name directories like the realm repo.

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-#lang racket
-
-#| 
-   The Dice of Doom game, the eager version  
-   ----------------------------------------
-
-   The Dice of Doom game is a turn-based game for two players sharing one keyboard. 
-   Since this implementation employs an eager strategy to build the complete game 
-   tree of all possible moves, it is only a step in the right direction. 
-
-   Each player owns hexagonal territories, which are arranged into a planar game
-   board. A territory comes with a number of dice. When it is a player's turn, 
-   she marks one of her territories as a launching pad for an attack at a 
-   neigboring territory of the other player. Such an attack is enabled only if 
-   her chosen territory has more dice than the territory of the other player. 
-   The effect of the attack is that the territory changes ownership and that all
-   but one of the attack dice are moved to the newly conquered territory. A 
-   player may continue her turn as long as she can launch attacks. Optionally, 
-   she may choose to pass after her first attack is executed, meaning she ends 
-   her turn. At the end of a turn, a number of dices are distributed across the 
-   players' territories. The game is over when a player whose turn it is cannot
-   attack on her first move. 
-
-   A player can use the following five keys to play the game:
-    -- with ← and → (arrow keys), the player changes the territory focus 
-    -- with enter, the player marks a territory the launching pad for an attack
-    -- with the "d" key, the player unmarks a territory 
-    -- with the "p" key the player passes. 
-   Once a player passes, the game announces whose turn it is next. 
-
-   Play
-   ----
- 
-   Run and evaluate 
-     (roll-the-dice)
-   This will pop up a window that the game board, and instructions. 
-|#
-
-(require 2htdp/image (except-in 2htdp/universe left right)) 
-
-;                                                                                  
-;                                                                                  
-;                                                                                  
-;                                                                                  
-;   ;;;;       ;                            ;;; ;;;                   ;;        ;; 
-;    ;  ;                                    ;   ;                     ;         ; 
-;    ;   ;   ;;;     ;;; ;   ;;;;            ;   ;   ;;;;   ;; ;;;     ;     ;;; ; 
-;    ;   ;     ;    ;   ;;  ;    ;           ; ; ;  ;    ;   ;;        ;    ;   ;; 
-;    ;   ;     ;    ;       ;;;;;;           ; ; ;  ;    ;   ;         ;    ;    ; 
-;    ;   ;     ;    ;       ;                ; ; ;  ;    ;   ;         ;    ;    ; 
-;    ;  ;      ;    ;    ;  ;                ; ; ;  ;    ;   ;         ;    ;   ;; 
-;   ;;;;     ;;;;;   ;;;;    ;;;;;            ; ;    ;;;;   ;;;;;    ;;;;;   ;;; ;;
-;                                                                                  
-;                                                                                  
-;                                                                                  
-;                                                                                  
-
-;; ---------------------------------------------------------------------------------------------------
-;; Data
-
-(struct dice-world (src board gt) #:transparent)
-;; DiceWorld = (dice-world (U #false Natural) Board GameTree)
-;; in (dice-world i b gt)
-;; -- if i is a Natural, it is an index for the territory that the player has marked for an attack
-;; -- if i is #f, no territory has been marked yet 
-;; b is the current board
-;; gt is the game-tree for the given i and b 
-
-(struct game (board player moves) #:transparent)
-;; GameTree = (game Board Player [Listof Move]) 
-;; in (game-tree b p lm)
-;; -- b is the current board 
-;; -- p is the current player 
-;; -- lm is the list of moves that that player may execute 
-
-;; Board = [List-of Territory]
-;; the first field in the list is the currently marked  territory
-
-;; Player ∈ [0, PLAYER#) | Natural 
-
-(struct move (action gt) #:transparent)
-;; Move = (move Action GameTree)
-;; in (move a gt)
-;; -- a represents the actione to be takem 
-;; -- gt is the game-tree resulting from that action 
-
-;; Action is one of:
-;; -- '()                      a passing move
-;; -- (list Natural Natural)   the move where the first attacks the second
-
-(struct territory (index player dice x y) #:transparent)
-;; Territory = (territory Natural Player Dice Integer Integer)
-;; in (territory i p d x y)
-;; -- i is a unique identifier for the territory; it also determines its initial location
-;; -- p is the player who owns this territory
-;; -- d is the number of dice on this board
-;; -- x is the x coordiate of this territory in pixels
-;; -- y is the y coordiate of this territory in pixels
-
-;; Territory Natural -> Territory 
-;; updates number of dice on territory 
-(define (territory-set-dice t d)
-  (territory (territory-index t) (territory-player t) d (territory-x t) (territory-y t)))
-
-;; Territory Player -> Territory 
-;; updates owner of territory 
-(define (territory-set-player t p)
-  (territory (territory-index t) p (territory-dice t) (territory-x t) (territory-y t)))
-
-;; ---------------------------------------------------------------------------------------------------
-;; sample game tree for BOOK 
-
-(define b1
-  (list (territory 1 0 1 'a 'b)
-        (territory 0 0 1 'x 'y)))
-
-(define b1-alternative 
-  (list (territory 0 0 1 'x 'y)
-        (territory 1 0 1 'a 'b)))
-
-(define b3
-  (list (territory 0 0 2 'x 'y)
-        (territory 1 1 1 'a 'b)))
-
-(define gt1 (game b1 1 '()))
-
-(define mv2 (move '() gt1))
-
-(define gt2 (game b1-alternative 0 (list mv2)))
-
-(define mv3 (move '(0 1) gt2))
-
-(define gt3 (game b3 0 (list mv3)))
-
-;; ---------------------------------------------------------------------------------------------------
-;; Constants
-
-; initalization constants
-(define PLAYER# 2)
-(define DICE# 3)
-(define BOARD 2)
-(define GRID (* BOARD BOARD))
-(define INIT-PLAYER 0)
-(define INIT-SPARE-DICE 10)
-; The depth at which to limit the gametree
-(define AI-DEPTH 4)
-(define AI 1)
-
-; graphical constants: territories
-(define DICE-OFFSET 6)
-(define SIDE 75)
-(define OFFSET0 (* 2 SIDE))
-(define ROTATION 30)
-(define HEX 6)
-(define (hexagon color)
-  (rotate ROTATION (regular-polygon SIDE HEX "solid" color)))
-(define X-OFFSET (image-width (hexagon "black")))
-(define Y-OFFSET (* (image-height (hexagon "black")) 3/4))
-
-; graphical constants
-(define COLORS 
-  (list (make-color 255 0 0 100) 
-        (make-color 0 255 0 100) 
-        (make-color 0 0 255 100)))
-(define FOCUS (rotate ROTATION (regular-polygon SIDE 6 "outline" "black")))
-(define D1 (bitmap "graphics/dice1.png"))
-(define D2 (bitmap "graphics/dice2.png"))
-(define D3 (bitmap "graphics/dice3.png"))
-(define D4 (bitmap "graphics/dice4.png"))
-(define IMG-LIST (list D1 D2 D3 D4)) 
-
-(define TEXT-SIZE 25)
-(define TEXT-COLOR "black")
