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100 prisoners

From Rosetta Code
Task
100 prisoners
You are encouraged to solve this task according to the task description, using any language you may know.


The Problem
  • 100 prisoners are individually numbered 1 to 100
  • A room having a cupboard of 100 opaque drawers numbered 1 to 100, that cannot be seen from outside.
  • Cards numbered 1 to 100 are placed randomly, one to a drawer, and the drawers all closed; at the start.
  • Prisoners start outside the room
  • They can decide some strategy before any enter the room.
  • Prisoners enter the room one by one, can open a drawer, inspect the card number in the drawer, then close the drawer.
  • A prisoner can open no more than 50 drawers.
  • A prisoner tries to find his own number.
  • A prisoner finding his own number is then held apart from the others.
  • If all 100 prisoners find their own numbers then they will all be pardoned. If any don't then all sentences stand.


The task
  1. Simulate several thousand instances of the game where the prisoners randomly open drawers
  2. Simulate several thousand instances of the game where the prisoners use the optimal strategy mentioned in the Wikipedia article, of:
  • First opening the drawer whose outside number is his prisoner number.
  • If the card within has his number then he succeeds otherwise he opens the drawer with the same number as that of the revealed card. (until he opens his maximum).


Show and compare the computed probabilities of success for the two strategies, here, on this page.


References
  1. The unbelievable solution to the 100 prisoner puzzle standupmaths (Video).
  2. wp:100 prisoners problem
  3. 100 Prisoners Escape Puzzle DataGenetics.
  4. Random permutation statistics#One hundred prisoners on Wikipedia.



Ada[edit]

 
package Prisoners is
 
type Win_Percentage is digits 2 range 0.0 .. 100.0;
type Drawers is array (1 .. 100) of Positive;
 
function Play_Game
(Repetitions : in Positive;
Strategy  : not null access function
(Cupboard  : in Drawers; Max_Prisoners : Integer;
Max_Attempts : Integer; Prisoner_Number : Integer) return Boolean)
return Win_Percentage;
-- Play the game with a specified number of repetitions, the chosen strategy
-- is passed to this function
 
function Optimal_Strategy
(Cupboard : in Drawers; Max_Prisoners : Integer; Max_Attempts : Integer;
Prisoner_Number : Integer) return Boolean;
 
function Random_Strategy
(Cupboard : in Drawers; Max_Prisoners : Integer; Max_Attempts : Integer;
Prisoner_Number : Integer) return Boolean;
 
end Prisoners;
 
 
pragma Ada_2012;
with Ada.Numerics.Discrete_Random;
with Ada.Text_IO; use Ada.Text_IO;
 
package body Prisoners is
 
subtype Drawer_Range is Positive range 1 .. 100;
package Random_Drawer is new Ada.Numerics.Discrete_Random (Drawer_Range);
use Random_Drawer;
 
-- Helper procedures to initialise and shuffle the drawers
 
procedure Swap (A, B : Positive; Cupboard : in out Drawers) is
Temp : Positive;
begin
Temp  := Cupboard (B);
Cupboard (B) := Cupboard (A);
Cupboard (A) := Temp;
end Swap;
 
procedure Shuffle (Cupboard : in out Drawers) is
G : Generator;
begin
Reset (G);
for I in Cupboard'Range loop
Swap (I, Random (G), Cupboard);
end loop;
end Shuffle;
 
procedure Initialise_Drawers (Cupboard : in out Drawers) is
begin
for I in Cupboard'Range loop
Cupboard (I) := I;
end loop;
Shuffle (Cupboard);
end Initialise_Drawers;
 
-- The two strategies for playing the game
 
function Optimal_Strategy
(Cupboard : in Drawers; Max_Prisoners : Integer; Max_Attempts : Integer;
Prisoner_Number : Integer) return Boolean
is
Current_Card : Positive;
begin
Current_Card := Cupboard (Prisoner_Number);
if Current_Card = Prisoner_Number then
return True;
else
for I in Integer range 1 .. Max_Attempts loop
Current_Card := Cupboard (Current_Card);
if Current_Card = Prisoner_Number then
return True;
end if;
end loop;
end if;
return False;
end Optimal_Strategy;
 
function Random_Strategy
(Cupboard : in Drawers; Max_Prisoners : Integer; Max_Attempts : Integer;
Prisoner_Number : Integer) return Boolean
is
Current_Card : Positive;
G  : Generator;
begin
Reset (G);
Current_Card := Cupboard (Prisoner_Number);
if Current_Card = Prisoner_Number then
return True;
else
for I in Integer range 1 .. Max_Attempts loop
Current_Card := Cupboard (Random (G));
if Current_Card = Prisoner_Number then
return True;
end if;
end loop;
end if;
return False;
end Random_Strategy;
 
function Prisoners_Attempts
(Cupboard : in Drawers; Max_Prisoners : Integer; Max_Attempts : Integer;
Strategy : not null access function
(Cupboard  : in Drawers; Max_Prisoners : Integer;
Max_Attempts : Integer; Prisoner_Number : Integer) return Boolean)
return Boolean
is
begin
for Prisoner_Number in Integer range 1 .. Max_Prisoners loop
if not Strategy
(Cupboard, Max_Prisoners, Max_Attempts, Prisoner_Number)
then
return False;
end if;
end loop;
return True;
end Prisoners_Attempts;
 
-- The function to play the game itself
 
function Play_Game
(Repetitions : in Positive;
Strategy  : not null access function
(Cupboard  : in Drawers; Max_Prisoners : Integer;
Max_Attempts : Integer; Prisoner_Number : Integer) return Boolean)
return Win_Percentage
is
Cupboard  : Drawers;
Win, Game_Count  : Natural  := 0;
Number_Of_Prisoners : constant Integer := 100;
Max_Attempts  : constant Integer := 50;
begin
loop
Initialise_Drawers (Cupboard);
if Prisoners_Attempts
(Cupboard => Cupboard, Max_Prisoners => Number_Of_Prisoners,
Max_Attempts => Max_Attempts, Strategy => Strategy)
then
Win := Win + 1;
end if;
Game_Count := Game_Count + 1;
exit when Game_Count = Repetitions;
end loop;
return Win_Percentage ((Float (Win) / Float (Repetitions)) * 100.0);
end Play_Game;
 
end Prisoners;
 
 
with Prisoners; use Prisoners;
with Ada.Text_IO; use Ada.Text_IO;
 
procedure Main is
Wins : Win_Percentage;
package Win_Percentage_IO is new Float_IO (Win_Percentage);
begin
Wins := Play_Game (100_000, Optimal_Strategy'Access);
Put ("Optimal Strategy = ");
Win_Percentage_IO.Put (Wins, 2, 2, 0);
Put ("%");
New_Line;
Wins := Play_Game (100_000, Random_Strategy'Access);
Put ("Random Strategy = ");
Win_Percentage_IO.Put (Wins, 2, 2, 0);
Put ("%");
end Main;
 
Output:
Optimal Strategy = 31.80%
Random Strategy =  0.00%

Applesoft BASIC[edit]

This is modified from the 100_prisoners#Commodore_BASIC listing. Here are some noted differences between the BASICs and platforms:

  • UPPER CASE, for the 1970's Apple II and Apple II+
  • GET in Applesoft waits for a keypress, so : IF K$ = "" THEN 1110 is not needed
  • CLear Screen: PRINT CHR$ (147); on Commodore BASIC, HOME in Applesoft
  • "{LEFT-CRSR}" is CHR$(8) on Apple II, but numbers printed in Applesoft don't have spaces appended to them
  • but spaces need to be added in front and after numbers in Applesoft
  •  ; is optional for string concatenation
  • Replace bare PRINT statement with M$ embedded in PRINT statements to visually compact the listing


And, minor speed tweaks:

  • Remove REMs, adjust line numbers, move the two compacted methods to the beginning of the program
  • Rename some two character variable names to single character names: 's/DR(/D(/' 's/IG(/J(/'
  • Start at 0 and go up to 99, but don't regress into off by one bugs
  • Inline the shuffle subroutine and hoist it out of the methods
  • Embed the results in the loop because feedback can be helpful, otherwise it looks like the program froze


Actual test of 4000 trials for each method were run on the KEGSMAC emulator with MHz set to No Limit.

0 GOTO 9
 
1 FOR X = 0 TO N:J(X) = X: NEXT: FOR I = 0 TO N:FOR X = 0 TO N:T = J(X):NP = INT ( RND (1) * H):J(X) = J(NP):J(NP) = T: NEXT :FOR G = 1 TO W:IF D(J(G)) = I THEN IP = IP + 1: NEXT I: RETURN
2 NEXT G:RETURN
 
3 FOR I = 0 TO N:NG = I: FOR G = 0 TO W:CD = D(NG):IF CD = I THEN IP = IP + 1: NEXT I: RETURN
4 NG = CD:IF CD = I THEN STOP
5 NEXT G: RETURN
 
9 H=100:N=H-1:DIM D(99),J(99):FOR I = 0 TO N:D(I) = I: NEXT:W=INT(H/2)-1:M$=CHR$(13):M$(1)="RANDOM GUESSING":M$(2)="CHAINED NUMBER PICKING"
 
1000 FOR Q = 0 TO 1 STEP 0 : HOME : PRINT "100 PRISONERS"M$: INPUT "HOW MANY TRIALS FOR EACH METHOD? "; TT
1010 VTAB 2:CALL-958:PRINT M$"RESULTS:"M$
1020 FOR M = 1 TO 2: SU(M) = 0:FA(M) = 0
1030 FOR TN = 1 TO TT
1040 VTAB 4:PRINT M$ " OUT OF " TT " TRIALS, THE RESULTS ARE"M$" AS FOLLOWS...";
1050 IP = 0: X = RND ( - TI): FOR I = 0 TO N:R = INT ( RND (1) * N):T = D(I):D(I) = D(R):D(R) = T: NEXT
1060 ON M GOSUB 1,3 : SU(M) = SU(M) + (IP = H):FA(M) = FA(M) + (IP < H)
1070 FOR Z = 1 TO 2
1071 PRINT M$M$Z". "M$(Z)":"M$
1073 PRINT " "SU(Z)" SUCCESSES"TAB(21)
1074 PRINT " "FA(Z)" FAILURES"M$
1075 PRINT " "(SU(Z) / TT) * 100"% SUCCESS RATE.";:CALL-868
1090 NEXT Z,TN,M
 
1100 PRINT M$M$"AGAIN?"
1110 GET K$
1120 Q = K$ <> "Y" AND K$ <> CHR$(ASC("Y") + 32) : NEXT Q
 
Output:
100 PRISONERS

RESULTS:

   OUT OF 4000 TRIALS, THE RESULTS ARE
   AS FOLLOWS...

1. RANDOM GUESSING:

   0 SUCCESSES         4000 FAILURES

   0% SUCCESS RATE.

2. CHAINED NUMBER PICKING:

   1278 SUCCESSES      2722 FAILURES

   31.95% SUCCESS RATE.

