Algorithm Implementation/Simulation/Monty Hall problem
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PHP
[edit | edit source]class MontyHall { private $rounds = 10; private $doors = 3; private $wins = array( "changing" => 0, "keeping" => 0 ); public function setDoors( $doors ) { $this->doors = $doors; return $this; } public function play( $rounds = false ) { if ( $rounds ) $this->rounds = $rounds; for ( $i = 0; $i < $this->rounds; $i++ ) { $prizeDoor = $this->randomDoor(); $playerChoiseDoor = $this->randomDoor(); $hostOpenDoor = $this->chooseDoor( $prizeDoor, $playerChoiseDoor ); $playerChangeDoor = $this->chooseDoor( $playerChoiseDoor, $hostOpenDoor ); if( $playerChoiseDoor == $prizeDoor ) $this->wins["keeping"]++; if( $playerChangeDoor == $prizeDoor ) $this->wins["changing"]++; } return $this; } public function getResults() { echo " Winnings: " . "<br>" . " - Changing the door: " . ( $this->wins["changing"] * 100 ) / $this->rounds . "%<br>" . " - Not Changing the door: " . ( $this->wins["keeping"] * 100 ) / $this->rounds . "%<br>" . " Simulation Statistics: " . "<br>" . " - Games played: " . $this->rounds . "<br>" . " - Doors used: " . $this->doors . "<br>" ; } private function randomDoor() { return rand( 1, $this->doors ); } private function chooseDoor( $number1 = null, $number2 = null ) { do $result = $this->randomDoor(); while ( $result == $number1 OR $result == $number2 ); return $result; } } // Use the MontyHall Simulation $montyhall = new MontyHall(); $montyhall->setDoors(3)->play(10000)->getResults(); Javascript
[edit | edit source]Array.prototype.remove = function(i) { this.splice(i, 1); }; SimulationEngine = function(){ } SimulationEngine.prototype = { simulate: function(maxSim){ if(!maxSim || maxSim < 0) maxSim = 1000; var winSwitching = 0; var loseSwitching = 0; var carCard = 0; var goat = 1; function userPickOne(cards){ var index = Math.floor(Math.random()*11)%3; cards.remove(index); } function hostDiscardOne(cards){ if(cards[0] === goat) cards.remove(0); else cards.remove(1); } function updateStatus(cards){ if(cards[0] === carCard) winSwitching++; else loseSwitching++; } for(var sim = 0; sim < maxSim; sim++){ var cards = [carCard,goat,goat]; userPickOne(cards); hostDiscardOne(cards); updateStatus(cards); } return { winSwitching: winSwitching, loseSwitching: loseSwitching } } } function simulate(){ var maxSim = 10000; var engine = new SimulationEngine(); var result = engine.simulate(maxSim); var strResult = "Total simulations are " + maxSim + ", WIN by switching = " + result.winSwitching * 100 / maxSim + ", LOST by switching = " + result.loseSwitching * 100 / maxSim; alert(strResult); } Java
[edit | edit source]import java.util.Random; public class MontyHall { public static final Random gen = new Random(); public static final int ROUNDS = 10000; /** chooses a random door other than door1 or door2 */ private static int chooseAnotherDoor(int door1, int door2) { int result; do result = gen.nextInt(3); while (result == door1 || result == door2); return result; } public static void main(String[] args) { System.out.println("begin playing " + ROUNDS + " rounds"); int wins = 0; for (int i = 0; i < ROUNDS; i++) { int prize = gen.nextInt(3); int userChoice1 = gen.nextInt(3); // host opens door other than user's choice without prize int hostChoice = chooseAnotherDoor(prize, userChoice1); // user always switches int userChoice2 = chooseAnotherDoor(userChoice1, hostChoice); if (userChoice2 == prize) wins++; } System.out.println(wins + " wins by switching"); } } C++
