+template <typename T, int D, int Size>
+struct Stats<T, D, Size> : public std::array<StatsEntry<T, D>, Size> {};
+
+/// In stats table, D=0 means that the template parameter is not used
+enum StatsParams { NOT_USED = 0 };
+enum StatsType { NoCaptures, Captures };
+
+/// ButterflyHistory records how often quiet moves have been successful or
+/// unsuccessful during the current search, and is used for reduction and move
+/// ordering decisions. It uses 2 tables (one for each color) indexed by
+/// the move's from and to squares, see www.chessprogramming.org/Butterfly_Boards
+typedef Stats<int16_t, 10692, COLOR_NB, int(SQUARE_NB) * int(SQUARE_NB)> ButterflyHistory;
+
+/// LowPlyHistory at higher depths records successful quiet moves on plies 0 to 3
+/// and quiet moves which are/were in the PV (ttPv)
+/// It get cleared with each new search and get filled during iterative deepening
+constexpr int MAX_LPH = 4;
+typedef Stats<int16_t, 10692, MAX_LPH, int(SQUARE_NB) * int(SQUARE_NB)> LowPlyHistory;
+
+/// CounterMoveHistory stores counter moves indexed by [piece][to] of the previous
+/// move, see www.chessprogramming.org/Countermove_Heuristic
+typedef Stats<Move, NOT_USED, PIECE_NB, SQUARE_NB> CounterMoveHistory;
+
+/// CapturePieceToHistory is addressed by a move's [piece][to][captured piece type]
+typedef Stats<int16_t, 10692, PIECE_NB, SQUARE_NB, PIECE_TYPE_NB> CapturePieceToHistory;
+
+/// PieceToHistory is like ButterflyHistory but is addressed by a move's [piece][to]
+typedef Stats<int16_t, 29952, PIECE_NB, SQUARE_NB> PieceToHistory;
+
+/// ContinuationHistory is the combined history of a given pair of moves, usually
+/// the current one given a previous one. The nested history table is based on
+/// PieceToHistory instead of ButterflyBoards.
+typedef Stats<PieceToHistory, NOT_USED, PIECE_NB, SQUARE_NB> ContinuationHistory;