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#lang racket
#lang racket
(struct wins [stay switch] #:transparent)
(require rackunit)
(define (random-door)
(+ 1 (random 3)))
(define (one-in-three choice)
;;Part 1: Defining Monty, a selection of three doors
;;--------------------------------------------------------------------------------------------------
(struct Monty [door1 door2 door3] #:transparent)
;; -> Monty
(define (init-Monty) (Monty -1 -1 -1))
;;Integer->Monty
(define (set-Monty choice)
(cond
[(= choice 1) (Monty 1 0 0)]
[(= choice 2) (Monty 0 1 0)]
[(= choice 3) (Monty 0 0 1)]
[else (error "ERROR: Incorrect choice given for scenario!")]
))
;; ->Integer
(define (random-door) (+ 1 (random 3)))
;; ->Monty
(define (random-Monty)
(set-Monty (random-door)))
;; Monty->list
(define (Monty-to-list uMonty) (list (Monty-door1 uMonty) (Monty-door2 uMonty) (Monty-door3 uMonty)))
;; Monty-list, Monty-> Monty
(define (list-to-Monty-handler M-list uMonty)
(cond
[(= (length M-list) 3) (list-to-Monty-handler (rest M-list)
(Monty (first M-list) (Monty-door2 uMonty) (Monty-door3 uMonty)))
]
[(= (length M-list) 2) (list-to-Monty-handler (rest M-list)
(Monty (Monty-door1 uMonty) (first M-list) (Monty-door3 uMonty)))
]
[(= (length M-list) 1) (Monty (Monty-door1 uMonty) (Monty-door2 uMonty) (first M-list))
]
[else (error "ERROR: list is not representative of choice")]
))
;;Monty-list -> Monty
(define (list-to-Monty M-list) (list-to-Monty-handler M-list (init-Monty)))
;; type, list -> list
(define (append-list item list)
(reverse (cons item (reverse list)))
)
;; int, list -> list of Montys
(define (random-lom-handler size list)
(cond
[(= (length list) size) list]
[else (random-lom-handler size (append-list (random-Monty) list))]
))
(define (random-lom size) (random-lom-handler size '()))
;;==================================================================================================
;;Monty tests
;;Test-Monty
(define test-Monty (random-Monty))
;;Test symmetry for list->Monty/Monty->list functions
(check-equal? (list-to-Monty (Monty-to-list test-Monty)) test-Monty)
;;Part 2: Defining Choice, a choice for each door
;;--------------------------------------------------------------------------------------------------
(struct Choice [chosen1 chosen2 chosen3] #:transparent)
;; -> Choice
(define (init-Choice) (Choice 0 0 0))
;; Choice -> list
(define (Choice-to-list uChoice)
(list (Choice-chosen1 uChoice) (Choice-chosen2 uChoice) (Choice-chosen3 uChoice)
))
;; Choice-list, Choice -> Choice
(define (list-to-Choice-handler C-list uChoice)
(cond
[(= (length C-list) 3) (list-to-Choice-handler (rest C-list)
(Choice (first C-list) (Choice-chosen2 uChoice) (Choice-chosen3 uChoice)))
]
[(= (length C-list) 2) (list-to-Choice-handler (rest C-list)
(Choice (Choice-chosen1 uChoice) (first C-list) (Choice-chosen3 uChoice)))
]
[(= (length C-list) 1) (Choice (Choice-chosen1 uChoice) (Choice-chosen2 uChoice) (first C-list))
]
[else (error "ERROR: list is not representative of choice")]
))
;; Choice-list -> Choice
(define (list-to-Choice C-list) (list-to-Choice-handler C-list (init-Choice)))
;; int, Choice-> Choice
(define (set-Choice index uChoice)
(cond
[(= index 1) (Choice 1 0 0)]
[(= index 2) (Choice 0 1 0)]
[(= index 3) (Choice 0 0 1)]
[else (error "ERROR: choice not contained in scenario!")]
