of our work on artificial intelligence (AI) and artificial general intelligence (AGI), suggesting possible avenues for future research.

cs.AI↗

arXiv2021

Karpov's Queen Sacrifices and AI

Anatoly Karpov's Queen sacrifices are analyzed. Stockfish 14 NNUE -- an AI chess engine -- evaluates how efficient Karpov's sacrifices are. For comparative purposes, we provide a dataset on Karpov's Rook and Knight sacrifices to test whether Karpov achieves a similar level of accuracy. Our study has implications for human-AI interaction and how humans can better understand the strategies employed by black-box AI algorithms. Finally, we conclude with implications for human study in. chess with computer engines.

cs.AI↗