-(define INSTRUCT 
-  "← and → to move among territories, <enter> to mark, <d> to unmark, and <p> to pass")
-(define AI-TURN "It's the Mighty AI's turn")
-(define YOUR-TURN "It's your turn")
-(define INFO-X-OFFSET 100)
-(define INFO-Y-OFFSET 50)
-
-(define INSTRUCTIONS (text INSTRUCT TEXT-SIZE TEXT-COLOR))
-(define WIDTH (+ (image-width INSTRUCTIONS) 50))
-(define HEIGHT 600)
-(define (PLAIN)
-  (define iw (image-width INSTRUCTIONS))
-  (define bw (* SIDE 2 BOARD))
-  (set! WIDTH  (+ (max iw bw) 50))
-  (set! HEIGHT (+ (* SIDE 2 BOARD) 50))
-  (empty-scene WIDTH HEIGHT))
-(define (ISCENE)
-  (define mt (PLAIN))
-  (when (or (> (image-width mt) 1280) (> (image-height mt) 800))
-    (error 'scene "it is impossible to draw a ~s x ~s game scene for a 1280 x 800 laptop screen" (image-width mt) (image-height mt)))
-  (place-image INSTRUCTIONS (* .5 WIDTH) (* .9 HEIGHT) mt))
-
-;                                  
-;                                  
-;                                  
-;                                  
-;   ;;; ;;;            ;           
-;    ;; ;;                         
-;    ;; ;;   ;;;;    ;;;    ;; ;;  
-;    ; ; ;  ;    ;     ;     ;;  ; 
-;    ; ; ;   ;;;;;     ;     ;   ; 
-;    ;   ;  ;    ;     ;     ;   ; 
-;    ;   ;  ;   ;;     ;     ;   ; 
-;   ;;; ;;;  ;;; ;;  ;;;;;  ;;; ;;;
-;                                  
-;                                  
-;                                  
-;                                  
-
-;; ---------------------------------------------------------------------------------------------------
-
-;; start the game 
-(define (roll-the-dice)
-  (big-bang (create-world-of-dice-and-doom)             
-            (on-key interact-with-board)
-            (to-draw draw-dice-world)
-            (stop-when no-more-moves-in-world? 
-                       draw-end-of-dice-world)))
-
-;;  -> DiceWorld
-;; Returns a randomly generated world. If the world that
-;; has been generated starts as a tie, the world is regenerated.
-;; property: world is not in endgame state (no-more-moves? returns false)
-(define (create-world-of-dice-and-doom)
-  (define board (territory-build))
-  (define gamet (game-tree board INIT-PLAYER INIT-SPARE-DICE))
-  (define new-world (dice-world #f board gamet))
-  (if (no-more-moves-in-world? new-world) 
-      (create-world-of-dice-and-doom)
-      new-world))
-
-;; DiceWorld Key -> DiceWorld
-;; Handles key events from a player
-(define (interact-with-board w k)
-  (cond [(key=? "left" k)
-         (refocus-board w left)]
-        [(key=? "right" k)
-         (refocus-board w right)]
-        [(key=? "p" k)
-         (pass w)]
-        [(key=? "\r" k)
-         (mark w)]
-        [(key=? "d" k)
-         (unmark w)]
-        [else w]))
-
-;; Diceworld -> Scene
-;; draws the world
-(define (draw-dice-world w)
-  (add-player-info 
-   (game-player (dice-world-gt w)) 
-   (add-winning-probability w (add-board-to-scene w (ISCENE)))))
-
-;; DiceWorld -> Boolean
-;; is it possible to play any moves from this world state? 
-(define (no-more-moves-in-world? w)
-  (define tree (dice-world-gt w))
-  (define board (dice-world-board w))
-  (define player (game-player tree))
-  (or (no-more-moves? tree)
-      (for/and ((t board)) (= (territory-player t) player))))
-
-;; DiceWorld -> Image
-;; render the endgame screen
-(define (draw-end-of-dice-world w)
-  (define board (dice-world-board w))
-  (define message (text (won board) TEXT-SIZE TEXT-COLOR))
-  (define background (add-board-to-scene w (PLAIN)))
-  (overlay message background))
-
-;; Board -> String
-;; Which player has won the game -- eager is for N human players 
-(define (won board)
-  (define-values (best-score w) (winners board))
-  (if (cons? (rest w)) "It's a tie." "You won."))
-
-;                                  
-;                                  
-;                                  
-;                                  
-;    ;;;;;             ;           
-;      ;                     ;     
-;      ;    ;; ;;    ;;;    ;;;;;  
-;      ;     ;;  ;     ;     ;     
-;      ;     ;   ;     ;     ;     
-;      ;     ;   ;     ;     ;     
-;      ;     ;   ;     ;     ;   ; 
-;    ;;;;;  ;;; ;;;  ;;;;;    ;;;  
-;                                  
-;                                  
-;                                  
-;                                  
-
-;; ---------------------------------------------------------------------------------------------------
-;; Making A Board
-
-;; -> Board
-;; Creates a list of territories the size of GRID with given x and y coordinates
-;; properties: dice is (0,MAX-DICE]
-;;             returns list of size GRID
-(define (territory-build)
-  (for/list ([n (in-range GRID)])
-    (territory n (modulo n PLAYER#) (dice) (get-x n) (get-y n))))
-
-;; -> Natural
-;; the number of initial die on a territory
-(define (dice)
-  (add1 (random DICE#)))
-
-;; Natural -> Number
-;; the x coordinate for territory n of a board 
-(define (get-x n)
-  (+ OFFSET0
-     (if (odd? (get-row n)) 0 (/ X-OFFSET 2))
-     (* X-OFFSET (modulo n BOARD))))
-
-;; Natural -> Number 
-;; the y coordinate for territory n of a board 
-(define (get-y n)
-  (+ OFFSET0 (* Y-OFFSET (get-row n))))
-
-;; ---------------------------------------------------------------------------------------------------
-;; Making a Game Tree
-
-;; Board Player Natural -> GameTree
-;; creates a complete game-tree from the given board, player, and spare dice
-(define (game-tree board player dice)
-  ;; create tree of attacks from this position; add passing move
-  (define (attacks board) 
-    (for*/list ([src board] 
-                [dst (neighbors (territory-index src))]
-                #:when (attackable? board player src dst))
-      (define from (territory-index src))
-      (define dice (territory-dice src))
-      (define newb (execute board player from dst dice))
-      (define attacks-from-newb 
-        (game newb player (cons (passes newb) (attacks newb))))
-      (move (list from dst) attacks-from-newb)))
-  ;; create a passing move , distribute dice, continue
-  (define (passes board)
-    (define-values (new-dice newb) (distribute board player dice))
-    (move '() (game-tree newb (switch player) new-dice)))
-  ;; -- START: -- 
-  (game board player (attacks board)))
-
-;; Player -> Player
-;; switches from one player to the next
-(define (switch player)
-  (modulo (+ player 1) PLAYER#))
-
-;; Board Player Natural -> Natural Board
-;; adds reinforcements to the game board
-;; > (add-new-dice (list (territory 0 2 2 9 0)) 2 2))
-;; (list (territory 0 2 2 9 0))
-(define (distribute board player spare-dice)
-  (for/fold ([dice spare-dice] [new-board '()]) ([t board])
-    (if (and (= (territory-player t) player)
-             (< (territory-dice t) DICE#)
-             (not (zero? dice)))
-        (values (- dice 1) (cons (add-dice-to t) new-board))
-        (values dice (cons t new-board)))))
-
-;; Territory -> Territory 
-;; adds one dice to the given territory
-(define (add-dice-to t)
-  (territory-set-dice t (add1 (territory-dice t))))
-
-;; Board Player Territory Natural -> Boolean
-;; can player attack dst from src?
