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docs/AlphaDeepChess/Capitulos/AnalysisOfImprovements.tex

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\end{table}
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\subsection*{Transposition table}
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\label{sec:tt}
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\noindent This experiment evaluates the impact of integrating a transposition table into the search process. The only modification compared to the baseline engine is in the search component.
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docs/AlphaDeepChess/Capitulos/EstadoDeLaCuestion.tex

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\noindent Throughout this process, branches that cannot possibly influence the final decision are pruned, significantly reducing the number of nodes that need to be evaluated. This demonstrates the efficiency of alpha-beta pruning in minimizing the search space while guaranteeing the same result as a full minimax search.
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\begin{figure}
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\begin{figure}[htbp]
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\centering
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\begin{tikzpicture}[
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level distance=1.5cm,
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\draw[-] (c) -- (f);
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\draw[-] (c) -- (g);
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\end{tikzpicture}
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\caption{Alpha-beta pruning - step 1}\label{fig:alphaBetaExample}
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\end{figure}
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\hspace{3em}
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\begin{figure}[htbp]\ContinuedFloat
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\centering
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\begin{tikzpicture}[
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level distance=1.5cm,
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\draw[-] (c) -- (f);
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\draw[-] (c) -- (g);
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\end{tikzpicture}
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\caption{Alpha-beta pruning - step 2}
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\end{figure}
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\begin{figure}[htbp]\ContinuedFloat
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\centering
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\begin{tikzpicture}[
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level distance=1.5cm,
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\draw[-] (c) -- (f);
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\draw[-] (c) -- (g);
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\end{tikzpicture}
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\caption{Alpha-beta pruning - step 3}
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\end{figure}
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\begin{figure}[htbp]\ContinuedFloat
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\draw[-, draw=red] (c) -- (f);
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\draw[-, draw=gray, dashed] (c) -- (g);
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\end{tikzpicture}
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\caption{Alpha-beta pruning - step 4}
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\end{figure}
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\begin{figure}[htbp]\ContinuedFloat
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\draw[-] (f) -- (c);
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\draw[-, draw=gray, dashed] (c) -- (g);
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\caption{Example of alpha-beta pruning with $\alpha$ and $\beta$ values.}\label{fig:alphaBetaExample}
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\caption{Alpha-beta pruning - step 5}
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\end{figure}
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\newpage

docs/AlphaDeepChess/Capitulos/ImprovementTechniques.tex

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\item Search with late move reductions.
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\end{itemize}
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\section{Transposition table}\label{sec:tt}
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\section{Transposition table}
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\noindent As discused in the previous chapter (see~\cref{sec:iterativeDeepening}), the basic implementation of the chess engine generates a large amount of redundant calculations due to the iterative deepening approach and also the concept of transpositions: situations in which the same board position is reached through different sequences of moves in the game tree.
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\noindent~\cref{fig:transposition_example} illustrates a position that can arise through multiple move orders. Where the white king could go to the g3 square from multiple paths.
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\caption{Principal variation splitting~\cite{PVSplitting}.}\label{fig:pvsplitting}
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\end{figure}
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\section{Late move reductions}
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\noindent We experiment with the use of late move reductions, a search optimization technique that selectively reduces the search depth for moves that appear late in the move ordering and are therefore considered less promising~\cite{LateMoveReductions}. The technique is based on the assumption that a strong move ordering heuristic will place the best move in the position earlier in the list. As a result, moves evaluated later can be searched at a reduced depth to save computation time.

docs/AlphaDeepChess/TFGTeXiS.pdf

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docs/AlphaDeepChess/TeXiS/TeXiS_pream.tex

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\crefname{equation}{Equation}{Equations}
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\usepackage{enumitem}
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\usepackage{caption}
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% Variable local para emacs, para que encuentre el fichero maestro de
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% compilación y funcionen mejor algunas teclas rápidas de AucTeX

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