))
;; ->Choice
(define (random-Choice) (set-Choice (random-door) (init-Choice)))
;; int, list -> list of Choices
(define (random-loc-handler size list)
(cond
[(= (length list) size) list]
[else (random-loc-handler size (append-list (random-Choice) list))]
))
(define (random-loc size) (random-loc-handler size '()))
;;==================================================================================================
;;Choice tests
;;Test-Monty
(define test-Choice (random-Choice))
;;Test symmetry for list->Monty/Monty->list functions
(check-equal? (list-to-Choice (Choice-to-list test-Choice)) test-Choice)
;;Part 3: Collection, an accumulator to report straight wins and switch wins
;;--------------------------------------------------------------------------------------------------
(struct Clct [strt switch] #:transparent)
;;->Clct
(define (init-Clct) (Clct 0 0))
;;Clct->Clct
(define (strt-win uClct)
(Clct (add1 (Clct-strt uClct)) (Clct-switch uClct))
)
;;Clct->Clct
(define (switch-win uClct)
(Clct (Clct-strt uClct) (add1 (Clct-switch uClct)))
)
;;Clct->int
(define (game-total uClct) (+ (Clct-strt uClct) (Clct-switch uClct)))
;;Clct->pClct (Percent Collection)
(define (report-stats uClct)
(Clct (* 100 (/ (exact->inexact (Clct-strt uClct)) (game-total uClct)))
(* 100 (/ (exact->inexact (Clct-switch uClct)) (game-total uClct)))
))
;;==================================================================================================
;;Collection tests
(define test-Collect (init-Clct))
(check-equal? test-Collect (Clct 0 0 ))
(check-equal? (strt-win test-Collect) (Clct 1 0 ))
(check-equal? (switch-win test-Collect) (Clct 0 1 ))
(define test-Collect2 (Clct 1 1 ))
(check-equal? (game-total test-Collect2) 2)
(check-equal? (report-stats test-Collect2) (Clct 50.0 50.0))
;;Part 4: Defining Gameshow, a representation of the choices and the doors
;;--------------------------------------------------------------------------------------------------
(struct Gameshow [Choice Monty] #:transparent)
;;Choice, Monty-> Gameshow
(define (set-Gameshow uChoice uMonty) (Gameshow uChoice uMonty))
;; ->Gameshow
(define (random-Gameshow) (Gameshow (random-Choice) (random-Monty)))
;; int, (empty) list -> list of Gameshows
(define (random-log-handler size list)
(cond
[(= (length list) size) list]
[else (random-log-handler size (append-list (random-Gameshow) list))]
))
;; int -> list of Gameshows
(define (random-log size) (random-log-handler size '()))
;;==================================================================================================
;;Gameshow tests
;;Part 5: Host functions
;;--------------------------------------------------------------------------------------------------
;;Choice, Monty -> Gameshow
(define (Host-reveal-handler uChoice uMonty)
(cond
[(zero? (+ (Choice-chosen1 uChoice) (Monty-door1 uMonty)))
(Gameshow (Choice -1 (Choice-chosen2 uChoice) (Choice-chosen3 uChoice)) uMonty)]
[(zero? (+ (Choice-chosen2 uChoice) (Monty-door2 uMonty)))
(Gameshow (Choice (Choice-chosen1 uChoice) -1 (Choice-chosen3 uChoice)) uMonty)]
[(zero? (+ (Choice-chosen3 uChoice) (Monty-door3 uMonty)))
(Gameshow (Choice (Choice-chosen1 uChoice) (Choice-chosen2 uChoice) -1) uMonty)]
[else (error "ERROR: Host could not find a goat!")]
