Finished bit on static eval.

report/comp3130report.tex

@@ -60,7 +60,7 @@ \section*{\emph{Static Evaluation}}
 \]
 Where $F_i$ is the $i$\textsuperscript{th} feature function, $W_i$ is the corresponding feature weight, $p$ is the player (with $\neg p$ corresponding to the other player), and $b$ is the board state.
 
-Our evaluation function in principle uses 103 different features. However, these features can be broken down as:
+Our evaluation function in principle uses 103 different features. These features can be broken down as:
     \begin{itemize}
   \item
     Mobility: number of moves the player would have if it was their turn.
@@ -72,7 +72,14 @@ \section*{\emph{Static Evaluation}}
     Control: 100 features, corresponding to control of each of the 100 squares on the board.
   \end{itemize}
 
-In practice, only 15 of the weights for control of the board are stored, corresponding to an 8-way symmetric subregion of the board. These weights are then mirrored out to the other 7 symmetric regions.
+In practice, only 15 of the weights for control of the board are stored, corresponding to an 8-way symmetric subregion of the board. These weights are then mirrored out to the other 7 symmetric regions. When updated weights are restored, we take the average of each of the corresponding 4 or 8 symmetric squares as the new value.
+
+It is notable that in principle there is actually only a 4-way symmetry to the Othello board, due to the difference in starting positions. However, it is unlikely that the difference between using the actual 4-way symmetry versus approximating it with an 8-way symmetry would be significant enough to warrant the extra overhead.
+
+\begin{center}
+\includegraphics[scale=0.25]{symmetries.png}\\
+The red area shows the 8-way symmetric region. The red and yellow region together constitute the 4-way symmetric region.
+\end{center}
 
 \section*{\emph{\textmd{Piece Stability}}}
 \hrule