;;;; -*- Mode: Lisp; Syntax: Common-Lisp -*-
;;;; Code from Paradigms of AI Programming
;;;; Copyright (c) 1991 Peter Norvig
;;;; File othello2.lisp: More strategies for othello.lisp,
;;;; from section 18.9 onward (alpha-beta2, alpha-beta3, iago).
;;;; If a compiled version of edge-table.lisp exists, then merely
;;;; load it after you load this file. Otherwise, load this file,
;;;; evaluate (init-edge-table) (this will take a really long time),
;;;; then compile edge-table.lisp. This will save the edge-table for
;;;; future use.
(requires "othello")
(defconstant all-squares
(sort (loop for i from 11 to 88
when (<= 1 (mod i 10) 8) collect i)
#'> :key #'(lambda (sq) (elt *weights* sq))))
(defstruct (node) square board value)
(defun alpha-beta-searcher2 (depth eval-fn)
"Return a strategy that does A-B search with sorted moves."
#'(lambda (player board)
(multiple-value-bind (value node)
(alpha-beta2
player (make-node :board board
:value (funcall eval-fn player board))
losing-value winning-value depth eval-fn)
(declare (ignore value))
(node-square node))))
(defun alpha-beta2 (player node achievable cutoff ply eval-fn)
"A-B search, sorting moves by eval-fn"
;; Returns two values: achievable-value and move-to-make
(if (= ply 0)
(values (node-value node) node)
(let* ((board (node-board node))
(nodes (legal-nodes player board eval-fn)))
(if (null nodes)
(if (any-legal-move? (opponent player) board)
(values (- (alpha-beta2 (opponent player)
(negate-value node)
(- cutoff) (- achievable)
(- ply 1) eval-fn))
nil)
(values (final-value player board) nil))
(let ((best-node (first nodes)))
(loop for move in nodes
for val = (- (alpha-beta2
(opponent player)
(negate-value move)
(- cutoff) (- achievable)
(- ply 1) eval-fn))
do (when (> val achievable)
(setf achievable val)
(setf best-node move))
until (>= achievable cutoff))
(values achievable best-node))))))
(defun negate-value (node)
"Set the value of a node to its negative."
(setf (node-value node) (- (node-value node)))
node)
(defun legal-nodes (player board eval-fn)
"Return a list of legal moves, each one packed into a node."
(let ((moves (legal-moves player board)))
(sort (map-into
moves
#'(lambda (move)
(let ((new-board (make-move move player
(copy-board board))))
(make-node
:square move :board new-board
:value (funcall eval-fn player new-board))))
moves)
#'> :key #'node-value)))
(defvar *ply-boards*
(apply #'vector (loop repeat 40 collect (initial-board))))
(defun alpha-beta3 (player board achievable cutoff ply eval-fn
killer)
"A-B search, putting killer move first."
(if (= ply 0)
(funcall eval-fn player board)
(let ((moves (put-first killer (legal-moves player board))))
(if (null moves)
(if (any-legal-move? (opponent player) board)
(- (alpha-beta3 (opponent player) board
(- cutoff) (- achievable)
(- ply 1) eval-fn nil))
(final-value player board))
(let ((best-move (first moves))
(new-board (aref *ply-boards* ply))
(killer2 nil)
(killer2-val winning-value))
(loop for move in moves
do (multiple-value-bind (val reply)
(alpha-beta3
(opponent player)
(make-move move player
(replace new-board board))
(- cutoff) (- achievable)
(- ply 1) eval-fn killer2)
(setf val (- val))
(when (> val achievable)
(setf achievable val)
(setf best-move move))
(when (and reply (< val killer2-val))
(setf killer2 reply)
(setf killer2-val val)))
until (>= achievable cutoff))
(values achievable best-move))))))
(defun alpha-beta-searcher3 (depth eval-fn)
"Return a strategy that does A-B search with killer moves."
#'(lambda (player board)
(multiple-value-bind (value move)
(alpha-beta3 player board losing-value winning-value
depth eval-fn nil)
(declare (ignore value))
move)))
(defun put-first (killer moves)
"Move the killer move to the front of moves,
if the killer move is in fact a legal move."