))
;; Gameshow -> Gameshow
(define (Host-reveal uGameshow)
(Host-reveal-handler (Gameshow-Choice uGameshow) (Gameshow-Monty uGameshow)))
;;int, list-> list of Gameshows
(define (random-rlog-handler size list)
(cond
[(= (length list) size) list]
[else (random-rlog-handler size (append-list (Host-reveal (random-Gameshow)) list))]
))
;;int -> list of Gameshows
(define (random-rlog size) (random-rlog-handler size '()))
;;==================================================================================================
;;Host tests
;;(define test-Gameshow (random-Gameshow))
;;(Host-reveal test-Gameshow)
;;Part 6: Evaluation Function
;;--------------------------------------------------------------------------------------------------
;; list of Choices, list of Montys, Collection -> Collection
(define (game-evaluation-handler Clist Mlist uClct)
(cond
(cond
[(= 1 (first Clist))
[(= choice 1) '(1 0 0)]
(cond
[(= choice 2) '(0 1 0)]
[(= 1 (first Mlist)) (strt-win uClct)]
[(= choice 3) '(0 0 1)]
[(zero? (first Mlist)) (switch-win uClct)]
[else (error "ERROR: Monty contains unknown door value.")]
)]
[(zero? (first Clist))
(cond
[(= 1 (first Mlist)) (switch-win uClct)]
[(zero? (first Mlist)) (strt-win uClct)]
[else (error "ERROR: Monty contains unknown door value.")]
)]
[(= -1 (first Clist))
(cond
[(zero? (first Mlist)) (game-evaluation-handler (rest Clist) (rest Mlist) uClct)]
[else (error "ERROR: Host DID NOT choose a goat.")]
)]
[else (error "ERROR: List was either empty or did not contain correct information.")]
))
))
(define (gen3) (one-in-three 3))
;;Gameshow, Collection -> Collection
(define (trials size winc counter)
(define (game-evaluation uGameshow uClct)
(game-evaluation-handler (Choice-to-list (Gameshow-Choice uGameshow)) (Monty-to-list (Gameshow-Monty uGameshow)) uClct))
;;revealed list of Gameshows, Collection -> Collection
(define (rlog-evaluation rlog uClct)
(cond
(cond
[(empty? rlog) uClct]
[(= counter size) winc]
[else (rlog-evaluation (rest rlog) (game-evaluation (first rlog) uClct))]
[(false? (= 1 (list-ref (gen3) (- (random-door) 1))))
(trials size (wins (wins-stay winc) (+ 1(wins-switch winc))) (+ 1 counter))]
[else (trials size (wins (+ 1 (wins-stay winc)) (wins-switch winc)) (+ 1 counter))]
))
))
(define (Monty-Hall size)
(trials size (wins 0 0) 0))
;;^Woohoo, twenty lines! (1 struct, five functions)
;;==================================================================================================
;;==================================================================================================
;;Evaluation tests
;;Finale: Begin the simulation!
;;--------------------------------------------------------------------------------------------------
(define size 100000)
(fprintf (current-output-port)
"Generating sample size of ~a\n"
size)
(define test (random-rlog size))
;;test
;;^Uncomment to see the generated list
#|
A generated list of "Gameshows"
Each Gameshow is composed of a "Choice" and a "Monty"
A Choice is three integers that represents the user's choice, and the host's reveal.
A zero means the corresponding door was not chosen.
A -1 means that this is the door the 'host' revealed as a goat.
A 1 means that this is the door the user randomly chose.
A Monty is representative of the three door scenario
A 1 indicates this is the door containing the car
A zero indicates this is a door containing a goat.
|#
(define tClct (init-Clct))
#|
A "Collection"
Each Collection is composed of "strt-win" and "switch-win"
A strt-win is when a player wins by keeping their current selection.
A switch-win is when a player 'would have' won by switching their door.
|#
(define answer (rlog-evaluation test tClct))
#|
rlog-evaluation evaluates each Gameshow, and updates the Collection.
When the list has been emptied, it returns the Collection.
|#
(fprintf (current-output-port)
"\nResults:\nYou would win ~a games by keeping your door.\nYou would win ~a games by switching.\n"
(Clct-strt answer)
(Clct-switch answer)
)
(define percentages (report-stats answer))
#|
Transforms Collection into percentage collection.
|#
(fprintf (current-output-port)
"\nPercentages:\nYou would win ~a% of the time keeping your door.\nYou would win ~a% of the time by switching.\n"
(Clct-strt percentages)
(Clct-switch percentages)
)
;;==================================================================================================
(Monty-Hall 100000)