C[edit]

 
#include<stdbool.h>
#include<stdlib.h>
#include<stdio.h>
#include<time.h>
 
#define LIBERTY false
#define DEATH true
 
typedef struct{
int id;
int cardNum;
bool hasBeenOpened;
}drawer;
 
typedef struct{
int id;
bool foundCard;
}prisoner;
 
drawer *drawerSet;
prisoner *prisonerGang;
 
void initialize(int prisoners){
int i,j,card;
bool unique;
 
drawerSet = (drawer*)malloc(prisoners * sizeof(drawer));
prisonerGang = (prisoner*)malloc(prisoners * sizeof(prisoner));
 
for(i=0;i<prisoners;i++){
prisonerGang[i] = (prisoner){.id = i+1, .foundCard = false};
 
card = rand()%prisoners + 1;
 
if(i==0)
drawerSet[i] = (drawer){.id = i+1, .cardNum = card, .hasBeenOpened = false};
else{
unique = false;
while(unique==false){
for(j=0;j<i;j++){
if(drawerSet[j].cardNum == card){
card = rand()%prisoners + 1;
break;
}
}
if(j==i){
unique = true;
}
}
drawerSet[i] = (drawer){.id = i+1, .cardNum = card, .hasBeenOpened = false};
}
}
}
 
void closeAllDrawers(int prisoners){
int i;
for(i=0;i<prisoners;i++)
drawerSet[i].hasBeenOpened = false;
}
 
bool libertyOrDeathAtRandom(int prisoners,int chances){
int i,j,chosenDrawer;
 
for(i=0;i<prisoners;i++){
for(j=0;j<chances;j++){
do{
chosenDrawer = rand()%prisoners;
}while(drawerSet[chosenDrawer].hasBeenOpened==true);
if(drawerSet[chosenDrawer].cardNum == prisonerGang[i].id){
prisonerGang[i].foundCard = true;
break;
}
drawerSet[chosenDrawer].hasBeenOpened = true;
}
closeAllDrawers(prisoners);
if(prisonerGang[i].foundCard == false)
return DEATH;
}
 
return LIBERTY;
}
 
bool libertyOrDeathPlanned(int prisoners,int chances){
int i,j,chosenDrawer;
for(i=0;i<prisoners;i++){
chosenDrawer = rand()%prisoners;
for(j=1;j<chances;j++){
if(drawerSet[chosenDrawer].cardNum == prisonerGang[i].id){
prisonerGang[i].foundCard = true;
break;
}
if(chosenDrawer+1 == drawerSet[chosenDrawer].id){
do{
chosenDrawer = rand()%prisoners;
}while(drawerSet[chosenDrawer].hasBeenOpened==true);
}
else{
chosenDrawer = drawerSet[chosenDrawer].cardNum - 1;
}
drawerSet[chosenDrawer].hasBeenOpened = true;
}
closeAllDrawers(prisoners);
if(prisonerGang[i].foundCard == false)
return DEATH;
}
 
return LIBERTY;
}
 
int main(int argc,char** argv)
{
int prisoners, chances;
unsigned long long int trials,i,count = 0;
char* end;
 
if(argc!=4)
return printf("Usage : %s <Number of prisoners> <Number of chances> <Number of trials>",argv[0]);
 
prisoners = atoi(argv[1]);
chances = atoi(argv[2]);
trials = strtoull(argv[3],&end,10);
 
srand(time(NULL));
 
printf("Running random trials...");
for(i=0;i<trials;i+=1L){
initialize(prisoners);
 
count += libertyOrDeathAtRandom(prisoners,chances)==DEATH?0:1;
}
 
printf("\n\nGames Played : %llu\nGames Won : %llu\nChances : %lf % \n\n",trials,count,(100.0*count)/trials);
 
count = 0;
 
printf("Running strategic trials...");
for(i=0;i<trials;i+=1L){
initialize(prisoners);
 
count += libertyOrDeathPlanned(prisoners,chances)==DEATH?0:1;
}
 
printf("\n\nGames Played : %llu\nGames Won : %llu\nChances : %lf % \n\n",trials,count,(100.0*count)/trials);
return 0;
}
 

C's random number generator, at least the one on my machine, doesn't give the prisoners any chance, even for a million trials.

C:\My Projects\networks>a 100 50 100000
Running random trials...

Games Played : 100000
Games Won : 0
Chances : 0.000000%

Running strategic trials...

Games Played : 100000
Games Won : 0
Chances : 0.000000


C:\My Projects\networks>a 100 50 1000000
Running random trials...

Games Played : 1000000
Games Won : 0
Chances : 0.000000

Running strategic trials...

Games Played : 1000000
Games Won : 0
Chances : 0.000000

C#[edit]

Translation of: D
using System;
using System.Linq;
 
namespace Prisoners {
class Program {
static bool PlayOptimal() {
var secrets = Enumerable.Range(0, 100).OrderBy(a => Guid.NewGuid()).ToList();
 
for (int p = 0; p < 100; p++) {
bool success = false;
 
var choice = p;
for (int i = 0; i < 50; i++) {
if (secrets[choice] == p) {
success = true;
break;
}
choice = secrets[choice];
}
 
if (!success) {
return false;
}
}
 
return true;
}
 
static bool PlayRandom() {
var secrets = Enumerable.Range(0, 100).OrderBy(a => Guid.NewGuid()).ToList();
 
for (int p = 0; p < 100; p++) {
var choices = Enumerable.Range(0, 100).OrderBy(a => Guid.NewGuid()).ToList();
 
bool success = false;
for (int i = 0; i < 50; i++) {
if (choices[i] == p) {
success = true;
break;
}
}
 
if (!success) {
return false;
}
}
 
return true;
}
 
static double Exec(uint n, Func<bool> play) {
uint success = 0;
for (uint i = 0; i < n; i++) {
if (play()) {
success++;
}
}
return 100.0 * success / n;
}
 
static void Main() {
const uint N = 1_000_000;
Console.WriteLine("# of executions: {0}", N);
Console.WriteLine("Optimal play success rate: {0:0.00000000000}%", Exec(N, PlayOptimal));
Console.WriteLine(" Random play success rate: {0:0.00000000000}%", Exec(N, PlayRandom));
}
}
}
Output:
# of executions: 1000000
Optimal play success rate: 31.21310000000%
 Random play success rate: 0.00000000000%

C++[edit]

#include <iostream>	//for output
#include <algorithm> //for shuffle
#include <stdlib.h> //for rand()
 
using namespace std;
 
int* setDrawers() {
int drawers[100];
for (int i = 0; i < 100; i++) {
drawers[i] = i;
}
random_shuffle(&drawers[0], &drawers[99]);
return drawers;
}
 
bool playRandom()
{
int* drawers = setDrawers();
bool openedDrawers[100] = { 0 };
for (int prisonerNum = 0; prisonerNum < 100; prisonerNum++) { //loops through prisoners numbered 0 through 99
bool prisonerSuccess = false;
for (int i = 0; i < 50; i++) { //loops through 50 draws for each prisoner
int drawerNum;
while (true) {
drawerNum = rand() % 100;
if (!openedDrawers[drawerNum]) {
openedDrawers[drawerNum] = true;
cout << endl;
break;
}
}
if (*(drawers + drawerNum) == prisonerNum) {
prisonerSuccess = true;
break;
}
}
if (!prisonerSuccess)
return false;
}
return true;
}
 
bool playOptimal()
{
int* drawers = setDrawers();
for (int prisonerNum = 0; prisonerNum < 100; prisonerNum++) {
bool prisonerSuccess = false;
int checkDrawerNum = prisonerNum;
for (int i = 0; i < 50; i++) {
if (*(drawers + checkDrawerNum) == prisonerNum) {
prisonerSuccess = true;
break;
}
else
checkDrawerNum = *(drawers + checkDrawerNum);
}
if (!prisonerSuccess)
return false;
}
return true;
}
 
double simulate(string strategy)
{
int numberOfSuccesses = 0;
for (int i = 0; i <= 10000; i++) {
if ((strategy == "random" && playRandom()) || (strategy == "optimal" && playOptimal())) //will run playRandom or playOptimal but not both becuase of short-circuit evaluation
numberOfSuccesses++;
}
return numberOfSuccesses / 100.0;
}
 
int main()
{
cout << "Random Strategy: " << simulate("random") << "%" << endl;
cout << "Optimal Strategy: " << simulate("optimal") << "%" << endl;
system("PAUSE");
return 0;
}
Output:
Random Strategy: 0%
Optimal Strategy: 31.51%

Clojure[edit]

(ns clojure-sandbox.prisoners)
 
(defn random-drawers []
"Returns a list of shuffled numbers"
(-> 100
range
shuffle))
 
(defn search-50-random-drawers [prisoner-number drawers]
"Select 50 random drawers and return true if the prisoner's number was found"
(->> drawers
shuffle ;; Put drawer contents in random order
(take 50) ;; Select first 50, equivalent to selecting 50 random drawers
(filter (fn [x] (= x prisoner-number))) ;; Filter to include only those that match prisoner number
count
(= 1))) ;; Returns true if the number of matching numbers is 1
 
(defn search-50-optimal-drawers [prisoner-number drawers]
"Open 50 drawers according to the agreed strategy, returning true if prisoner's number was found"
(loop [next-drawer prisoner-number ;; The drawer index to start on is the prisoner's number
drawers-opened 0] ;; To keep track of how many have been opened as 50 is the maximum
(if (= drawers-opened 50)
false ;; If 50 drawers have been opened, the prisoner's number has not been found
(let [result (nth drawers next-drawer)] ;; Open the drawer given by next number
(if (= result prisoner-number) ;; If prisoner number has been found
true ;; No need to keep opening drawers - return true
(recur result (inc drawers-opened))))))) ;; Restart the loop using the resulting number as the drawer number
 
(defn try-luck [drawers drawer-searching-function]
"Returns 1 if all prisoners find their number otherwise 0"
(loop [prisoners (range 100)] ;; Start with 100 prisoners
(if (empty? prisoners) ;; If they've all gone and found their number
1 ;; Return true- they'll all live
(let [res (-> prisoners
first
(drawer-searching-function drawers))] ;; Otherwise, have the first prisoner open drawers according to the specified method
(if (false? res) ;; If this prisoner didn't find their number
0 ;; no prisoners will be freed so we can return false and stop
(recur (rest prisoners))))))) ;; Otherwise they've found the number, so we remove them from the queue and repeat with the others
 
(defn simulate-100-prisoners []
"Simulates all prisoners searching the same drawers by both strategies, returns map showing whether each was successful"
(let [drawers (random-drawers)] ;; Create 100 drawers with randomly ordered prisoner numbers
{:random (try-luck drawers search-50-random-drawers) ;; True if all prisoners found their number using random strategy
 :optimal (try-luck drawers search-50-optimal-drawers)})) ;; True if all prisoners found their number using optimal strategy
 
(defn simulate-n-runs [n]
"Simulate n runs of the 100 prisoner problem and returns a success count for each search method"
(loop [random-successes 0
optimal-successes 0
run-count 0]
(if (= n run-count) ;; If we've done the loop n times
{:random-successes random-successes ;; return results
 :optimal-successes optimal-successes
 :run-count run-count}
(let [next-result (simulate-100-prisoners)] ;; Otherwise, run for another batch of prisoners
(recur (+ random-successes (:random next-result)) ;; Add result of run to the total successs count
(+ optimal-successes (:optimal next-result))
(inc run-count)))))) ;; increment run count and run again
 
(defn -main [& args]
"For 5000 runs, print out the success frequency for both search methods"
(let [{:keys [random-successes optimal-successes run-count]} (simulate-n-runs 5000)]
(println (str "Probability of survival with random search: " (float (/ random-successes run-count))))
(println (str "Probability of survival with ordered search: " (float (/ optimal-successes run-count))))))
Output:
Probability of survival with random search: 0.0
Probability of survival with ordered search: 0.3062

Commodore BASIC[edit]

It should be noted that this is a very time consuming process for a ~1 MHz 8-bit computer. Evaluating 1000 trials of each method with the algorithm below takes about 3.5 hours on the BASIC system clock (TIME$) of a stock NTSC Commodore 64, even with screen blanking. (Screen blanking seems to achieve only a 3% improvement in speed.) Actual test of 4000 trials for each method were run on the VICE emulator with warp speed engaged, otherwise the user would have had to wait a day and a half for results.

Another concern is when the prisoner's number is found. When this happens it becomes unnecessary to use whatever guesses are remaining; we should simply move on to the next prisoner. Furthermore, if any prisoner uses all 50 guesses with no luck, then everyone is out of luck and the trial is over, which means no other prisoner needs to make the attempt.

This potentially could cause problems on the stack with unfinished guessing (or prisoner) loops, especially where stack limits are extremely small however, a few things are happening to prevent this (See C64-Wiki "NEXT: Early Exits..." for reference.):

  1. The prisoner loop, and each prisoner's 50-guesses loop, are contained within a subroutine. The RETURN at the end of either subroutine terminates any unfinished loops and keeps the stack clean.
  2. When the NEXT belonging to loop 'i' is encountered, any inner loops ('g') are terminated.
  3. Similar to above, any new loop using an existing loop's variable terminates the old loop, and any nested loops within it.