-(define (attackable? board player src dst)
-  (define dst-t 
-    (findf (lambda (t) (= (territory-index t) dst)) board))
-  (and dst-t
-       (= (territory-player src) player)
-       (not (= (territory-player dst-t) player))
-       (> (territory-dice src) (territory-dice dst-t))))
-
-;; Board Natural Natural Natural Natural -> Board
-;; Creates a new board after an attack
-;; updates only src and dst
-(define (execute board player src dst dice)
-  (for/list ([t board])
-    (define idx (territory-index t))
-    (cond [(= idx src) (territory-set-dice t 1)]
-          [(= idx dst) 
-           (define s (territory-set-dice t (- dice 1)))
-           (territory-set-player s player)]
-          [else t])))
-
-;; ---------------------------------------------------------------------------------------------------
-;; Getting Neigbors
-
-;; Natural -> [List-of Natural]
-;; returns the neighbors of the current spot
-;; > (neighbors 0)
-;; '(1 2 3)
-(define (neighbors pos)  
-  (define top?      (< pos BOARD))
-  (define bottom?   (= (get-row pos) (sub1 BOARD)))
-  (define even-row? (zero? (modulo (get-row pos) 2)))
-  (define right?    (zero? (modulo (add1 pos) BOARD)))
-  (define left?     (zero? (modulo pos BOARD)))
-  (if even-row?
-      (even-row pos top? bottom? right? left?)
-      (odd-row  pos top? bottom? right? left?)))
-
-;; Natural Boolean Boolean Boolean Boolean -> [Listof Naturals]
-;; gets the neighbors for a territory on an even row
-(define (even-row pos top? bottom? right? left?)
-  (append (add (or top? right?)    (add1 (- pos BOARD)))
-          (add (or bottom? right?) (add1 (+ pos BOARD)))
-          (add top?                (- pos BOARD))
-          (add bottom?             (+ pos BOARD))
-          (add right?              (add1 pos))
-          (add left?               (sub1 pos))))
-
-;; Natural Boolean Boolean Boolean Boolean -> [Listof Naturals]
-;; gets the neighbors for a territory on an odd row
-(define (odd-row pos top? bottom? right? left?)
-  (append (add top?               (- pos BOARD))
-          (add bottom?            (+ pos BOARD))
-          (add (or top? left?)    (sub1 (- pos BOARD)))
-          (add (or bottom? left?) (sub1 (+ pos BOARD)))
-          (add right?             (add1 pos))
-          (add left?              (sub1 pos))))
-
-;; Boolean X -> [Listof X]
-;; returns (list x) if (not b) else empty
-(define (add b x)
-  (if b '() (list x)))
-
-;                                                                          
-;                                                                          
-;                                                                          
-;                                                                          
-;   ;;; ;;;                 ;;;;;;                                         
-;    ;   ;                   ;   ;                           ;             
-;    ;  ;    ;;;;   ;;; ;;;  ; ;   ;;;  ;;;  ;;;;   ;; ;;   ;;;;;    ;;;;; 
-;    ; ;    ;    ;   ;   ;   ;;;    ;    ;  ;    ;   ;;  ;   ;      ;    ; 
-;    ;;;    ;;;;;;   ;   ;   ; ;     ;  ;   ;;;;;;   ;   ;   ;       ;;;;  
-;    ;  ;   ;         ; ;    ;       ;  ;   ;        ;   ;   ;           ; 
-;    ;   ;  ;         ; ;    ;   ;    ;;    ;        ;   ;   ;   ;  ;    ; 
-;   ;;;  ;;  ;;;;;     ;    ;;;;;;    ;;     ;;;;;  ;;; ;;;   ;;;   ;;;;;  
-;                      ;                                                   
-;                    ;;;                                                   
-;                                                                          
-;                                                                          
-
-;; ---------------------------------------------------------------------------------------------------
-;; Territory Focusing and Marking 
-
-;; DiceWorld [Board -> Board] -> World
-;; Creates a new World that has a rotated territory list
-;; > (define lterritory (territory 0 0 1 9 2))
-;; > (define rterritory (territory 0 0 1 9 0))
-;; > (refocus-board-action (dice-world -1 (list rterritory lterritory ...) GT) left)
-;; (dice-world -1 (list lterritory ... rterritory) GT)
-;; > (refocus-board-action (dice-world -1 (list lterritory ... rterritory) GT) left)
-;; (dice-world -1 (list rterritory lterritory ...) GT)
-(define (refocus-board w direction)
-  (define source (dice-world-src w))
-  (define board  (dice-world-board w))
-  (define tree   (dice-world-gt w))
-  (define player (game-player tree))
-  (define (owner? tid)
-    (if source (not (= tid player)) (= tid player)))
-  (define new-board (rotate-until owner? board direction))
-  (dice-world source new-board tree))
-
-;; [Player -> Boolean] Board (Board -> Board) -> Board 
-;; rotate until the first element of the list satisfies owned-by 
-(define (rotate-until owned-by board rotate)
-  (define next-list (rotate board))
-  (if (owned-by (territory-player (first next-list))) 
-      next-list
-      (rotate-until owned-by next-list rotate)))
-
-;; Board -> Board
-;; rotate a list to the left 
-(define (left l)
-  (append (rest l) (list (first l))))
-
-;; Board -> Board
-;; rotate a list to the right
-(define (right l)
-  (reverse (left (reverse l))))
-
-;; ---------------------------------------------------------------------------------------------------
-;; Handling Moves
-
-;; DiceWorld -> DiceWorld
-;; executes a passing move on the world state
-;; THIS DEFINITION IS NOT USED FOR THE ABSTRACT VERSION OF THE MODULE. 