[edit | edit source]#include <iostream> #include <cstdlib> #include <ctime> #include <vector> #include <algorithm> using namespace std; int main() { srand(time(NULL)); random_device rd; mt19937 gen{ rd() }; unsigned long long stay = 0; unsigned long long change = 0; while(true) { vector<bool> boxes(3, false); boxes[0] = true; // Place a car shuffle(boxes.begin(), boxes.end(), gen); if(boxes[rand() % 3]) { stay++; cout << "STAY wins\n"; } else { change++; cout << "CHANGE wins\n"; } cout << "STAY: " << int((double)stay/(stay + change) * 100 + 0.5) << "%; " << "CHANGE: " << int((double)change/(stay + change) * 100 + 0.5) << "%\n" << endl; } } Phix
[edit | edit source]integer swapWins = 0, stayWins = 0, winner, choice, reveal, other atom t0 = time() for game=1 to 1_000_000 do winner = rand(3) choice = rand(3) while 1 do reveal = rand(3) if reveal!=winner and reveal!=choice then exit end if end while stayWins += (choice==winner) other = 6-choice-reveal -- (as 1+2+3=6, and reveal!=choice) swapWins += (other==winner) end for printf(1, "Stay: %,d\nSwap: %,d\nTime: %3.2fs\n",{stayWins,swapWins,time()-t0}) #!/usr/bin/python import sys,random rounds = 10000 wins = 0 random.seed() # The "-n" commandline option makes us run without ever switching. if len(sys.argv) > 1 and sys.argv[1] == "-n": swap = False else: swap = True for i in range(rounds) : # Generate random door contents doors = ["goat", "goat", "car"] random.shuffle(doors) # Pick a door door_choice = random.randrange(3) print("Selecting door", door_choice) # Show a door with a goat for j, contents in enumerate(doors): if j != door_choice and contents == "goat": goat_door = j print("The host reveals a goat behind door", goat_door) break if swap: # Swap to the other door for j, contents in enumerate(doors): if j != door_choice and j != goat_door: swap_to = j print("Swapping to door", swap_to) else: swap_to = door_choice if doors[swap_to] == "car": wins += 1 print("You won the car!!") else: print("Sorry, but you're stuck with a goat") print("You played", rounds, "rounds, and won", wins, "of them!") R
[edit | edit source] numsim = 100000 doors = 1:3 opendoor = function(x) { if (x[1]==x[2]) return(sample(doors[-c(x[1])], 1)) else return(doors[-c(x[1],x[2])]) } swapdoor = function(x) { return(doors[-c(x[1], x[2])]) } winner = sample(doors, numsim, replace=TRUE) choice = sample(doors, numsim, replace=TRUE) open = apply(cbind(winner, choice), 1, opendoor) newchoice = apply(cbind(open, choice), 1, swapdoor) # cat("without switching, won ", round(sum(winner==choice)/numsim*100,1)," percent of the time.\n", sep="") cat("with switching, won ", round(sum(winner==newchoice)/numsim*100,1)," percent of the time.\n", sep="") [from http://sas-and-r.blogspot.com/search?q=7.23]
Ruby
[edit | edit source]def createDoors doors = [false, false, false] doors[rand(3)] = true doors end def openADoorThatHasADonkey(doors, userChoice) ([0, 1, 2] - [userChoice, doors.index(true)]).first end def changeUserChoice(choices) ([0, 1, 2] - choices).first end def play doors = createDoors() userChoice1 = rand(3) hostChoice = openADoorThatHasADonkey(doors, userChoice1) userChoice2 = changeUserChoice([userChoice1, hostChoice]) # note: to change # script so that user DOESN'T change her choice and demonstrate the fallacy # of that approach, comment the userChoice2 line above and uncomment the # line below: # userChoice2 = userChoice1 doors.index(true) == userChoice2 end games, wins = 10000, 0 games.times { wins += 1 if play() } print 100*wins/games, " %" Another implementation