The key here is avoiding the use of GOTO as a means of exiting a loop early.

 
10 rem 100 prisoners
20 rem set arrays
30 rem dr = drawers containing card values
40 rem ig = a list of numbers 1 through 100, shuffled to become the
41 rem guess sequence for each inmate - method 1
50 dim dr(100),ig(100)
55 rem initialize drawers with own card in each drawer
60 for i=1 to 100:dr(i)=i:next
 
1000 print chr$(147);"how many trials for each method";:input tt
1010 for m=1 to 2:su(m)=0:fa(m)=0
1015 for tn=1 to tt
1020 on m gosub 2000,3000
1025 rem ip = number of inmates who passed
1030 if ip=100 then su(m)=su(m)+1
1040 if ip<100 then fa(m)=fa(m)+1
1045 next tn
1055 next m
 
1060 print chr$(147);"Results:":print
1070 print "Out of";tt;"trials, the results are"
1071 print "as follows...":print
1072 print "1. Random Guessing:"
1073 print " ";su(1);"successes"
1074 print " ";fa(1);"failures"
1075 print " ";su(1)/tn;"{left-crsr}% success rate.":print
1077 print "2. Chained Number Picking:"
1078 print " ";su(2);"successes"
1079 print " ";fa(2);"failures"
1080 print " ";(su(2)/tn)*100;"{left-crsr}% success rate.":print
1100 print:print "Again?"
1110 get k$:if k$="" then 1110
1120 if k$="y" then 1000
1500 end
 
2000 rem random guessing method
2005 for x=1 to 100:ig(x)=x:next:ip=0:gosub 4000
2007 for i=1 to 100
2010 for x=1 to 100:t=ig(x):np=int(rnd(1)*100)+1:ig(x)=ig(np):ig(np)=t:next
2015 for g=1 to 50
2020 if dr(ig(g))=i then ip=ip+1:next i:return
2025 next g
2030 return
 
3000 rem chained method
3005 ip=0:gosub 4000
3007 rem iterate through each inmate
3010 fori=1to100
3015 ng=i:forg=1to50
3020 cd=dr(ng)
3025 ifcd=ithenip=ip+1:nexti:return
3030 ifcd<>ithenng=cd
3035 nextg:return
 
4000 rem shuffle the drawer cards randomly
4010 x=rnd(-ti)
4020 for i=1 to 100
4030 r=int(rnd(1)*100)+1:t=dr(i):dr(i)=dr(r):dr(r)=t:next
4040 return
 
Output:
Results:

Out of 4000 trials the percentage of
success is as follows...

1. Random Guessing:
   0 successes
   4000 failures
   0% success rate.

2. Chained Number Picking:
   1274 successes
   2726 failures
   31.85% success rate.

Common Lisp[edit]

Translation of: Racket
 
(defparameter *samples* 10000)
(defparameter *prisoners* 100)
(defparameter *max-guesses* 50)
 
(defun range (n)
"Returns a list from 0 to N."
(loop
for i below n
collect i))
 
(defun nshuffle (list)
"Returns a shuffled LIST."
(loop
for i from (length list) downto 2
do (rotatef (nth (random i) list)
(nth (1- i) list)))
list)
 
(defun build-drawers ()
"Returns a list of shuffled drawers."
(nshuffle (range *prisoners*)))
 
(defun strategy-1 (drawers p)
"Returns T if P is found in DRAWERS under *MAX-GUESSES* using a random strategy."
(loop
for i below *max-guesses*
thereis (= p (nth (random *prisoners*) drawers))))
 
(defun strategy-2 (drawers p)
"Returns T if P is found in DRAWERS under *MAX-GUESSES* using an optimal strategy."
(loop
for i below *max-guesses*
for j = p then (nth j drawers)
thereis (= p (nth j drawers))))
 
(defun 100-prisoners-problem (strategy &aux (drawers (build-drawers)))
"Returns T if all prisoners find their number using the given STRATEGY."
(every (lambda (e) (eql T e))
(mapcar (lambda (p) (funcall strategy drawers p)) (range *prisoners*))))
 
(defun sampling (strategy)
(loop
repeat *samples*
for result = (100-prisoners-problem strategy)
count result))
 
(defun compare-strategies ()
(format t "Using a random strategy in ~4,2F % of the cases the prisoners are free.~%" (* (/ (sampling #'strategy-1) *samples*) 100))
(format t "Using an optimal strategy in ~4,2F % of the cases the prisoners are free.~%" (* (/ (sampling #'strategy-2) *samples*) 100)))
 
Output:
CL-USER> (compare-strategies)
Using a random strategy in 0.00 % of the cases the prisoners are free.
Using an optimal strategy in 31.34 % of the cases the prisoners are free.

Crystal[edit]

Based on the Ruby implementation

prisoners = (1..100).to_a
N = 100_000
generate_rooms = ->{ (1..100).to_a.shuffle }
 
res = N.times.count do
rooms = generate_rooms.call
prisoners.all? { |pr| rooms[1, 100].sample(50).includes?(pr) }
end
puts "Random strategy : %11.4f %%" % (res.fdiv(N) * 100)
 
res = N.times.count do
rooms = generate_rooms.call
prisoners.all? do |pr|
cur_room = pr
50.times.any? do
cur_room = rooms[cur_room - 1]
found = (cur_room == pr)
found
end
end
end
puts "Optimal strategy: %11.4f %%" % (res.fdiv(N) * 100)
Output:
Random strategy :      0.0000 %
Optimal strategy:     31.3190 %

D[edit]

Translation of: Kotlin
import std.array;
import std.random;
import std.range;
import std.stdio;
import std.traits;
 
bool playOptimal() {
auto secrets = iota(100).array.randomShuffle();
 
prisoner:
foreach (p; 0..100) {
auto choice = p;
foreach (_; 0..50) {
if (secrets[choice] == p) continue prisoner;
choice = secrets[choice];
}
return false;
}
 
return true;
}
 
bool playRandom() {
auto secrets = iota(100).array.randomShuffle();
 
prisoner:
foreach (p; 0..100) {
auto choices = iota(100).array.randomShuffle();
foreach (i; 0..50) {
if (choices[i] == p) continue prisoner;
}
return false;
}
 
return true;
}
 
double exec(const size_t n, bool function() play) {
size_t success = 0;
for (int i = n; i > 0; i--) {
if (play()) {
success++;
}
}
return 100.0 * success / n;
}
 
void main() {
enum N = 1_000_000;
writeln("# of executions: ", N);
writefln("Optimal play success rate: %11.8f%%", exec(N, &playOptimal));
writefln(" Random play success rate: %11.8f%%", exec(N, &playRandom));
}
Output:
# of executions: 1000000
Optimal play success rate: 31.16100000%
 Random play success rate:  0.00000000%

EasyLang[edit]

for i range 100
drawer[] &= i
sampler[] &= i
.
subr shuffle_drawer
for i = len drawer[] downto 2
r = random i
swap drawer[r] drawer[i - 1]
.
.
subr play_random
call shuffle_drawer
found = 1
prisoner = 0
while prisoner < 100 and found = 1
found = 0
i = 0
while i < 50 and found = 0
r = random (100 - i)
card = drawer[sampler[r]]
swap sampler[r] sampler[100 - i - 1]
if card = prisoner
found = 1
.
i += 1
.
prisoner += 1
.
.
subr play_optimal
call shuffle_drawer
found = 1
prisoner = 0
while prisoner < 100 and found = 1
reveal = prisoner
found = 0
i = 0
while i < 50 and found = 0
card = drawer[reveal]
if card = prisoner
found = 1
.
reveal = card
i += 1
.
prisoner += 1
.
.
n = 10000
pardoned = 0
for round range n
call play_random
pardoned += found
.
print "random: " & 100.0 * pardoned / n & "%"
#
pardoned = 0
for round range n
call play_optimal
pardoned += found
.
print "optimal: " & 100.0 * pardoned / n & "%"
Output:
random: 0.000%
optimal: 30.800%

Factor[edit]

USING: arrays formatting fry io kernel math random sequences ;
 
: setup ( -- seq seq ) 100 <iota> dup >array randomize ;
 
: rand ( -- ? )
setup [ 50 sample member? not ] curry find nip >boolean not ;
 
: trail ( m seq -- n )
50 pick '[ [ nth ] keep over _ = ] replicate [ t = ] any?
2nip ;
 
: optimal ( -- ? ) setup [ trail ] curry [ and ] map-reduce ;
 
: simulate ( m quot -- x )
dupd replicate [ t = ] count swap /f 100 * ; inline
 
"Simulation count: 10,000" print
10,000 [ rand ] simulate "Random play success: "
10,000 [ optimal ] simulate "Optimal play success: "
[ write "%.2f%%\n" printf ] [email protected]
Output:
Simulation count: 10,000
Random play success: 0.00%
Optimal play success: 31.11%

FreeBASIC[edit]

#include once "knuthshuf.bas"   'use the routines in https://rosettacode.org/wiki/Knuth_shuffle#FreeBASIC
 
function gus( i as long, strat as boolean ) as long
if strat then return i
return 1+int(rnd*100)
end function
 
sub trials( byref c_success as long, byref c_fail as long, byval strat as boolean )
dim as long i, j, k, guess, drawer(1 to 100)
for i = 1 to 100
drawer(i) = i
next i
for j = 1 to 1000000 'one million trials of prisoners
knuth_up( drawer() ) 'shuffles the cards in the drawers
for i = 1 to 100 'prisoner number
guess = gus(i, strat)
for k = 1 to 50 'each prisoner gets 50 tries
if drawer(guess) = i then goto next_prisoner
guess = gus(drawer(guess), strat)
next k
c_fail += 1
goto next_trial
next_prisoner:
next i
c_success += 1
next_trial:
next j
end sub
 
randomize timer
dim as long c_fail=0, c_success=0
 
trials( c_success, c_fail, false )
 
print using "For prisoners guessing randomly we had ####### successes and ####### failures.";c_success;c_fail
 
c_success = 0
c_fail = 0
 
trials( c_success, c_fail, true )
 
print using "For prisoners using the strategy we had ####### successes and ####### failures.";c_success;c_fail

Go[edit]

package main
 
import (
"fmt"
"math/rand"
"time"
)
 
// Uses 0-based numbering rather than 1-based numbering throughout.
func doTrials(trials, np int, strategy string) {
pardoned := 0
trial:
for t := 0; t < trials; t++ {
var drawers [100]int
for i := 0; i < 100; i++ {
drawers[i] = i
}
rand.Shuffle(100, func(i, j int) {
drawers[i], drawers[j] = drawers[j], drawers[i]
})
prisoner:
for p := 0; p < np; p++ {
if strategy == "optimal" {
prev := p
for d := 0; d < 50; d++ {
this := drawers[prev]
if this == p {
continue prisoner
}
prev = this
}
} else {
// Assumes a prisoner remembers previous drawers (s)he opened
// and chooses at random from the others.
var opened [100]bool
for d := 0; d < 50; d++ {
var n int
for {
n = rand.Intn(100)
if !opened[n] {
opened[n] = true
break
}
}
if drawers[n] == p {
continue prisoner
}
}
}
continue trial
}
pardoned++
}
rf := float64(pardoned) / float64(trials) * 100
fmt.Printf(" strategy = %-7s pardoned = %-6d relative frequency = %5.2f%%\n\n", strategy, pardoned, rf)
}
 
func main() {
rand.Seed(time.Now().UnixNano())
const trials = 100_000
for _, np := range []int{10, 100} {
fmt.Printf("Results from %d trials with %d prisoners:\n\n", trials, np)
for _, strategy := range [2]string{"random", "optimal"} {
doTrials(trials, np, strategy)
}
}
}
Output:
Results from 100000 trials with 10 prisoners:

  strategy = random   pardoned = 99     relative frequency =  0.10%

  strategy = optimal  pardoned = 31205  relative frequency = 31.20%

Results from 100000 trials with 100 prisoners:

  strategy = random   pardoned = 0      relative frequency =  0.00%

  strategy = optimal  pardoned = 31154  relative frequency = 31.15%

Groovy[edit]