-(define (pass.10 w)
-  (define m (find-move (game-moves (dice-world-gt w)) '()))
-  (cond [(not m) w]
-        [else ;; (no-more-moves? m)
-         (dice-world #f (game-board m) m)]))
-
-;; DiceWorld -> DiceWorld
-;; unmarks a marked territory
-(define (unmark w)
-  (dice-world #f (dice-world-board w) (dice-world-gt w)))
-
-;; DiceWorld -> DiceWorld
-;; marks a territory as the launching pad for an attack or launches the attack 
-(define (mark w)
-  (define tree   (dice-world-gt w))
-  (define board  (dice-world-board w))
-  (define source (dice-world-src w))
-  (define focus  (territory-index (first board)))
-  (if source 
-      (attacking w source focus)
-      (dice-world focus board tree)))
-
-;; DiceWorld Natural Natural -> DiceWorld
-(define (attacking w source target)
-  (define feasible (game-moves (dice-world-gt w)))
-  (define attack   (list source target))
-  (define next     (find-move feasible attack))
-  (define src-t    (findf (lambda (t) (= (territory-index t) source))
-                          (dice-world-board w)))
-  (define dst-t    (findf (lambda (t) (= (territory-index t) target))
-                          (dice-world-board w)))
-  (define win? (dice-attack-win src-t dst-t))
-  (cond [(not next) w]
-        [win? (dice-world #f (game-board next) next)]
-        [else (dice-world-attack-lost w src-t)]))
-
-;; [List-of Moves] [or '() [List Natural Natural]] -> [or #f Game-tree] 
-;; find the move from the current list of moves
-(define (find-move moves a)
-  (define m (findf (lambda (m) (equal? (move-action m) a)) moves))
-  (and m (move-gt m)))
-
-;; Game -> Boolean 
-;; are there any moves in this game record? 
-(define (no-more-moves? g)
-  (empty? (game-moves g)))
-
-;; Territory Territory -> Boolean
-;; attack from src territory to destination territory
-;; and see who wins
-(define (dice-attack-win src-t dst-t)
-  (define (roll-dice n)
-    (for/list ([i n])
-      (random 1 7)))
-  (define (sum l)
-    (foldl + 0 l))
-  (define src-attack (sum (roll-dice (territory-dice src-t))))
-  (define dst-defend (sum (roll-dice (territory-dice dst-t))))
-  (if (> src-attack dst-defend) #t #f))
-
-
-(define (probability-of-winning st dt)
-  "Find the probability of source territory defeating destination territory.
-
-  `st` is the source territory.
-  `dt` is the destination territory."
-
-  ; Given the number of dice, returns a list all dice combinations.
-  (define (dice-all-combination dice-num)
-    (cond [(= dice-num 1)
-           (for/list ([i (in-range 1 7)])
-             (list i))]
-          [else
-           (for*/list ([i (in-range 1 7)]
-                       [r (dice-all-combination
-                           (- dice-num 1))])
-             (cons i r))]))
-
-
-  ; Given a list of dice combinations, returns a hashmap where the key
-  ; is the 'dice sum' and the value is the number of combinations
-  ; whose sum is the 'dice sum'.
-  (define (dice-sum-hash dice-combinations)
-    (for/foldr
-        ([h (make-hash)]) ([c dice-combinations])
-        (let ((sum (for/sum ([n c]) n)))
-          (hash-set! h sum (+ (hash-ref h sum 0) 1))
-          h)))
-
-
-  ; sh: -> hashmap
-  ;  key: dice sum,
-  ;  value: number of ways we can arrive at sum
-  (define sh (dice-sum-hash
-              (dice-all-combination (territory-dice st))))
-
-  ; dh: -> hashmap
-  ;  key: dice sum,
-  ;  value: number of ways we can arrive at sum
-  (define dh (dice-sum-hash
-              (dice-all-combination (territory-dice dt))))
-
-  ; Generic probability function.
-  (define (probability f t)
-    (/ (* 1.0 f) t))
-
-  ; Computes the total number of favorable outcomes for the source
-  ; territory when its dice sum is `s-ds` against the
-  ; destination's territory.
-  ;
-  ; s-ds -> source dice sum.
-  ; n    -> number of we can arrive at sum `s-ds`.
-  (define (favorable-outcomes s-ds n)
-    (* (for/sum [(d-ds (hash-keys dh))]
-         (if (< d-ds s-ds)
-             (hash-ref dh d-ds)
-             0))
-       n))
-
-  ; Computes the total number of favorable outcomes for the source
-  ; territory against the destination's territory.