car = wins = 0 many = 100000 many.times do choice1 = rand(3) host_opts = [0, 1, 2] - [choice1, car] choice2 = [0, 1, 2] - [choice1, host_opts.first] wins += 1 if choice2 == [car] end puts "#{(wins * 100) / many}%" SAS
[edit | edit source] data mh; do i = 1 to 100000; prize = rand("TABLE",.333,.333); * Monty puts the prize behind a random door; initial_guess = rand("TABLE",.333,.333); * We make a random initial guess; * if the initial guess is right, Monte can open either of the others; * which means that player can switch to either of the other doors; if initial_guess eq prize then do; new_guess = initial_guess; * choose a door until it's different from the initial guess—that's the door we switch to; do until (new_guess ne initial_guess); new_guess = rand("TABLE",.333,.333); end; end; * If the initial guess was wrong, Monte can rule out only one of the other doors; * which means that we must switch to the right door; if initial_guess ne prize then new_guess = prize; output; end; run; *; data mh2; set mh; win_by_keep = (initial_guess eq prize); win_by_switch = (new_guess eq prize); run; *; proc means data = mh2 mean; var win_by_keep win_by_switch; run; [from http://sas-and-r.blogspot.com/search?q=7.23]
Option Explicit Option Base 1 Sub simulate() Dim iCount As Long Dim wins As Long Dim games As Long games = 10000000 For iCount = 1 To games If Play Then wins = wins + 1 Next MsgBox Round(((wins / games) * 100), 1) & "%" End Sub Function Play() Dim doors() As Boolean Dim userChoice1 As Integer Dim hostchoice As Integer Dim userChoice2 As Integer doors = createDoors() userChoice1 = Int(3 * Rnd() + 1) hostchoice = openADoorThatHasADonkey(doors(), userChoice1) userChoice2 = changeUserChoice(userChoice1, hostchoice) Play = doors(userChoice2) End Function Function createDoors() As Boolean() Dim temp(3) As Boolean temp(1) = False temp(2) = False temp(3) = False temp(Int(3 * Rnd() + 1)) = True createDoors = temp End Function Function openADoorThatHasADonkey(doors() As Boolean, userChoice) Dim iCount As Integer Dim temp As Integer For iCount = 1 To 3 If Not doors(iCount) And userChoice <> iCount Then temp = iCount Exit For End If Next iCount openADoorThatHasADonkey = temp End Function Function changeUserChoice(userChoice1 As Integer, hostchoice As Integer) Dim iCount As Integer Dim temp As Integer For iCount = 1 To 3 If userChoice1 <> iCount And hostchoice <> iCount Then temp = iCount Next iCount changeUserChoice = temp End Function Progress 4GL
[edit | edit source]DEF TEMP-TABLE deur NO-UNDO FIELD deurnr AS INT FIELD prijsdeur AS LOG. DEF VAR iprijsDeur AS INT NO-UNDO. CREATE deur. ASSIGN deur.deurnr = 1 deur.prijsdeur = FALSE. CREATE deur. ASSIGN deur.deurnr = 2 deur.prijsdeur = FALSE. CREATE deur. ASSIGN deur.deurnr = 3 deur.prijsdeur = FALSE. iPrijsdeur = RANDOM(1,3). FIND deur WHERE deurnr = iPrijsdeur. ASSIGN prijsdeur = TRUE. DEF VAR mijnkeuze AS INT NO-UNDO. DEF VAR gamehostKeuze AS INT NO-UNDO. DEF VAR mijnkeuze2 AS INT NO-UNDO. DEF VAR i AS INT NO-UNDO. DEF VAR g AS INT NO-UNDO. DEF VAR v AS INT NO-UNDO. DO i = 1 TO 100: mijnkeuze = RANDOM(1,3). gamehostkeuze = DYNAMIC-FUNCTION("openDeurZonderPrijs"). mijnkeuze2 = DYNAMIC-FUNCTION("wisselDeur"). /*mijnkeuze2 = mijnkeuze.*/ IF mijnkeuze2 = iPrijsdeur THEN g = g + 1. ELSE v = v + 1. END. MESSAGE "van" i "ronden won je er" g "en verloor je" v "keer". FUNCTION openDeurZonderPrijs RETURNS INT: FIND FIRST deur WHERE NOT deurnr EQ iPrijsdeur AND NOT deurnr EQ mijnkeuze. RETURN deur.deurnr. END FUNCTION. FUNCTION WisselDeur RETURN INT: FIND deur WHERE NOT deurnr EQ mijnkeuze AND NOT deurnr EQ gamehostkeuze. RETURN deur.deurnr. END FUNCTION.