Translation of: Java
import java.util.function.Function
import java.util.stream.Collectors
import java.util.stream.IntStream
 
class Prisoners {
private static boolean playOptimal(int n) {
List<Integer> secretList = IntStream.range(0, n).boxed().collect(Collectors.toList())
Collections.shuffle(secretList)
 
prisoner:
for (int i = 0; i < secretList.size(); ++i) {
int prev = i
for (int j = 0; j < secretList.size() / 2; ++j) {
if (secretList.get(prev) == i) {
continue prisoner
}
prev = secretList.get(prev)
}
return false
}
return true
}
 
private static boolean playRandom(int n) {
List<Integer> secretList = IntStream.range(0, n).boxed().collect(Collectors.toList())
Collections.shuffle(secretList)
 
prisoner:
for (Integer i : secretList) {
List<Integer> trialList = IntStream.range(0, n).boxed().collect(Collectors.toList())
Collections.shuffle(trialList)
 
for (int j = 0; j < trialList.size() / 2; ++j) {
if (Objects.equals(trialList.get(j), i)) {
continue prisoner
}
}
 
return false
}
return true
}
 
private static double exec(int n, int p, Function<Integer, Boolean> play) {
int succ = 0
for (int i = 0; i < n; ++i) {
if (play.apply(p)) {
succ++
}
}
return (succ * 100.0) / n
}
 
static void main(String[] args) {
final int n = 100_000
final int p = 100
System.out.printf("# of executions: %d\n", n)
System.out.printf("Optimal play success rate: %f%%\n", exec(n, p, Prisoners.&playOptimal))
System.out.printf("Random play success rate: %f%%\n", exec(n, p, Prisoners.&playRandom))
}
}
Output:
# of executions: 100000
Optimal play success rate: 31.215000%
Random play success rate: 0.000000%

Haskell[edit]

import System.Random
import Control.Monad.State
 
numRuns = 10000
numPrisoners = 100
numDrawerTries = 50
type Drawers = [Int]
type Prisoner = Int
type Prisoners = [Int]
 
main = do
gen <- getStdGen
putStrLn $ "Chance of winning when choosing randomly: " ++ (show $ evalState runRandomly gen)
putStrLn $ "Chance of winning when choosing optimally: " ++ (show $ evalState runOptimally gen)
 
 
runRandomly :: State StdGen Double
runRandomly =
let runResults = replicateM numRuns $ do
drawers <- state $ shuffle [1..numPrisoners]
allM (\prisoner -> openDrawersRandomly drawers prisoner numDrawerTries) [1..numPrisoners]
in ((/ fromIntegral numRuns) . fromIntegral . sum . map fromEnum) `liftM` runResults
 
openDrawersRandomly :: Drawers -> Prisoner -> Int -> State StdGen Bool
openDrawersRandomly drawers prisoner triesLeft = go triesLeft []
where go 0 _ = return False
go triesLeft seenDrawers = do
try <- state $ randomR (1, numPrisoners)
case try of
x | x == prisoner -> return True
| x `elem` seenDrawers -> go triesLeft seenDrawers
| otherwise -> go (triesLeft - 1) (x:seenDrawers)
 
runOptimally :: State StdGen Double
runOptimally =
let runResults = replicateM numRuns $ do
drawers <- state $ shuffle [1..numPrisoners]
return $ all (\prisoner -> openDrawersOptimally drawers prisoner numDrawerTries) [1..numPrisoners]
in ((/ fromIntegral numRuns) . fromIntegral . sum . map fromEnum) `liftM` runResults
 
openDrawersOptimally :: Drawers -> Prisoner -> Int -> Bool
openDrawersOptimally drawers prisoner triesLeft = go triesLeft prisoner
where go 0 _ = False
go triesLeft drawerToTry =
let thisDrawer = drawers !! (drawerToTry - 1)
in if thisDrawer == prisoner then True else go (triesLeft - 1) thisDrawer
 
 
-- Haskel stdlib is lacking big time, so here some necessary 'library' functions
 
-- make a list of 'len' random values in range 'range' from 'gen'
randomLR :: Integral a => Random b => a -> (b, b) -> StdGen -> ([b], StdGen)
randomLR 0 range gen = ([], gen)
randomLR len range gen =
let (x, newGen) = randomR range gen
(xs, lastGen) = randomLR (len - 1) range newGen
in (x : xs, lastGen)
 
 
-- shuffle a list by a generator
shuffle :: [a] -> StdGen -> ([a], StdGen)
shuffle list gen = (shuffleByNumbers numbers list, finalGen)
where
n = length list
(numbers, finalGen) = randomLR n (0, n-1) gen
shuffleByNumbers :: [Int] -> [a] -> [a]
shuffleByNumbers [] _ = []
shuffleByNumbers _ [] = []
shuffleByNumbers (i:is) xs = let (start, x:rest) = splitAt (i `mod` length xs) xs
in x : shuffleByNumbers is (start ++ rest)
 
-- short-circuit monadic all
allM :: Monad m => (a -> m Bool) -> [a] -> m Bool
allM func [] = return True
allM func (x:xs) = func x >>= \res -> if res then allM func xs else return False
 
Output:
Chance of winning when choosing randomly: 0.0
Chance of winning when choosing optimally: 0.3188

J[edit]

 
NB. game is solvable by optimal strategy when the length (#) of the
NB. longest (>./) cycle (C.) is at most 50.
opt=: 50 >: [: >./ [: > [: #&.> C.
 
NB. for each prisoner randomly open 50 boxes ((50?100){y) and see if
NB. the right card is there (p&e.). if not return 0.
rand=: monad define
for_p. i.100 do. if. -.p e.(50?100){y do. 0 return. end.
end. 1
)
 
NB. use both strategies on the same shuffles y times.
simulate=: monad define
'o r'=. y %~ 100 * +/ ((rand,opt)@?~)"0 y # 100
('strategy';'win rate'),('random';(":o),'%'),:'optimal';(":r),'%'
)
Output:
   simulate 10000000
┌────────┬────────┐
│strategy│win rate│
├────────┼────────┤
│random  │0%      │
├────────┼────────┤
│optimal │31.1816%│
└────────┴────────┘

Java[edit]

Translation of: Kotlin
import java.util.Collections;
import java.util.List;
import java.util.Objects;
import java.util.function.Function;
import java.util.function.Supplier;
import java.util.stream.Collectors;
import java.util.stream.IntStream;
 
public class Main {
private static boolean playOptimal(int n) {
List<Integer> secretList = IntStream.range(0, n).boxed().collect(Collectors.toList());
Collections.shuffle(secretList);
 
prisoner:
for (int i = 0; i < secretList.size(); ++i) {
int prev = i;
for (int j = 0; j < secretList.size() / 2; ++j) {
if (secretList.get(prev) == i) {
continue prisoner;
}
prev = secretList.get(prev);
}
return false;
}
return true;
}
 
private static boolean playRandom(int n) {
List<Integer> secretList = IntStream.range(0, n).boxed().collect(Collectors.toList());
Collections.shuffle(secretList);
 
prisoner:
for (Integer i : secretList) {
List<Integer> trialList = IntStream.range(0, n).boxed().collect(Collectors.toList());
Collections.shuffle(trialList);
 
for (int j = 0; j < trialList.size() / 2; ++j) {
if (Objects.equals(trialList.get(j), i)) {
continue prisoner;
}
}
 
return false;
}
return true;
}
 
private static double exec(int n, int p, Function<Integer, Boolean> play) {
int succ = 0;
for (int i = 0; i < n; ++i) {
if (play.apply(p)) {
succ++;
}
}
return (succ * 100.0) / n;
}
 
public static void main(String[] args) {
final int n = 100_000;
final int p = 100;
System.out.printf("# of executions: %d\n", n);
System.out.printf("Optimal play success rate: %f%%\n", exec(n, p, Main::playOptimal));
System.out.printf("Random play success rate: %f%%\n", exec(n, p, Main::playRandom));
}
}
Output:
# of executions: 100000
Optimal play success rate: 31.343000%
Random play success rate: 0.000000%

JavaScript[edit]

Translation of: C#
Works with: Node.js
 
const _ = require('lodash');
 
const numPlays = 100000;
 
const setupSecrets = () => {
// setup the drawers with random cards
let secrets = [];
 
for (let i = 0; i < 100; i++) {
secrets.push(i);
}
 
return _.shuffle(secrets);
}
 
const playOptimal = () => {
 
let secrets = setupSecrets();
 
 
// Iterate once per prisoner
loop1:
for (let p = 0; p < 100; p++) {
 
// whether the prisoner succeedss
let success = false;
 
// the drawer number the prisoner chose
let choice = p;
 
 
// The prisoner can choose up to 50 cards
loop2:
for (let i = 0; i < 50; i++) {
 
// if the card in the drawer that the prisoner chose is his card
if (secrets[choice] === p){
success = true;
break loop2;
}
 
// the next drawer the prisoner chooses will be the number of the card he has.
choice = secrets[choice];
 
} // each prisoner gets 50 chances
 
 
if (!success) return false;
 
} // iterate for each prisoner
 
return true;
}
 
const playRandom = () => {
 
let secrets = setupSecrets();
 
// iterate for each prisoner
for (let p = 0; p < 100; p++) {
 
let choices = setupSecrets();
 
let success = false;
 
for (let i = 0; i < 50; i++) {
 
if (choices[i] === p) {
success = true;
break;
}
}
 
if (!success) return false;
}
 
return true;
}
 
const execOptimal = () => {
 
let success = 0;
 
for (let i = 0; i < numPlays; i++) {
 
if (playOptimal()) success++;
 
}
 
return 100.0 * success / 100000;
}
 
const execRandom = () => {
 
let success = 0;
 
for (let i = 0; i < numPlays; i++) {
 
if (playRandom()) success++;
 
}
 
return 100.0 * success / 100000;
}
 
console.log("# of executions: " + numPlays);
console.log("Optimal Play Success Rate: " + execOptimal());
console.log("Random Play Success Rate: " + execRandom());
 

Julia[edit]

Translation of: Python
using Random, Formatting
 
function randomplay(n, numprisoners=100)
pardoned, indrawer, found = 0, collect(1:numprisoners), false
for i in 1:n
shuffle!(indrawer)
for prisoner in 1:numprisoners
found = false
for reveal in randperm(numprisoners)[1:div(numprisoners, 2)]
indrawer[reveal] == prisoner && (found = true) && break
end
 !found && break
end
found && (pardoned += 1)
end
return 100.0 * pardoned / n
end
 
function optimalplay(n, numprisoners=100)
pardoned, indrawer, found = 0, collect(1:numprisoners), false
for i in 1:n
shuffle!(indrawer)
for prisoner in 1:numprisoners
reveal = prisoner
found = false
for j in 1:div(numprisoners, 2)
card = indrawer[reveal]
card == prisoner && (found = true) && break
reveal = card
end
 !found && break
end
found && (pardoned += 1)
end
return 100.0 * pardoned / n
end
 
const N = 100_000
println("Simulation count: $N")
println("Random play wins: ", format(randomplay(N), precision=8), "% of simulations.")
println("Optimal play wins: ", format(optimalplay(N), precision=8), "% of simulations.")
 
Output:
Simulation count: 100000
Random play wins: 0.00000000% of simulations.
Optimal play wins: 31.18100000% of simulations.