-  (define (all-favorable-outcomes)
-    (foldr + 0
-           (for/list [(s-ds (hash-keys sh))]
-             (favorable-outcomes
-              s-ds
-              (hash-ref sh s-ds)))))
-
-  (define (all-outcomes)
-    (let ((sd (territory-dice st))
-          (dd (territory-dice dt)))
-      (* (expt 6 sd) (expt 6 dd))))
-
-  (probability (all-favorable-outcomes) (all-outcomes)))
-
-
-;; DiceWorld Territory -> DiceWorld
-;; generate dice world for the case where player
-;; loses the dice attack
-(define (dice-world-attack-lost w src-t)
-  (define src (territory-index src-t))
-  (define player (territory-player src-t))
-  (define newb (for/list ([t (dice-world-board w)])
-                 (define idx (territory-index t))
-                 (cond [(= idx src) (territory-set-dice t 1)]
-                       [else t])))
-  (define new-gt (game-tree newb player 0))
-  (dice-world #f newb new-gt))
-
-;                                                                          
-;                                                                          
-;                                                                          
-;                                                                          
-;   ;;;;;                       ;;                     ;                   
-;    ;   ;                       ;                                         
-;    ;   ;   ;;;;   ;; ;;    ;;; ;   ;;;;   ;; ;;;   ;;;    ;; ;;    ;;; ;;
-;    ;   ;  ;    ;   ;;  ;  ;   ;;  ;    ;   ;;        ;     ;;  ;  ;   ;; 
-;    ;;;;   ;;;;;;   ;   ;  ;    ;  ;;;;;;   ;         ;     ;   ;  ;    ; 
-;    ;  ;   ;        ;   ;  ;    ;  ;        ;         ;     ;   ;  ;    ; 
-;    ;   ;  ;        ;   ;  ;   ;;  ;        ;         ;     ;   ;  ;   ;; 
-;   ;;;   ;  ;;;;;  ;;; ;;;  ;;; ;;  ;;;;;  ;;;;;    ;;;;;  ;;; ;;;  ;;; ; 
-;                                                                        ; 
-;                                                                    ;;;;  
-;                                                                          
-;                                            
-
-;; Player Scene-> Scene
-;; Draws the world
-(define (add-player-info player s)
-  (define str (whose-turn player))
-  (define txt (text str TEXT-SIZE TEXT-COLOR))
-  (place-image txt (- WIDTH INFO-X-OFFSET) INFO-Y-OFFSET s))
-
-(define (add-winning-probability w s)
-  (define board  (dice-world-board w))
-  (define source (dice-world-src w))
-  (define target (territory-index (first board)))
-  (define feasible (game-moves (dice-world-gt w)))
-  (define attack   (list source target))
-  (define next     (find-move feasible attack))
-
-  (define (find-territory index)
-    (findf (lambda (t) (= (territory-index t) index))
-           (dice-world-board w)))
-
-  (if (and source next)
-      (place-image
-       (text (string-append
-              "Winning Probability "
-              (~r
-               (probability-of-winning (find-territory source)
-                                       (find-territory target))
-               #:precision 2))
-             TEXT-SIZE TEXT-COLOR)
-       (- WIDTH 150) 100 s)
-      s))
-
-;; DiceWorld Scene -> Scene
-;; folds through the board and creates an image representation of it
-(define (add-board-to-scene w s)
-  (define board   (dice-world-board w))
-  (define player  (game-player (dice-world-gt w)))
-  (define focus?  (dice-world-src w))
-  (define trtry1  (first board))
-  (define p-focus (territory-player trtry1))
-  (define t-image (draw-territory trtry1))
-  (define image (draw-focus focus? p-focus player t-image))
-  (define base-s  (add-territory trtry1 image s))
-  (for/fold ([s base-s]) ([t (rest board)])
-    (add-territory t (draw-territory t) s)))
-
-;; Nat Player Player Image -> Image 
-;; add focus marker to territory if needed 
-(define (draw-focus marked? p-in-focus p t-image)
-  (if (or (and (not marked?) (= p-in-focus p))
-          (and marked? (not (= p-in-focus p))))
-      (overlay FOCUS t-image)
-      t-image))
-
-;; Image Territory Image -> Image 
-(define (add-territory t image scene)
-  (place-image image (territory-x t) (territory-y t) scene))
-
-;; Territory -> Image
-;; renders a single territory
-(define (draw-territory t)
-  (define color (color-chooser (territory-player t)))
-  (overlay (hexagon color) (draw-dice (territory-dice t))))
-
-;; Natural -> Image
-;; renders all n >= 1 dice as a stack of dice 
-(define (draw-dice n)
-  (define first-die  (get-dice-image 0))
-  (define height-die (image-height first-die))
-  (for/fold ([s first-die]) ([i (- n 1)])
-    (define dice-image (get-dice-image (+ i 1)))
-    (define y-offset  (* height-die (+ .5 (* i .25))))
-    (overlay/offset s 0 y-offset dice-image)))
-
-;; Player -> Color
-;; Determines a color for each player
-(define (color-chooser p)
-  (list-ref COLORS p))
-
-;; -> Image
-;; returns an image from the list of dice images 
-(define (get-dice-image i)
-  (list-ref IMG-LIST (modulo i (length IMG-LIST))))
-
-;                                                  
-;                                                  
-;                                                  
-;                                                  
-;   ;;;;;;              ;;     ;                   
-;    ;   ;               ;                         
-;    ; ;    ;; ;;    ;;; ;   ;;;    ;; ;;    ;;; ;;
-;    ;;;     ;;  ;  ;   ;;     ;     ;;  ;  ;   ;; 
-;    ; ;     ;   ;  ;    ;     ;     ;   ;  ;    ; 
-;    ;       ;   ;  ;    ;     ;     ;   ;  ;    ; 
-;    ;   ;   ;   ;  ;   ;;     ;     ;   ;  ;   ;; 
-;   ;;;;;;  ;;; ;;;  ;;; ;;  ;;;;;  ;;; ;;;  ;;; ; 
-;                                                ; 
-;                                            ;;;;  
-;                                                  
-;                                                  
-
-;; Board ->* Natural [non-empty-listof Player]
-;; gives the number of winning territories and the players(s) who have them
-;; > (winners (list (territory 0 0 1 9 0) (territory 0 0 1 9 1)))
-;; (values 2 '(0))
-;; > (winners (list (territory 0 1 1 9 0) (territory 0 0 1 9 1)))
-;; (values 1 '(0 1))
-(define (winners board)
-  (for/fold ([best 0][winners '()]) ([p PLAYER#])
-    (define p-score (sum-territory board p))
-    (cond [(> p-score best) (values p-score (list p))]
-          [(< p-score best) (values best winners)]
-          [(= p-score best) (values best (cons p winners))])))
-
-;; Board Player -> Natural
-;; counts the number of territorys the player owns
-;; > (sum-territory (list (territory 0 1 1 9 0) (territory 0 1 1 9 1)) 1)
-;; 2
-(define (sum-territory board player)
-  (for/fold ([result 0]) ([t board])
-    (if (= (territory-player t) player) (+ result 1) result)))
-
-
-;                      
-;                      
-;                      
-;                      
-;                      
-;     ;;;     ;;;;;;;  
-;      ;;        ;     
-;     ;  ;       ;     
-;     ;  ;       ;     
-;     ;  ;       ;     
-;    ;;;;;;      ;     
-;    ;    ;      ;     
-;   ;      ;     ;     
-;  ;;;    ;;; ;;;;;;;  
-;                      
-;                      
-;                      
-;                      
-
-;; Player -> {AI-TURN, YOUR-TURN}
-;; THIS REQUIRES A DIFFERENT DEFINITION FOR PLAIN CHAPTER 10. 
-(define (whose-turn player)
-  (if (= player AI) AI-TURN YOUR-TURN))
-
-;; DiceWorld -> DiceWorld
-;; executes a passing move on the world state
-;; THIS REQUIRES A DIFFERENT DEFINITION FOR PLAIN CHAPTER 10.