(if (member killer moves)
(cons killer (delete killer moves))
moves))
(defun mobility (player board)
"Current Mobility is the number of legal moves.
Potential mobility is the number of blank squares
adjacent to an opponent that are not legal moves.
Returns current and potential mobility for player."
(let ((opp (opponent player))
(current 0) ; player's current mobility
(potential 0)) ; player's potential mobility
(dolist (square all-squares)
(when (eql (bref board square) empty)
(cond ((legal-p square player board)
(incf current))
((some #'(lambda (sq) (eql (bref board sq) opp))
(neighbors square))
(incf potential)))))
(values current (+ current potential))))
(defvar *edge-table* (make-array (expt 3 10))
"Array of values to player-to-move for edge positions.")
(defconstant edge-and-x-lists
'((22 11 12 13 14 15 16 17 18 27)
(72 81 82 83 84 85 86 87 88 77)
(22 11 21 31 41 51 61 71 81 72)
(27 18 28 38 48 58 68 78 88 77))
"The four edges (with their X-squares).")
(defun edge-index (player board squares)
"The index counts 1 for player; 2 for opponent,
on each square---summed as a base 3 number."
(let ((index 0))
(dolist (sq squares)
(setq index (+ (* index 3)
(cond ((eql (bref board sq) empty) 0)
((eql (bref board sq) player) 1)
(t 2)))))
index))
(defun edge-stability (player board)
"Total edge evaluation for player to move on board."
(loop for edge-list in edge-and-x-lists
sum (aref *edge-table*
(edge-index player board edge-list))))
(defconstant top-edge (first edge-and-x-lists))
(defun init-edge-table ()
"Initialize *edge-table*, starting from the empty board."
;; Initialize the static values
(loop for n-pieces from 0 to 10 do
(map-edge-n-pieces
#'(lambda (board index)
(setf (aref *edge-table* index)
(static-edge-stability black board)))
black (initial-board) n-pieces top-edge 0))
;; Now iterate five times trying to improve:
(dotimes (i 5)
;; Do the indexes with most pieces first
(loop for n-pieces from 9 downto 1 do
(map-edge-n-pieces
#'(lambda (board index)
(setf (aref *edge-table* index)
(possible-edge-moves-value
black board index)))
black (initial-board) n-pieces top-edge 0))))
(defun map-edge-n-pieces (fn player board n squares index)
"Call fn on all edges with n pieces."
;; Index counts 1 for player; 2 for opponent
(cond
((< (length squares) n) nil)
((null squares) (funcall fn board index))
(t (let ((index3 (* 3 index))
(sq (first squares)))
(map-edge-n-pieces fn player board n (rest squares) index3)
(when (and (> n 0) (eql (bref board sq) empty))
(setf (bref board sq) player)
(map-edge-n-pieces fn player board (- n 1) (rest squares)
(+ 1 index3))
(setf (bref board sq) (opponent player))
(map-edge-n-pieces fn player board (- n 1) (rest squares)
(+ 2 index3))
(setf (bref board sq) empty))))))
(defun possible-edge-moves-value (player board index)
"Consider all possible edge moves.
Combine their values into a single number."
(combine-edge-moves
(cons
(list 1.0 (aref *edge-table* index)) ;; no move
(loop for sq in top-edge ;; possible moves
when (eql (bref board sq) empty)
collect (possible-edge-move player board sq)))
player))
(defun possible-edge-move (player board sq)
"Return a (prob val) pair for a possible edge move."
(let ((new-board (replace (aref *ply-boards* player) board)))
(make-move sq player new-board)
(list (edge-move-probability player board sq)
(- (aref *edge-table*
(edge-index (opponent player)
new-board top-edge))))))
(defun combine-edge-moves (possibilities player)
"Combine the best moves."