Kotlin[edit]

val playOptimal: () -> Boolean = {
val secrets = (0..99).toMutableList()
var ret = true
secrets.shuffle()
prisoner@ for(i in 0 until 100){
var prev = i
draw@ for(j in 0 until 50){
if (secrets[prev] == i) continue@prisoner
prev = secrets[prev]
}
ret = false
break@prisoner
}
ret
}
 
val playRandom: ()->Boolean = {
var ret = true
val secrets = (0..99).toMutableList()
secrets.shuffle()
prisoner@ for(i in 0 until 100){
val opened = mutableListOf<Int>()
val genNum : () ->Int = {
var r = (0..99).random()
while (opened.contains(r)) {
r = (0..99).random()
}
r
}
for(j in 0 until 50){
val draw = genNum()
if ( secrets[draw] == i) continue@prisoner
opened.add(draw)
}
ret = false
break@prisoner
}
ret
}
 
fun exec(n:Int, play:()->Boolean):Double{
var succ = 0
for (i in IntRange(0, n-1)){
succ += if(play()) 1 else 0
}
return (succ*100.0)/n
}
 
fun main() {
val N = 100_000
println("# of executions: $N")
println("Optimal play success rate: ${exec(N, playOptimal)}%")
println("Random play success rate: ${exec(N, playRandom)}%")
}
Output:
# of executions: 100000
Optimal play success rate: 31.451%
Random play success rate: 0.0%

Lua[edit]

Translation of: lang
function shuffle(tbl)
for i = #tbl, 2, -1 do
local j = math.random(i)
tbl[i], tbl[j] = tbl[j], tbl[i]
end
return tbl
end
 
function playOptimal()
local secrets = {}
for i=1,100 do
secrets[i] = i
end
shuffle(secrets)
 
for p=1,100 do
local success = false
 
local choice = p
for i=1,50 do
if secrets[choice] == p then
success = true
break
end
choice = secrets[choice]
end
 
if not success then
return false
end
end
 
return true
end
 
function playRandom()
local secrets = {}
for i=1,100 do
secrets[i] = i
end
shuffle(secrets)
 
for p=1,100 do
local choices = {}
for i=1,100 do
choices[i] = i
end
shuffle(choices)
 
local success = false
for i=1,50 do
if choices[i] == p then
success = true
break
end
end
 
if not success then
return false
end
end
 
return true
end
 
function exec(n,play)
local success = 0
for i=1,n do
if play() then
success = success + 1
end
end
return 100.0 * success / n
end
 
function main()
local N = 1000000
print("# of executions: "..N)
print(string.format("Optimal play success rate: %f", exec(N, playOptimal)))
print(string.format("Random play success rate: %f", exec(N, playRandom)))
end
 
main()
Output:
# of executions: 1000000
Optimal play success rate: 31.237500
Random play success rate: 0.000000

MATLAB[edit]

function [randSuccess,idealSuccess]=prisoners(numP,numG,numT)
%numP is the number of prisoners
%numG is the number of guesses
%numT is the number of trials
randSuccess=0;
 
%Random
for trial=1:numT
drawers=randperm(numP);
won=1;
for i=1:numP
correct=0;
notopened=drawers;
for j=1:numG
ind=randi(numel(notopened));
m=notopened(ind);
if m==i
correct=1;
break;
end
notopened(ind)=[];
end
if correct==0
won=0;
break;
end
end
randSuccess=randSuccess*(trial-1)/trial+won/trial;
end
 
 
%Ideal
idealSuccess=0;
 
for trial=1:numT
drawers=randperm(numP);
won=1;
for i=1:numP
correct=0;
guess=i;
for j=1:numG
m=drawers(guess);
if m==i
correct=1;
break;
end
guess=m;
end
if correct==0
won=0;
break;
end
end
idealSuccess=idealSuccess*(trial-1)/trial+won/trial;
end
disp(['Probability of success with random strategy: ' num2str(randSuccess*100) '%']);
disp(['Probability of success with ideal strategy: ' num2str(idealSuccess*100) '%']);
end
Output:
>> [randSuccess,idealSuccess]=prisoners(100,50,10000);
Probability of success with random strategy: 0%
Probability of success with ideal strategy: 31.93%

MiniScript[edit]

Translation of: Python
playRandom = function(n)
// using 0-99 instead of 1-100
pardoned = 0
numInDrawer = range(99)
choiceOrder = range(99)
for round in range(1, n)
numInDrawer.shuffle
choiceOrder.shuffle
for prisoner in range(99)
found = false
for card in choiceOrder[:50]
if card == prisoner then
found = true
break
end if
end for
if not found then break
end for
if found then pardoned = pardoned + 1
end for
return pardoned / n * 100
end function
 
playOptimal = function(n)
// using 0-99 instead of 1-100
pardoned = 0
numInDrawer = range(99)
for round in range(1, n)
numInDrawer.shuffle
for prisoner in range(99)
found = false
drawer = prisoner
for i in range(1,50)
card = numInDrawer[drawer]
if card == prisoner then
found = true
break
end if
drawer = card
end for
if not found then break
end for
if found then pardoned = pardoned + 1
end for
return pardoned / n * 100
end function
 
print "Random: " + playRandom(10000) + "%"
print "Optimal: " + playOptimal(10000) + "%"
Output:
Random:  0%
Optimal: 31.06%

Nim[edit]

Imperative style.

import random, sequtils, strutils
 
type
Sample = tuple
succ: int
fail: int
 
const
numPrisoners = 100
numDrawsEachPrisoner = numPrisoners div 2
numDrawings: Positive = 1_000_000 div 1
 
proc `$`(s: Sample): string =
"Succs: $#\tFails: $#\tTotal: $#\tSuccess Rate: $#%." % [$s.succ, $s.fail, $(s.succ + s.fail), $(s.succ.float / (s.succ + s.fail).float * 100.0)]
 
proc prisonersWillBeReleasedSmart(): bool =
result = true
var drawers = toSeq(0..<numPrisoners)
drawers.shuffle
for prisoner in 0..<numPrisoners:
var drawer = prisoner
block inner:
for _ in 0..<numDrawsEachPrisoner:
if drawers[drawer] == prisoner: break inner
drawer = drawers[drawer]
return false
 
proc prisonersWillBeReleasedRandom(): bool =
result = true
var drawers = toSeq(0..<numPrisoners)
drawers.shuffle
for prisoner in 0..<numPrisoners:
var selectDrawer = toSeq(0..<numPrisoners)
selectDrawer.shuffle
block inner:
for i in 0..<numDrawsEachPrisoner:
if drawers[selectDrawer[i]] == prisoner: break inner
return false
 
proc massDrawings(prisonersWillBeReleased: proc(): bool): Sample =
var success = 0
for i in 1..numDrawings:
if prisonersWillBeReleased():
inc(success)
return (success, numDrawings - success)
 
randomize()
echo $massDrawings(prisonersWillBeReleasedSmart)
echo $massDrawings(prisonersWillBeReleasedRandom)
Output:
Succs: 312225   Fails: 687775   Total: 1000000  Success Rate: 31.2225%.
Succs: 0        Fails: 1000000  Total: 1000000  Success Rate: 0.0%.

Pascal[edit]

Works with: Free Pascal

searching the longest cycle length as stated on talk page and increment an counter for that cycle length.

program Prisoners100;
 
const
rounds = 100000;
 
type
tValue = Uint32;
tPrisNum = array of tValue;
var
drawers,
PrisonersChoice : tPrisNum;
 
procedure shuffle(var N:tPrisNum);
var
i,j,lmt : nativeInt;
tmp: tValue;
Begin
lmt := High(N);
For i := lmt downto 1 do
begin
//take on from index i..limit
j := random(i+1);
//exchange with i
tmp := N[i];N[i]:= N[j];N[j]:= tmp;
end;
end;
 
function PardonedRandom(maxTestNum: NativeInt):boolean;
var
PrisNum,TestNum,Lmt : NativeUint;
Pardoned : boolean;
Begin
IF maxTestNum <=0 then
Begin
PardonedRandom := false;
EXIT;
end;
Lmt := High(drawers);
IF (maxTestNum >= Lmt) then
Begin
PardonedRandom := true;
EXIT;
end;
 
shuffle(drawers);
PrisNum := 0;
repeat
//every prisoner uses his own list of drawers
shuffle(PrisonersChoice);
TestNum := 0;
repeat
Pardoned := drawers[PrisonersChoice[TestNum]] = PrisNum;
inc(TestNum);
until Pardoned OR (TestNum>=maxTestNum);
IF Not(Pardoned) then
BREAK;
inc(PrisNum);
until PrisNum>=Lmt;
PardonedRandom:= Pardoned;
end;
 
function PardonedOptimized(maxTestNum: NativeUint):boolean;
var
PrisNum,TestNum,NextNum,Cnt,Lmt : NativeUint;
Pardoned : boolean;
Begin
IF maxTestNum <=0 then
Begin
PardonedOptimized := false;
EXIT;
end;
Lmt := High(drawers);
IF (maxTestNum >= Lmt) then
Begin
PardonedOptimized := true;
EXIT;
end;
 
shuffle(drawers);
Lmt := High(drawers);
IF maxTestNum >= Lmt then
Begin
PardonedOptimized := true;
EXIT;
end;
PrisNum := 0;
repeat
Cnt := 0;
NextNum := PrisNum;
repeat
TestNum := NextNum;
NextNum := drawers[TestNum];
inc(cnt);
Pardoned := NextNum = PrisNum;
until Pardoned OR (cnt >=maxTestNum);
 
IF Not(Pardoned) then
BREAK;
inc(PrisNum);
until PrisNum>Lmt;
PardonedOptimized := Pardoned;
end;
 
procedure CheckRandom(testCount : NativeUint);
var
i,cnt : NativeInt;
Begin
cnt := 0;
For i := 1 to rounds do
IF PardonedRandom(TestCount) then
inc(cnt);
writeln('Randomly ',cnt/rounds*100:7:2,'% get pardoned out of ',rounds,' checking max ',TestCount);
end;
 
procedure CheckOptimized(testCount : NativeUint);
var
i,cnt : NativeInt;
Begin
cnt := 0;
For i := 1 to rounds do
IF PardonedOptimized(TestCount) then
inc(cnt);
writeln('Optimized ',cnt/rounds*100:7:2,'% get pardoned out of ',rounds,' checking max ',TestCount);
end;
 
procedure OneCompareRun(PrisCnt:NativeInt);
var
i,lmt :nativeInt;
begin
setlength(drawers,PrisCnt);
For i := 0 to PrisCnt-1 do
drawers[i] := i;
PrisonersChoice := copy(drawers);
 
//test
writeln('Checking ',PrisCnt,' prisoners');
 
lmt := PrisCnt;
repeat
CheckOptimized(lmt);
dec(lmt,PrisCnt DIV 10);
until lmt < 0;
writeln;
 
lmt := PrisCnt;
repeat
CheckRandom(lmt);
dec(lmt,PrisCnt DIV 10);
until lmt < 0;
writeln;
writeln;
end;
 
Begin
//init
randomize;
OneCompareRun(20);
OneCompareRun(100);
end.
Output:
Checking 20 prisoners
Optimized  100.00% get pardoned out of 100000 checking max 20
Optimized   89.82% get pardoned out of 100000 checking max 18
Optimized   78.25% get pardoned out of 100000 checking max 16
Optimized   65.31% get pardoned out of 100000 checking max 14
Optimized   50.59% get pardoned out of 100000 checking max 12
Optimized   33.20% get pardoned out of 100000 checking max 10
Optimized   15.28% get pardoned out of 100000 checking max 8
Optimized    3.53% get pardoned out of 100000 checking max 6
Optimized    0.10% get pardoned out of 100000 checking max 4
Optimized    0.00% get pardoned out of 100000 checking max 2
Optimized    0.00% get pardoned out of 100000 checking max 0

Randomly   100.00% get pardoned out of 100000 checking max 20
Randomly    13.55% get pardoned out of 100000 checking max 18
Randomly     1.38% get pardoned out of 100000 checking max 16
Randomly     0.12% get pardoned out of 100000 checking max 14
Randomly     0.00% get pardoned out of 100000 checking max 12
Randomly     0.00% get pardoned out of 100000 checking max 10
Randomly     0.00% get pardoned out of 100000 checking max 8
Randomly     0.00% get pardoned out of 100000 checking max 6
Randomly     0.00% get pardoned out of 100000 checking max 4
Randomly     0.00% get pardoned out of 100000 checking max 2
Randomly     0.00% get pardoned out of 100000 checking max 0