-(define (pass w)
-  (define m (find-move (game-moves (dice-world-gt w)) '()))
-  (cond [(not m) w]
-        [(or (no-more-moves? m) (not (= (game-player m) AI)))
-         (dice-world #f (game-board m) m)]
-        [else
-         (define ai (the-ai-plays m))
-         (dice-world #f (game-board ai) ai)]))
-
-;; GameTree -> GameTree
-;; Computer calls this function until it is no longer the player
-(define (the-ai-plays tree)
-  (define ratings  (rate-moves tree AI-DEPTH))
-  (define the-move (first (argmax second ratings)))
-  (define new-tree (move-gt the-move))
-  (if (= (game-player new-tree) AI)
-      (the-ai-plays new-tree)
-      new-tree))
-
-;; GameTree Natural -> [List-of (List Move Number)]
-;; assigns a value to each move that is being considered
-;; and return those values in a list
-(define (rate-moves tree depth)
-  (for/list ((move (game-moves tree)))
-    (list move (rate-position (move-gt move) (- depth 1)))))
-
-;; GameTree Natural -> Number
-;; Returns a number that is the best move for the given player.
-(define (rate-position tree depth)
-  (cond [(or (= depth 0) (no-more-moves? tree))
-         (define-values (best w) (winners (game-board tree)))
-         (if (member AI w) (/ 1 (length w)) 0)]
-        [else 
-         (define ratings (rate-moves tree depth))
-         (apply (if (= (game-player tree) AI) max min)
-                (map second ratings))]))
-
-;                                  
-;                                  
-;                                  
-;                                  
-;     ;;                           
-;      ;                           
-;     ; ;   ;;  ;;  ;;  ;;   ;;;;; 
-;     ; ;    ;   ;   ;  ;   ;    ; 
-;     ; ;    ;   ;    ;;     ;;;;  
-;     ;;;    ;   ;    ;;         ; 
-;    ;   ;   ;  ;;   ;  ;   ;    ; 
-;   ;;; ;;;   ;; ;; ;;  ;;  ;;;;;  
-;                                  
-;                                  
-;                                  
-;                                  
-
-;; Natural -> Natural
-;; gets the row that territory is on, indexed from 0
-;; [test vary on current board-size]
-(define (get-row pos)
-  (quotient pos BOARD))
-
-
-;                                                    
-;                                                    
-;                                                    
-;                                                    
-;                                                    
-;   ;;;;;;;                        ;                 
-;   ;  ;  ;                        ;                 
-;   ;  ;  ;     ;;;      ;;;; ;   ;;;;;;     ;;;; ;  
-;   ;  ;  ;    ;   ;    ;    ;;    ;        ;    ;;  
-;      ;      ;     ;   ;          ;        ;        
-;      ;      ;;;;;;;    ;;;;;     ;         ;;;;;   
-;      ;      ;               ;    ;              ;  
-;      ;       ;    ;   ;     ;    ;    ;   ;     ;  
-;    ;;;;;      ;;;;    ;;;;;;      ;;;;    ;;;;;;   
-;                                                    
-;                                                    
-;                                                    
-;                                 
-
-;; ---------------------------------------------------------------------------------------------------
-
-;; Natural -> Void 
-;; make the board larger 
-(define (set-grid n)
-  (set! BOARD n)
-  (set! GRID (* n n)))
-
-(module+ test 
-  
-  (require rackunit rackunit/text-ui)
-  
-  ;; (-> any) -> void
-  ;; runs the thunk PROP-NUM times
-  (define (check-property t)
-    (test-begin (for ((i 50)) (t))))
-  
-  ;; Properties
-  (define (property:starting-world-playable)
-    (unless (and (= BOARD 2) (= PLAYER# 2))
-      (error 'starting-world-playable "BOARD-SIZE != 2 or PLAYERS# != 2"))
-    (check-false (no-more-moves-in-world? (create-world-of-dice-and-doom))))
-  
-  (define (property:dice-in-range)
-    (check-true (andmap (λ (b) (>= DICE# (territory-dice b) 1)) (territory-build))
-                "dice out of range"))
-  
-  (define (property:board-correct-size)
-    (check-equal? (length (territory-build)) GRID
-                  "board incorrect-size"))
-  
-  (define (property:no-pass-on-first-move)
-    (define (move-action? m) (equal? (move-action m) '()))
-    (check-true (not (memf move-action? (game-moves (game-tree (territory-build) 0 0))))
-                "no pass on first move"))
-  
-  ;; ---------------------------------------------------------------------------------------------------
-  
-  
-  ;; testing game initialization
-  
-  (check-equal? (territory-index (first (territory-build))) 0)
-  (check-equal? (territory-player (first (territory-build))) 0)
-  (check-equal? (territory-index (second (territory-build))) 1)
-  (check-equal? (territory-player (second (territory-build))) 1)
-  (check-equal? (territory-index (third (territory-build))) 2)
-  (check-equal? (territory-player (third (territory-build))) 0)
-  (check-equal? (territory-index (fourth (territory-build))) 3)
-  (check-equal? (territory-player (fourth (territory-build))) 1)
-  
-  (check-property property:starting-world-playable)
-  (check-property property:board-correct-size)
-  (check-property property:dice-in-range)
-  (check-property property:no-pass-on-first-move)
-  
-  ;; ---------------------------------------------------------------------------------------------------
-  ;; testing territory manipulation
-  
-  ;; legal?