(let ((prob 1.0)
(val 0.0)
(fn (if (eql player black) #'> #'<)))
(loop for pair in (sort possibilities fn :key #'second)
while (>= prob 0.0)
do (incf val (* prob (first pair) (second pair)))
(decf prob (* prob (first pair))))
(round val)))
(let ((corner/xsqs '((11 . 22) (18 . 27) (81. 72) (88 . 77))))
(defun corner-p (sq) (assoc sq corner/xsqs))
(defun x-square-p (sq) (rassoc sq corner/xsqs))
(defun x-square-for (corner) (cdr (assoc corner corner/xsqs)))
(defun corner-for (xsq) (car (rassoc xsq corner/xsqs))))
(defun edge-move-probability (player board square)
"What's the probability that player can move to this square?"
(cond
((x-square-p square) .5) ;; X-squares
((legal-p square player board) 1.0) ;; immediate capture
((corner-p square) ;; move to corner depends on X-square
(let ((x-sq (x-square-for square)))
(cond
((eql (bref board x-sq) empty) .1)
((eql (bref board x-sq) player) 0.001)
(t .9))))
(t (/ (aref
'#2A((.1 .4 .7)
(.05 .3 *)
(.01 * *))
(count-edge-neighbors player board square)
(count-edge-neighbors (opponent player) board square))
(if (legal-p square (opponent player) board) 2 1)))))
(defun count-edge-neighbors (player board square)
"Count the neighbors of this square occupied by player."
(count-if #'(lambda (inc)
(eql (bref board (+ square inc)) player))
'(+1 -1)))
(defparameter *static-edge-table*
'#2A(;stab semi un
( * 0 -2000) ; X
( 700 * *) ; corner
(1200 200 -25) ; C
(1000 200 75) ; A
(1000 200 50) ; B
(1000 200 50) ; B
(1000 200 75) ; A
(1200 200 -25) ; C
( 700 * *) ; corner
( * 0 -2000) ; X
))
(defun static-edge-stability (player board)
"Compute this edge's static stability"
(loop for sq in top-edge
for i from 0
sum (cond
((eql (bref board sq) empty) 0)
((eql (bref board sq) player)
(aref *static-edge-table* i
(piece-stability board sq)))
(t (- (aref *static-edge-table* i
(piece-stability board sq)))))))
(let ((stable 0) (semi-stable 1) (unstable 2))
(defun piece-stability (board sq)
(cond
((corner-p sq) stable)
((x-square-p sq)
(if (eql (bref board (corner-for sq)) empty)
unstable semi-stable))
(t (let* ((player (bref board sq))
(opp (opponent player))
(p1 (find player board :test-not #'eql
:start sq :end 19))
(p2 (find player board :test-not #'eql
:start 11 :end sq
:from-end t)))
(cond
;; unstable pieces can be captured immediately
;; by playing in the empty square
((or (and (eql p1 empty) (eql p2 opp))
(and (eql p2 empty) (eql p1 opp)))
unstable)
;; Semi-stable pieces might be captured
((and (eql p1 opp) (eql p2 opp)
(find empty board :start 11 :end 19))
semi-stable)
((and (eql p1 empty) (eql p2 empty))
semi-stable)
;; Stable pieces can never be captured
(t stable)))))))
(defun Iago-eval (player board)
"Combine edge-stability, current mobility and
potential mobility to arrive at an evaluation."
;; The three factors are multiplied by coefficients
;; that vary by move number:
(let ((c-edg (+ 312000 (* 6240 *move-number*)))
(c-cur (if (< *move-number* 25)
(+ 50000 (* 2000 *move-number*))
(+ 75000 (* 1000 *move-number*))))
(c-pot 20000))
(multiple-value-bind (p-cur p-pot)
(mobility player board)
(multiple-value-bind (o-cur o-pot)
(mobility (opponent player) board)
;; Combine the three factors into one sum:
(+ (round (* c-edg (edge-stability player board)) 32000)
(round (* c-cur (- p-cur o-cur)) (+ p-cur o-cur 2))
(round (* c-pot (- p-pot o-pot)) (+ p-pot o-pot 2)))))))
(defun Iago (depth)
"Use an approximation of Iago's evaluation function."
(alpha-beta-searcher3 depth #'iago-eval))