Checking 100 prisoners
Optimized  100.00% get pardoned out of 100000 checking max 100
Optimized   89.48% get pardoned out of 100000 checking max 90
Optimized   77.94% get pardoned out of 100000 checking max 80
Optimized   64.48% get pardoned out of 100000 checking max 70
Optimized   49.35% get pardoned out of 100000 checking max 60
Optimized   31.10% get pardoned out of 100000 checking max 50
Optimized   13.38% get pardoned out of 100000 checking max 40
Optimized    2.50% get pardoned out of 100000 checking max 30
Optimized    0.05% get pardoned out of 100000 checking max 20
Optimized    0.00% get pardoned out of 100000 checking max 10
Optimized    0.00% get pardoned out of 100000 checking max 0

Randomly   100.00% get pardoned out of 100000 checking max 100
Randomly     0.01% get pardoned out of 100000 checking max 90
Randomly     0.00% get pardoned out of 100000 checking max 80
Randomly     0.00% get pardoned out of 100000 checking max 70
Randomly     0.00% get pardoned out of 100000 checking max 60
Randomly     0.00% get pardoned out of 100000 checking max 50
Randomly     0.00% get pardoned out of 100000 checking max 40
Randomly     0.00% get pardoned out of 100000 checking max 30
Randomly     0.00% get pardoned out of 100000 checking max 20
Randomly     0.00% get pardoned out of 100000 checking max 10
Randomly     0.00% get pardoned out of 100000 checking max 0

Alternative for optimized[edit]

program Prisoners100;
{$IFDEF FPC}
{$MODE DELPHI}{$OPTIMIZATION ON,ALL}
{$ELSE}
{$APPTYPE CONSOLE}
{$ENDIF}
type
tValue = NativeUint;
tpValue = pNativeUint;
tPrisNum = array of tValue;
 
const
rounds = 1000000;
cAlreadySeen = High(tValue);
var
drawers,
Visited,
CntToPardoned : tPrisNum;
PrisCount : NativeInt;
 
procedure shuffle(var N:tPrisNum;lmt : nativeInt = 0);
var
pN : tpValue;
i,j : nativeInt;
tmp: tValue;
Begin
pN := @N[0];
if lmt = 0 then
lmt := High(N);
For i := lmt downto 1 do
begin
//take one from index [0..i]
j := random(i+1);
//exchange with i
tmp := pN[i];pN[i]:= pN[j];pN[j]:= tmp;
end;
end;
 
procedure CopyDrawers2Visited;
//drawers and Visited are of same size, so only moving values
Begin
Move(drawers[0],Visited[0],SizeOf(tValue)*PrisCount);
end;
 
function GetMaxCycleLen:NativeUint;
var
pVisited : tpValue;
cycleLen,MaxCycLen,Num,NumBefore : NativeUInt;
Begin
CopyDrawers2Visited;
pVisited := @Visited[0];
MaxCycLen := 0;
cycleLen := MaxCycLen;
Num := MaxCycLen;
repeat
NumBefore := Num;
Num := pVisited[Num];
pVisited[NumBefore] := cAlreadySeen;
inc(cycleLen);
IF (Num= NumBefore) or (Num = cAlreadySeen) then
begin
IF Num = cAlreadySeen then
dec(CycleLen);
IF MaxCycLen < cycleLen then
MaxCycLen := cycleLen;
Num := 0;
while (Num< PrisCount) AND (pVisited[Num] = cAlreadySeen) do
inc(Num);
//all cycles found
IF Num >= PrisCount then
BREAK;
cycleLen :=0;
end;
until false;
GetMaxCycleLen := MaxCycLen-1;
end;
 
procedure CheckOptimized(testCount : NativeUint);
var
factor: extended;
i,sum,digit,delta : NativeInt;
Begin
For i := 1 to rounds do
begin
shuffle(drawers);
inc(CntToPardoned[GetMaxCycleLen]);
end;
 
digit := 0;
sum := rounds;
while sum > 100 do
Begin
inc(digit);
sum := sum DIV 10;
end;
factor := 100.0/rounds;
 
delta :=0;
sum := 0;
For i := 0 to High(drawers) do
Begin
inc(sum,CntToPardoned[i]);
dec(delta);
IF delta <= 0 then
Begin
writeln(sum*factor:Digit+5:Digit,'% get pardoned checking max ',i+1);
delta := delta+Length(drawers) DIV 10;
end;
end;
end;
 
procedure OneCompareRun(PrisCnt:NativeInt);
var
i,lmt :nativeInt;
begin
PrisCount := PrisCnt;
setlength(drawers,PrisCnt);
For i := 0 to PrisCnt-1 do
drawers[i] := i;
setlength(Visited,PrisCnt);
setlength(CntToPardoned,PrisCnt);
//test
writeln('Checking ',PrisCnt,' prisoners for ',rounds,' rounds');
lmt := PrisCnt;
CheckOptimized(lmt);
writeln;
 
setlength(CntToPardoned,0);
setlength(Visited,0);
setlength(drawers,0);
end;
 
Begin
randomize;
OneCompareRun(10);
OneCompareRun(100);
OneCompareRun(1000);
end.
Output:
Checking 10 prisoners for 1000000 rounds
   0.0000% get pardoned checking max 1
   0.2584% get pardoned checking max 2
   4.7431% get pardoned checking max 3
  17.4409% get pardoned checking max 4
  35.4983% get pardoned checking max 5
  52.1617% get pardoned checking max 6
  66.4807% get pardoned checking max 7
  78.9761% get pardoned checking max 8
  90.0488% get pardoned checking max 9
 100.0000% get pardoned checking max 10

Checking 100 prisoners for 1000000 rounds
   0.0000% get pardoned checking max 1
   0.0000% get pardoned checking max 10
   0.0459% get pardoned checking max 20
   2.5996% get pardoned checking max 30
  13.5071% get pardoned checking max 40
  31.2258% get pardoned checking max 50
  49.3071% get pardoned checking max 60
  64.6128% get pardoned checking max 70
  77.8715% get pardoned checking max 80
  89.5385% get pardoned checking max 90
 100.0000% get pardoned checking max 100

Checking 1000 prisoners for 1000000 rounds
   0.0000% get pardoned checking max 1
   0.0000% get pardoned checking max 100
   0.0374% get pardoned checking max 200
   2.3842% get pardoned checking max 300
  13.1310% get pardoned checking max 400
  30.7952% get pardoned checking max 500
  48.9710% get pardoned checking max 600
  64.3555% get pardoned checking max 700
  77.6950% get pardoned checking max 800
  89.4515% get pardoned checking max 900
 100.0000% get pardoned checking max 1000

real    0m9,975s

Perl[edit]

Translation of: Raku
use strict;
use warnings;
use feature 'say';
use List::Util 'shuffle';
 
sub simulation {
my($population,$trials,$strategy) = @_;
my $optimal = $strategy =~ /^o/i ? 1 : 0;
my @prisoners = 0..$population-1;
my $half = int $population / 2;
my $pardoned = 0;
 
for (1..$trials) {
my @drawers = shuffle @prisoners;
my $total = 0;
for my $prisoner (@prisoners) {
my $found = 0;
if ($optimal) {
my $card = $drawers[$prisoner];
if ($card == $prisoner) {
$found = 1;
} else {
for (1..$half-1) {
$card = $drawers[$card];
($found = 1, last) if $card == $prisoner
}
}
} else {
for my $card ( (shuffle @drawers)[0..$half]) {
($found = 1, last) if $card == $prisoner
}
}
last unless $found;
$total++;
}
$pardoned++ if $total == $population;
}
$pardoned / $trials * 100
}
 
my $population = 100;
my $trials = 10000;
say " Simulation count: $trials\n" .
(sprintf " Random strategy pardons: %6.3f%% of simulations\n", simulation $population, $trials, 'random' ) .
(sprintf "Optimal strategy pardons: %6.3f%% of simulations\n", simulation $population, $trials, 'optimal');
 
$population = 10;
$trials = 100000;
say " Simulation count: $trials\n" .
(sprintf " Random strategy pardons: %6.3f%% of simulations\n", simulation $population, $trials, 'random' ) .
(sprintf "Optimal strategy pardons: %6.3f%% of simulations\n", simulation $population, $trials, 'optimal');
Output:
 Simulation count: 10000
 Random strategy pardons:  0.000% of simulations
Optimal strategy pardons: 31.510% of simulations

 Simulation count: 1000000
 Random strategy pardons:  0.099% of simulations
Optimal strategy pardons: 35.420% of simulations

Phix[edit]

function play(integer prisoners, iterations, bool optimal)
sequence drawers = shuffle(tagset(prisoners))
integer pardoned = 0
bool found = false
for i=1 to iterations do
drawers = shuffle(drawers)
for prisoner=1 to prisoners do
found = false
integer drawer = iff(optimal?prisoner:rand(prisoners))
for j=1 to prisoners/2 do
drawer = drawers[drawer]
if drawer==prisoner then found = true exit end if
if not optimal then drawer = rand(prisoners) end if
end for
if not found then exit end if
end for
pardoned += found
end for
return 100*pardoned/iterations
end function
 
constant iterations = 100_000
printf(1,"Simulation count: %d\n",iterations)
for prisoners=10 to 100 by 90 do
atom random = play(prisoners,iterations,false),
optimal = play(prisoners,iterations,true)
printf(1,"Prisoners:%d, random:%g, optimal:%g\n",{prisoners,random,optimal})
end for
Output:
Simulation count: 100000
Prisoners:10, random:0.006, optimal:35.168
Prisoners:100, random:0, optimal:31.098

PowerShell[edit]

Translation of: Chris
 
### Clear Screen from old Output
Clear-Host
 
Function RandomOpening ()
{
$Prisoners = 1..100 | Sort-Object {Get-Random}
$Cupboard = 1..100 | Sort-Object {Get-Random}
## Loop for the Prisoners
$Survived = $true
for ($I=1;$I -le 100;$i++)
{
$OpeningListe = 1..100 | Sort-Object {Get-Random}
$Gefunden = $false
## Loop for the trys of every prisoner
for ($X=1;$X -le 50;$X++)
{
$OpenNumber = $OpeningListe[$X]
IF ($Cupboard[$OpenNumber] -eq $Prisoners[$I])
{
$Gefunden = $true
}
## Cancel loop if prisoner found his number (yeah i know, dirty way ^^ )
IF ($Gefunden)
{
$X = 55
}
}
IF ($Gefunden -eq $false)
{
$I = 120
$Survived = $false
}
}
Return $Survived
}
 
Function StrategyOpening ()
{
$Prisoners = 1..100 | Sort-Object {Get-Random}
$Cupboard = 1..100 | Sort-Object {Get-Random}
$Survived = $true
for ($I=1;$I -le 100;$i++)
{
$Gefunden = $false
$OpeningNumber = $Prisoners[$I-1]
for ($X=1;$X -le 50;$X++)
{
IF ($Cupboard[$OpeningNumber-1] -eq $Prisoners[$I-1])
{
$Gefunden = $true
}
else
{
$OpeningNumber = $Cupboard[$OpeningNumber-1]
}
IF ($Gefunden)
{
$X = 55
}
}
IF ($Gefunden -eq $false)
{
$I = 120
$Survived = $false
}
}
Return $Survived
}
 
$MaxRounds = 10000
 
Function TestRandom
{
$WinnerRandom = 0
for ($Round = 1; $Round -le $MaxRounds;$Round++)
{
IF (($Round%1000) -eq 0)
{
$Time = Get-Date
Write-Host "Currently we are at rount $Round at $Time"
}
$Rueckgabewert = RandomOpening
IF ($Rueckgabewert)
{
$WinnerRandom++
}
}
 
$Prozent = (100/$MaxRounds)*$WinnerRandom
Write-Host "There are $WinnerRandom survivors whit random opening. This is $Prozent percent"
}
 
Function TestStrategy
{
$WinnersStrategy = 0
for ($Round = 1; $Round -le $MaxRounds;$Round++)
{
IF (($Round%1000) -eq 0)
{
$Time = Get-Date
Write-Host "Currently we are at $Round at $Time"
}
$Rueckgabewert = StrategyOpening
IF ($Rueckgabewert)
{
$WinnersStrategy++
}
}
 