-  (check-true 
-   (and (attackable? (list (territory 0 0 2 9 0) (territory 3 1 1 9 0)) 0 (territory 0 0 2 9 0) 3) #t))
-  (check-false
-   (attackable? (list (territory 0 0 2 9 0) (territory 3 1 1 9 0)) 0 (territory 0 0 2 9 0) 0))
-  (check-false
-   (attackable? (list (territory 0 0 2 9 0) (territory 5 1 1 9 0)) 1 (territory 0 0 2 9 0) 5))
-  
-  ;; get-row
-  (check-equal? (get-row 0) 0)
-  (check-equal? (get-row 1) 0)
-  (check-equal? (get-row 2) 1)
-  (check-equal? (get-row 3) 1)
-  (check-equal? (get-row 12) 6) ;; checks math. actually invalid on board of size 2
-  (check-equal? (get-row 11) 5) ;; checks math. actually invalid on board of size 2
-  (check-equal? (get-row 13) 6) ;; checks math. actually invalid on board of size 2
-  (check-equal? (get-row 14) 7) ;; checks math. actually invalid on board of size 2
-  
-  ;; ---------------------------------------------------------------------------------------------------
-  (define board3 
-    (list (territory 0 1 1 9 0) (territory 1 1 1 8 0) (territory 2 1 3 43.5 5) (territory 3 1 1 6 5)))
-  (define b1+0+3
-    (list (territory 0 0 2 9 0) (territory 1 1 1 8 0) (territory 2 0 2 43.5 5) (territory 3 1 1 6 5)))
-  (define b2+1+2
-    (list (territory 0 0 1 9 0) (territory 1 1 3 8 0) (territory 2 0 2 43.5 5) (territory 3 1 2 6 5)))
-  (define board6
-    (list (territory 0 0 1 9 0) (territory 1 1 2 8 0) (territory 2 0 3 43.5 5) (territory 3 1 2 6 5)))
-  (define bard6+
-    (list (territory 0 0 1 9 0) (territory 1 1 2 8 0) (territory 2 0 3 43.5 5) (territory 3 1 2 6 5)))
-  
-  (define (distribute/list a b c)
-    (define-values (x y) (distribute a b c))
-    (list x y))
-  
-  (define board0 
-    (list (territory 0 0 1 9 0) (territory 1 1 2 8 0) (territory 2 0 2 43.5 5) (territory 3 1 1 6 5)))
-  (define board1 
-    (list (territory 0 0 1 9 0) (territory 1 1 1 8 0) (territory 2 0 1 43.5 5) (territory 3 1 1 6 5)))
-  (define b1+1+2 
-    (list (territory 0 0 1 9 0) (territory 1 1 2 8 0) (territory 2 0 1 43.5 5) (territory 3 1 2 6 5)))
-  (define board2 
-    (list (territory 0 0 1 9 0) (territory 1 1 1 8 0) (territory 2 0 3 43.5 5) (territory 3 1 1 6 5)))
-  
-  (define g-tree1 (game board1 0 '()))
-  (define g-tree2 (game-tree board0 0 0))
-  
-  ; (define world31 (dice-world #f board1 g-tree1))
-  (define world2 (dice-world #f board2 g-tree2))
-  
-  ;; testing book tree
-  
-  (check-equal? (game-tree (list (territory 0 0 2 'x 'y)
-                                 (territory 1 1 1 'a 'b))
-                           0
-                           0)
-                gt3)
-  
-  
-  ;; testing tree generation
-  
-  (define (property:attack-location-valid)
-    (define moves (game-moves (game-tree (territory-build) 0 0)))
-    (check-true (and (for/and ([m moves])
-                       (define m1 (move-action m))
-                       (member (second m1) (neighbors (first m1))))
-                     #t)
-                "invalid attack location"))
-  
-  (define (property:add-to-territory-always-up-one)
-    (define r (random 10000))
-    (check-equal? (add-dice-to (territory 0 0 r 0 0))
-                  (territory 0 0 (add1 r) 0 0)
-                  "add to territory always up one"))
-  
-  (define (property:attackable?-does-not-need-neighbores-check)
-    (define (check-attackable? gt)
-      (for/and ([move (game-moves gt)]
-                #:when (not (empty? (move-action move))))
-        (define action (move-action move))
-        (define gt (move-gt move))
-        (and (member (second action) (neighbors (first action)))
-             (check-attackable? gt))))
-    
-    ;;start
-    (define old-size BOARD)
-    (set-grid 2)
-    (define testing-gt (dice-world-gt (create-world-of-dice-and-doom)))
-    (check-true (check-attackable? testing-gt) "An attack move between non-neighbores was created")
-    (set-grid old-size))
-  
-  
-  ;; game-tree
-  (check-equal? (game-tree board1 0 0) g-tree1)
-  (check-equal? (game-tree board3 1 0) (game board3 1 '()))
-  (check-equal? (game-tree board3 0 0) (game board3 0 '()))
-  (check-property property:attackable?-does-not-need-neighbores-check)
-  
-  ;; find-move
-  (check-false (find-move '() '()))
-  (check-equal? (find-move (list (move '() (game '() 0 '()))) '()) (game '() 0 '()))
-  ;; Attacking-Moves
-  (check-property property:attack-location-valid)
-  
-  ;; switch-players
-  (check-equal? (switch 0) 1)
-  (check-equal? (switch 1) 0)
-  
-  ;; Add-New-Dice
-  (check-equal? (distribute/list (game-board g-tree1) 0 3) (list 1 (reverse b1+0+3)))
-  (check-equal? (distribute/list (game-board g-tree1) 1 2) (list 0 (reverse b1+1+2)))
-  (check-equal? (distribute/list (game-board g-tree2) 1 2) (list 0 (reverse b2+1+2)))
-  (check-equal? (distribute/list board6 0 0) (list 0 (reverse bard6+)))
-  
-  ;; add-to-territory
-  (check-equal? (add-dice-to (territory 0 1 2 9 0)) (territory 0 1 3 9 0))
-  (check-equal? (add-dice-to (territory 0 1 1 9 0)) (territory 0 1 2 9 0))
-  (check-equal? (add-dice-to (territory 0 1 5 9 0)) (territory 0 1 6 9 0))
-  (check-property property:add-to-territory-always-up-one)
-  
-  ;; ---------------------------------------------------------------------------------------------------
-  (define board7
-    (list (territory 0 0 1 9 0) (territory 1 1 1 8 0) (territory 2 0 2 43.5 5) (territory 3 1 1 6 5)))
-  (define board8
-    (list (territory 0 1 1 9 0) (territory 1 1 1 8 0) (territory 2 0 3 43.5 5) (territory 3 1 1 6 5)))
-  (define board9
-    (list (territory 0 0 1 9 0) (territory 1 1 1 8 0) (territory 2 0 2 43.5 5) (territory 3 0 1 6 5)))
-  (define board10
-    (list (territory 0 0 1 9 0) (territory 1 1 3 8 0) (territory 2 0 2 43.5 5) (territory 3 1 1 6 5)))
-  
-  ;; testing attacks
-  
-  (check-equal? 
-   (execute board7 0 2 1 2)
-   (list (territory 0 0 1 9 0) (territory 1 0 1 8 0) (territory 2 0 1 43.5 5) (territory 3 1 1 6 5)))
-  
-  (check-equal? 
-   (execute board8 0 2 1 3)
-   (list (territory 0 1 1 9 0) (territory 1 0 2 8 0) (territory 2 0 1 43.5 5) (territory 3 1 1 6 5)))
-  
-  (check-equal? 
-   (execute board9 0 2 1 2)
-   (list (territory 0 0 1 9 0) (territory 1 0 1 8 0) (territory 2 0 1 43.5 5) (territory 3 0 1 6 5)))
-  
-  (check-equal?