$Prozent = (100/$MaxRounds)*$WinnersStrategy
Write-Host "There are $WinnersStrategy survivors whit strategic opening. This is $Prozent percent"
}
 
Function Main ()
{
Clear-Host
TestRandom
TestStrategy
}
 
Main
 
Output:
# of executions: 10000
There are 0 survivors whit random opening. This is 0 percent
There are 3104 survivors whit strategic opening. This is 31,04 percent"

Python[edit]

Procedural[edit]

import random
 
def play_random(n):
# using 0-99 instead of ranges 1-100
pardoned = 0
in_drawer = list(range(100))
sampler = list(range(100))
for _round in range(n):
random.shuffle(in_drawer)
found = False
for prisoner in range(100):
found = False
for reveal in random.sample(sampler, 50):
card = in_drawer[reveal]
if card == prisoner:
found = True
break
if not found:
break
if found:
pardoned += 1
return pardoned / n * 100 # %
 
def play_optimal(n):
# using 0-99 instead of ranges 1-100
pardoned = 0
in_drawer = list(range(100))
for _round in range(n):
random.shuffle(in_drawer)
for prisoner in range(100):
reveal = prisoner
found = False
for go in range(50):
card = in_drawer[reveal]
if card == prisoner:
found = True
break
reveal = card
if not found:
break
if found:
pardoned += 1
return pardoned / n * 100 # %
 
if __name__ == '__main__':
n = 100_000
print(" Simulation count:", n)
print(f" Random play wins: {play_random(n):4.1f}% of simulations")
print(f"Optimal play wins: {play_optimal(n):4.1f}% of simulations")
Output:
 Simulation count: 100000
 Random play wins:  0.0% of simulations
Optimal play wins: 31.1% of simulations


Or, an alternative procedural approach:

# http://rosettacode.org/wiki/100_prisoners
 
import random
 
 
def main():
NUM_DRAWERS = 10
NUM_REPETITIONS = int(1E5)
 
print('{:15}: {:5} ({})'.format('approach', 'wins', 'ratio'))
for approach in PrisionersGame.approaches:
num_victories = 0
for _ in range(NUM_REPETITIONS):
game = PrisionersGame(NUM_DRAWERS)
num_victories += PrisionersGame.victory(game.play(approach))
 
print('{:15}: {:5} ({:.2%})'.format(
approach.__name__, num_victories, num_victories / NUM_REPETITIONS))
 
 
class PrisionersGame:
"""docstring for PrisionersGame"""
def __init__(self, num_drawers):
assert num_drawers % 2 == 0
self.num_drawers = num_drawers
self.max_attempts = int(self.num_drawers / 2)
self.drawer_ids = list(range(1, num_drawers + 1))
shuffled = self.drawer_ids[:]
random.shuffle(shuffled)
self.drawers = dict(zip(self.drawer_ids, shuffled))
 
def play_naive(self, player_number):
""" Randomly open drawers """
for attempt in range(self.max_attempts):
if self.drawers[random.choice(self.drawer_ids)] == player_number:
return True
 
return False
 
def play_naive_mem(self, player_number):
""" Randomly open drawers but avoiding repetitions """
not_attemped = self.drawer_ids[:]
for attempt in range(self.max_attempts):
guess = random.choice(not_attemped)
not_attemped.remove(guess)
 
if self.drawers[guess] == player_number:
return True
 
return False
 
def play_optimum(self, player_number):
""" Open the drawer that matches the player number and then open the drawer
with the revealed number.
"""

prev_attempt = player_number
for attempt in range(self.max_attempts):
if self.drawers[prev_attempt] == player_number:
return True
else:
prev_attempt = self.drawers[prev_attempt]
 
return False
 
@classmethod
def victory(csl, results):
"""Defines a victory of a game: all players won"""
return all(results)
 
approaches = [play_naive, play_naive_mem, play_optimum]
 
def play(self, approach):
"""Plays this game and returns a list of booleans with
True if a player one, False otherwise"""

return [approach(self, player) for player in self.drawer_ids]
 
 
if __name__ == '__main__':
main()
Output:
With 10 drawers (100k runs)
approach       : wins  (ratio)
play_naive     :    14 (0.01%)
play_naive_mem :    74 (0.07%)
play_optimum   : 35410 (35.41%)

With 100 drawers (10k runs)
approach       : wins  (ratio)
play_naive     :     0 (0.00%)
play_naive_mem :     0 (0.00%)
play_optimum   :  3084 (30.84%)

Functional[edit]

There is some inefficiency entailed in repeatedly re-calculating the fixed sequence of drawers defined by index-chasing in the optimal strategy. Parts of the same paths from drawer to drawer are followed by several different prisoners.

We can avoid redundant recalculation by first obtaining the full set of drawer-chasing cycles that are defined by the sequence of any given shuffle.

We may also notice that the collective fate of the prisoners turns on whether any of the cyclical paths formed by a given shuffle are longer than 50 items. If a shuffle produces a single over-sized cycle, then not every prisoner will be able to reach their card in 50 moves.

The computation below returns a survival failure as soon as a cycle of more than 50 items is found for any given shuffle:

Works with: Python version 3.7
'''100 Prisoners'''
 
from random import randint, sample
 
 
# allChainedPathsAreShort :: Int -> IO (0|1)
def allChainedPathsAreShort(n):
'''1 if none of the index-chasing cycles in a shuffled
sample of [1..n] cards are longer than half the
sample size. Otherwise, 0.
'''

limit = n // 2
xs = range(1, 1 + n)
shuffled = sample(xs, k=n)
 
# A cycle of boxes, drawn from a shuffled
# sample, which includes the given target.
def cycleIncluding(target):
boxChain = [target]
v = shuffled[target - 1]
while v != target:
boxChain.append(v)
v = shuffled[v - 1]
return boxChain
 
# Nothing if the target list is empty, or if the cycle which contains the
# first target is larger than half the sample size.
# Otherwise, just a cycle of enchained boxes containing the first target
# in the list, tupled with the residue of any remaining targets which
# fall outside that cycle.
def boxCycle(targets):
if targets:
boxChain = cycleIncluding(targets[0])
return Just((
difference(targets[1:])(boxChain),
boxChain
)) if limit >= len(boxChain) else Nothing()
else:
return Nothing()
 
# No cycles longer than half of total box count ?
return int(n == sum(map(len, unfoldr(boxCycle)(xs))))
 
 
# randomTrialResult :: RandomIO (0|1) -> Int -> (0|1)
def randomTrialResult(coin):
'''1 if every one of the prisoners finds their ticket
in an arbitrary half of the sample. Otherwise 0.
'''

return lambda n: int(all(
coin(x) for x in range(1, 1 + n)
))
 
 
# TEST ----------------------------------------------------
# main :: IO ()
def main():
'''Two sampling techniques constrasted with 100 drawers
and 100 prisoners, over 100,000 trial runs.
'''

halfOfDrawers = randomRInt(0)(1)
 
def optimalDrawerSampling(x):
return allChainedPathsAreShort(x)
 
def randomDrawerSampling(x):
return randomTrialResult(halfOfDrawers)(x)
 
# kSamplesWithNBoxes :: Int -> Int -> String
def kSamplesWithNBoxes(k):
tests = range(1, 1 + k)
return lambda n: '\n\n' + fTable(
str(k) + ' tests of optimal vs random drawer-sampling ' +
'with ' + str(n) + ' boxes: \n'
)(fName)(lambda r: '{:.2%}'.format(r))(
lambda f: sum(f(n) for x in tests) / k
)([
optimalDrawerSampling,
randomDrawerSampling,
])
 
print(kSamplesWithNBoxes(10000)(10))
 
print(kSamplesWithNBoxes(10000)(100))
 
print(kSamplesWithNBoxes(100000)(100))
 
 
# ------------------------DISPLAY--------------------------
 
# fTable :: String -> (a -> String) ->
# (b -> String) -> (a -> b) -> [a] -> String
def fTable(s):
'''Heading -> x display function -> fx display function ->
f -> xs -> tabular string.
'''

def go(xShow, fxShow, f, xs):
ys = [xShow(x) for x in xs]
w = max(map(len, ys))
return s + '\n' + '\n'.join(map(
lambda x, y: y.rjust(w, ' ') + ' -> ' + fxShow(f(x)),
xs, ys
))
return lambda xShow: lambda fxShow: lambda f: lambda xs: go(
xShow, fxShow, f, xs
)
 
 
# fname :: (a -> b) -> String
def fName(f):
'''Name bound to the given function.'''
return f.__name__
 
 
# ------------------------GENERIC -------------------------
 
# Just :: a -> Maybe a
def Just(x):
'''Constructor for an inhabited Maybe (option type) value.
Wrapper containing the result of a computation.
'''

return {'type': 'Maybe', 'Nothing': False, 'Just': x}
 
 
# Nothing :: Maybe a
def Nothing():
'''Constructor for an empty Maybe (option type) value.
Empty wrapper returned where a computation is not possible.
'''

return {'type': 'Maybe', 'Nothing': True}
 
 
# difference :: Eq a => [a] -> [a] -> [a]
def difference(xs):
'''All elements of xs, except any also found in ys.'''
return lambda ys: list(set(xs) - set(ys))
 
 
# randomRInt :: Int -> Int -> IO () -> Int
def randomRInt(m):
'''The return value of randomRInt is itself
a function. The returned function, whenever
called, yields a a new pseudo-random integer
in the range [m..n].
'''

return lambda n: lambda _: randint(m, n)
 
 
# unfoldr(lambda x: Just((x, x - 1)) if 0 != x else Nothing())(10)
# -> [10, 9, 8, 7, 6, 5, 4, 3, 2, 1]
# unfoldr :: (b -> Maybe (a, b)) -> b -> [a]
def unfoldr(f):
'''Dual to reduce or foldr.
Where catamorphism reduces a list to a summary value,
the anamorphic unfoldr builds a list from a seed value.
As long as f returns Just(a, b), a is prepended to the list,
and the residual b is used as the argument for the next
application of f.
When f returns Nothing, the completed list is returned.
'''

def go(v):
xr = v, v
xs = []
while True:
mb = f(xr[0])
if mb.get('Nothing'):
return xs
else:
xr = mb.get('Just')
xs.append(xr[1])
return xs
return lambda x: go(x)
 
 
# MAIN ---
if __name__ == '__main__':
main()
Output:
10000 tests of optimal vs random drawer-sampling with 10 boxes: 

optimalDrawerSampling -> 35.47%
 randomDrawerSampling -> 0.09%

10000 tests of optimal vs random drawer-sampling with 100 boxes: 

optimalDrawerSampling -> 30.40%
 randomDrawerSampling -> 0.00%

100000 tests of optimal vs random drawer-sampling with 100 boxes: 

optimalDrawerSampling -> 31.17%
 randomDrawerSampling -> 0.00%

Racket[edit]

#lang racket
(require srfi/1)
 
(define current-samples (make-parameter 10000))
(define *prisoners* 100)
(define *max-guesses* 50)
 
(define (evaluate-strategy instance-solved? strategy (s (current-samples)))
(/ (for/sum ((_ s) #:when (instance-solved? strategy)) 1) s))
 
(define (build-drawers)
(list->vector (shuffle (range *prisoners*))))
 
(define (100-prisoners-problem strategy)
(every (strategy (build-drawers)) (range *prisoners*)))
 
(define ((strategy-1 drawers) p)
(any (λ (_) (= p (vector-ref drawers (random *prisoners*)))) (range *max-guesses*)))
 
(define ((strategy-2 drawers) p)
(define-values (_ found?)
(for/fold ((d p) (found? #f)) ((_ *max-guesses*)) #:break found?
(let ((card (vector-ref drawers d))) (values card (= card p)))))
found?)
 