-   (execute board10 1 1 0 3)
-   (list(territory 0 1 2 9 0) (territory 1 1 1 8 0) (territory 2 0 2 43.5 5) (territory 3 1 1 6 5)))
-  
-  ;; Neighbors
-  (check-equal? (neighbors 2) '(0 3))
-  (check-equal? (neighbors 0) '(3 2 1))
-  (check-equal? (neighbors 1) '(3 0)) 
-  (check-equal? (neighbors 3) '(1 0 2))
-  
-  ;; ---------------------------------------------------------------------------------------------------
-  (define board20
-    (list (territory 0 0 1 9 2) (territory 1 0 1 9 0) (territory 2 2 1 9 0)))
-  (define board21 
-    (list (territory 0 1 1 9 0) (territory 1 1 1 8 0) (territory 2 1 1 43.5 5) (territory 3 1 1 6 5)))
-  
-  ;; testing focus manipulation 
-  ;; interact-with-board
-  (check-equal? 
-   (interact-with-board world2 "\r")
-   (dice-world (territory-index (car (dice-world-board world2))) (dice-world-board world2) g-tree2))
-  
-  (check-equal? (interact-with-board world2 "p") world2)
-  
-  ;; refocus-board-action
-  (check-equal? 
-   (refocus-board (dice-world #f (list (territory 0 0 1 9 0) (territory 0 0 1 9 2)) g-tree1) left)
-   (dice-world #f (list (territory 0 0 1 9 2) (territory 0 0 1 9 0)) g-tree1))
-  
-  (check-equal? 
-   (refocus-board (dice-world #f (list (territory 0 0 1 9 2) (territory 0 1 1 9 0)) g-tree1) right)
-   (dice-world #f (list (territory 0 0 1 9 2) (territory 0 1 1 9 0)) g-tree1))
-  
-  (check-equal? 
-   (refocus-board (dice-world 0 board20 g-tree1) left)
-   (dice-world 0 (list (territory 2 2 1 9 0) (territory 0 0 1 9 2) (territory 1 0 1 9 0)) g-tree1))
-  
-  (check-equal? 
-   (refocus-board (dice-world 0 (list (territory 0 0 1 9 2) (territory 0 1 1 9 0)) g-tree1) left)
-   (dice-world 0 (list  (territory 0 1 1 9 0) (territory 0 0 1 9 2)) g-tree1))
-  
-  (check-equal? 
-   (refocus-board (dice-world 0 (list(territory 0 0 1 9 2) (territory 0 1 1 9 0)) g-tree1) right)
-   (dice-world 0 (list  (territory 0 1 1 9 0) (territory 0 0 1 9 2)) g-tree1))
-  
-  ;;unmark
-  (check-equal? (unmark (dice-world 1 board21 g-tree1)) (dice-world #f board21 g-tree1))
-  
-  (check-equal? (unmark (dice-world 1 (list (territory 0 1 1 9 0) (territory 1 1 1 8 0)) g-tree1))
-                (dice-world #f (list (territory 0 1 1 9 0) (territory 1 1 1 8 0)) g-tree1))
-  (check-equal? (unmark (dice-world 0 (list (territory 0 1 1 9 0)) g-tree1))
-                (dice-world #f (list (territory 0 1 1 9 0)) g-tree1))
-  (check-equal? (unmark (dice-world #f (list (territory 0 1 1 9 0)) g-tree1))
-                (dice-world #f (list (territory 0 1 1 9 0)) g-tree1))
-  
-  ;; ---------------------------------------------------------------------------------------------------
-  (define (winners/list w)
-    (define-values (a b) (winners w))
-    (cons a b))
-  
-  ;; testing functions that determine 'winning' and declare the winner
-  
-  ;; winners
-  (check-equal? (winners/list (list (territory 0 0 1 9 0) (territory 0 0 1 9 1))) (list 2 0))
-  (check-equal? (winners/list (list (territory 0 1 1 9 0) (territory 0 0 1 9 1))) (list 1 1 0))
-  
-  ;; sum-territory
-  (check-equal? (sum-territory (list (territory 0 0 1 9 0) (territory 0 0 1 9 1)) 0) 2)
-  (check-equal? (sum-territory (list (territory 0 0 1 9 0) (territory 0 0 1 9 1)) 1) 0)
-  (check-equal? (sum-territory (list (territory 0 0 1 9 0) (territory 0 0 1 9 1)) 2) 0)
-  (check-equal? (sum-territory (list (territory 0 1 1 9 0) (territory 0 0 1 9 1)) 1) 1)
-  (check-equal? (sum-territory (list (territory 0 1 1 9 0) (territory 0 0 1 9 1)) 0) 1)
-  
-  ;; ---------------------------------------------------------------------------------------------------
-  ;; testing the AI 
-  
-  (define tree0
-    (game-tree (list (territory 0 1 3 0 0)
-                     (territory 1 0 2 0 0)
-                     (territory 2 0 2 0 0) 
-                     (territory 3 0 2 0 0))
-               1 15))
-  
-  (define territory1 (territory 3 0 3 280 262.5))
-  
-  (define board31 
-    (list territory1
-          (territory 2 0 3 150 262.5)
-          (territory 1 1 2 345 150)
-          (territory 0 0 2 215 150)))
-  
-  (define world1 
-    (dice-world #f board31 (game board31 1 '())))
-  
-  ;; testing the AI functions 
-  
-  ;; MF: one of these two tests should fail! 
-  (check-true (and (attackable? board31 0 territory1 1) #t))
-  (check-true (no-more-moves-in-world? world1))
-  
-  (check-equal? (interact-with-board (dice-world 3 '() '()) "d")
-                (dice-world #f '() '()))
-  
-  (check-equal? (game-board (the-ai-plays tree0))
-                (list (territory 3 1 3 0 0)
-                      (territory 2 0 2 0 0)
-                      (territory 1 0 2 0 0) 
-                      (territory 0 1 2 0 0)))
-  
-  (check-equal? (game-player (the-ai-plays tree0))
-                0)
-  
-  (check-equal? (game-board (move-gt (first (game-moves tree0))))
-                (list (territory 0 1 1 0 0)
-                      (territory 1 0 2 0 0)
-                      (territory 2 0 2 0 0)
-                      (territory 3 1 2 0 0)))
-  
-  (check-equal? (game-player (move-gt (first (game-moves tree0))))
-                1)
-  
-  (check-equal? (rate-position tree0 AI-DEPTH) 1/2)
-  (check-equal? (rate-position (move-gt (first (game-moves tree0))) AI-DEPTH)
-                1/2)
-  
-  "all tests run")