(define (print-sample-percentage caption f (s (current-samples)))
(printf "~a: ~a%~%" caption (real->decimal-string (* 100 f) (- (order-of-magnitude s) 2))))
 
(module+ main
(print-sample-percentage "random" (evaluate-strategy 100-prisoners-problem strategy-1))
(print-sample-percentage "optimal" (evaluate-strategy 100-prisoners-problem strategy-2)))
Output:
random: 0.00%
optimal: 31.18%

Raku[edit]

(formerly Perl 6)

Works with: Rakudo version 2019.07.1

Accepts command line parameters to modify the number of prisoners and the number of simulations to run.

Also test with 10 prisoners to verify that the logic is correct for random selection. Random selection should succeed with 10 prisoners at a probability of (1/2)**10, so in 100_000 simulations, should get pardons about .0977 percent of the time.

unit sub MAIN (:$prisoners = 100, :$simulations = 10000);
my @prisoners = ^$prisoners;
my $half = floor +@prisoners / 2;
 
sub random ($n) {
^$n .race.map( {
my @drawers = @prisoners.pick: *;
@prisoners.map( -> $prisoner {
my $found = 0;
for @drawers.pick($half) -> $card {
$found = 1 and last if $card == $prisoner
}
last unless $found;
$found
}
).sum == @prisoners
}
).grep( *.so ).elems / $n * 100
}
 
sub optimal ($n) {
^$n .race.map( {
my @drawers = @prisoners.pick: *;
@prisoners.map( -> $prisoner {
my $found = 0;
my $card = @drawers[$prisoner];
if $card == $prisoner {
$found = 1
} else {
for ^($half - 1) {
$card = @drawers[$card];
$found = 1 and last if $card == $prisoner
}
}
last unless $found;
$found
}
).sum == @prisoners
}
).grep( *.so ).elems / $n * 100
}
 
say "Testing $simulations simulations with $prisoners prisoners.";
printf " Random play wins: %.3f%% of simulations\n", random $simulations;
printf "Optimal play wins: %.3f%% of simulations\n", optimal $simulations;
Output:

With defaults

Testing 10000 simulations with 100 prisoners.
 Random play wins: 0.000% of simulations
Optimal play wins: 30.510% of simulations

With passed parameters: --prisoners=10, --simulations=100000

Testing 100000 simulations with 10 prisoners.
 Random play wins: 0.099% of simulations
Optimal play wins: 35.461% of simulations

Red[edit]

 
Red []
 
K_runs: 100000
repeat n 100 [append rand_arr: [] n] ;; define array/series with numbers 1..100
 
;;-------------------------------
strat_optimal: function [pris ][
;;-------------------------------
locker: pris ;; start with locker equal to prisoner number
loop 50 [
if Board/:locker = pris [ return true ] ;; locker with prisoner number found
locker: Board/:locker
]
false ;; number not found - fail
]
;;-------------------------------
strat_rand: function [pris ][
;;-------------------------------
random rand_arr ;; define set of random lockers
repeat n 50 [ if Board/(rand_arr/:n) = pris [ return true ] ] ;; try first 50, found ? then return success
false
]
 
;;------------------------------
check_board: function [ strat][
;;------------------------------
repeat pris 100 [ ;; for each prisoner
either strat = 'optimal [ unless strat_optimal pris [return false ] ]
[ unless strat_rand pris [return false ] ]
]
true ;; all 100 prisoners passed test
]
 
saved: saved_rand: 0 ;; count all saved runs per strategy
loop K_runs [
Board: random copy rand_arr ;; new board for every run
if check_board 'optimal [saved: saved + 1] ;; optimal stategy
if check_board 'rand [saved_rand: saved_rand + 1] ;; random strategy
]
 
print ["runs" k_runs newline "Percent saved opt.strategy:" saved * 100.0 / k_runs ]
print ["Percent saved random strategy:" saved_rand * 100.0 / k_runs ]
 
Output:

runs 100000 Percent saved opt.strategy: 31.165 Percent saved random strategy: 0.0

REXX[edit]

/*REXX program to simulate the problem of 100 prisoners:  random,  and optimal strategy.*/
parse arg men trials seed . /*obtain optional arguments from the CL*/
if men=='' | men=="," then men= 100 /*number of prisoners for this run.*/
if trials=='' | trials=="," then trials= 100000 /* " " simulations " " " */
if datatype(seed, 'W') then call random ,,seed /*seed for the random number generator.*/
try= men % 2; swaps= men * 3 /*number tries for searching for a card*/
$.1= ' a simple '; $.2= "an optimal" /*literals used for the SAY instruction*/
say center(' running' commas(trials) "trials with" commas(men) 'prisoners ', 70, "═")
say
do strategy=1 for 2; pardons= 0 /*perform the two types of strategies. */
 
do trials; call gCards /*do trials for a strategy; gen cards.*/
do p=1 for men until failure /*have each prisoner go through process*/
if strategy==1 then failure= simple() /*Is 1st strategy? Use simple strategy*/
else failure= picker() /* " 2nd " " optimal " */
end /*p*/ /*FAILURE ≡ 1? Then a prisoner failed.*/
if #==men then pardons= pardons + 1 /*was there a pardon of all prisoners? */
end /*trials*/ /*if 1 prisoner fails, then they all do*/
 
pc= format( pardons/trials*100, , 3); _= left('', pc<10)
say right('Using', 9) $.strategy "strategy yields pardons " _||pc"% of the time."
end /*strategy*/
exit /*stick a fork in it, we're all done. */
/*──────────────────────────────────────────────────────────────────────────────────────*/
commas: parse arg _; do c=length(_)-3 to 1 by -3; _= insert(',', _, c); end; return _
/*──────────────────────────────────────────────────────────────────────────────────────*/
gCards: #= 0; do j=1 for men; @.j= j /*define seq. of cards*/
end /*j*/ /*same as seq. of men.*/
do swaps; a= random(1, men) /*get 1st rand number.*/
do until b\==a; b= random(1, men) /* " 2nd " " */
end /*until*/ /* [↑] ensure A ¬== B */
parse value @.a @.b with @.b @.a /*swap 2 random cards.*/
end /*swaps*/; return
/*──────────────────────────────────────────────────────────────────────────────────────*/
simple: !.= 0; do try; do until !.?==0; ?= random(1, men) /*get random card ··· */
end /*until*/ /*··· not used before.*/
if @.?==p then do; #= #+1; return 0; end /*found his own card? */
 !.?= 1 /*flag as being used. */
end /*try*/; return 1 /*didn't find his card*/
/*──────────────────────────────────────────────────────────────────────────────────────*/
picker: ?= p; do try; if @.?==p then do; #= #+1; return 0 /*Found his own card? */
end /* [↑] indicate success for prisoner. */
 ?= @.? /*choose next drawer from current card.*/
end /*try*/; return 1 /*choose half of the number of drawers.*/
output   when using the default inputs:
══════════════ running 100,000 trials with 100 prisoners ══════════════

    Using  a simple  strategy yields pardons   0.000%  of the time.
    Using an optimal strategy yields pardons  31.186%  of the time.
output   when using the input of:     10
══════════════ running 100,000 trials with 10 prisoners ══════════════

    Using  a simple  strategy yields pardons   0.086%  of the time.
    Using an optimal strategy yields pardons  31.204%  of the time.

Ruby[edit]

prisoners = [*1..100]
N = 10_000
generate_rooms = ->{ [nil]+[*1..100].shuffle }
 
res = N.times.count do
rooms = generate_rooms[]
prisoners.all? {|pr| rooms[1,100].sample(50).include?(pr)}
end
puts "Random strategy : %11.4f %%" % (res.fdiv(N) * 100)
 
res = N.times.count do
rooms = generate_rooms[]
prisoners.all? do |pr|
cur_room = pr
50.times.any? do
found = (rooms[cur_room] == pr)
cur_room = rooms[cur_room]
found
end
end
end
puts "Optimal strategy: %11.4f %%" % (res.fdiv(N) * 100)
 
Output:
Random strategy :      0.0000 %
Optimal strategy:     30.7400 %

Rust[edit]

Fairly naive implementation. Could probably be made more idiomatic. Depends on extern rand crate.

Cargo.toml

[dependencies]
rand = '0.7.2'

src/main.rs

extern crate rand;
 
use rand::prelude::*;
 
// Do a full run of checking boxes in a random order for a single prisoner
fn check_random_boxes(prisoner: u8, boxes: &[u8]) -> bool {
let checks = {
let mut b: Vec<u8> = (1u8..=100u8).collect();
b.shuffle(&mut rand::thread_rng());
b
};
checks.into_iter().take(50).any(|check| boxes[check as usize - 1] == prisoner)
}
 
// Do a full run of checking boxes in the optimized order for a single prisoner
fn check_ordered_boxes(prisoner: u8, boxes: &[u8]) -> bool {
let mut next_check = prisoner;
(0..50).any(|_| {
next_check = boxes[next_check as usize - 1];
next_check == prisoner
})
}
 
fn main() {
let mut boxes: Vec<u8> = (1u8..=100u8).collect();
 
let trials = 100000;
 
let ordered_successes = (0..trials).filter(|_| {
boxes.shuffle(&mut rand::thread_rng());
(1u8..=100u8).all(|prisoner| check_ordered_boxes(prisoner, &boxes))
}).count();
 
let random_successes = (0..trials).filter(|_| {
boxes.shuffle(&mut rand::thread_rng());
(1u8..=100u8).all(|prisoner| check_random_boxes(prisoner, &boxes))
}).count();
 
println!("{} / {} ({:.02}%) successes in ordered", ordered_successes, trials, ordered_successes as f64 * 100.0 / trials as f64);
println!("{} / {} ({:.02}%) successes in random", random_successes, trials, random_successes as f64 * 100.0 / trials as f64);
 
}
Output:
31106 / 100000 (31.11%) successes in ordered
0 / 100000 (0.00%) successes in random

Scala[edit]

Translation of: Java
import scala.util.Random
import scala.util.control.Breaks._
 
object Main {
def playOptimal(n: Int): Boolean = {
val secretList = Random.shuffle((0 until n).toBuffer)
 
for (i <- secretList.indices) {
var prev = i
breakable {
for (_ <- 0 until secretList.size / 2) {
if (secretList(prev) == i) {
break()
}
prev = secretList(prev)
}
return false
}
}
 
true
}
 
def playRandom(n: Int): Boolean = {
val secretList = Random.shuffle((0 until n).toBuffer)
 
for (i <- secretList.indices) {
val trialList = Random.shuffle((0 until n).toBuffer)
 
breakable {
for (j <- 0 until trialList.size / 2) {
if (trialList(j) == i) {
break()
}
}
return false
}
}
 
true
}
 
def exec(n: Int, p: Int, play: Int => Boolean): Double = {
var succ = 0.0
for (_ <- 0 until n) {
if (play(p)) {
succ += 1
}
}
(succ * 100.0) / n
}
 
def main(args: Array[String]): Unit = {
val n = 100000
val p = 100
printf("# of executions: %,d\n", n)
printf("Optimal play success rate: %f%%\n", exec(n, p, playOptimal))
printf("Random play success rate: %f%%\n", exec(n, p, playRandom))
}
}
Output:
# of executions: 100,000
Optimal play success rate: 31.201000%
Random play success rate: 0.000000%

Swift[edit]

import Foundation
 
struct PrisonersGame {
let strategy: Strategy
let numPrisoners: Int
let drawers: [Int]
 
init(numPrisoners: Int, strategy: Strategy) {
self.numPrisoners = numPrisoners
self.strategy = strategy
self.drawers = (1...numPrisoners).shuffled()
}
 
@discardableResult
func play() -> Bool {
for num in 1...numPrisoners {
guard findNumber(num) else {
return false
}
}
 
return true
}
 
private func findNumber(_ num: Int) -> Bool {
var tries = 0
var nextDrawer = num - 1
 
while tries < 50 {
tries += 1
 
switch strategy {
case .random where drawers.randomElement()! == num:
return true
case .optimum where drawers[nextDrawer] == num:
return true
case .optimum:
nextDrawer = drawers[nextDrawer] - 1
case _:
continue
}
}
 
return false
}
 
enum Strategy {
case random, optimum
}
}
 
let numGames = 100_000
let lock = DispatchSemaphore(value: 1)
var done = 0
 
print("Running \(numGames) games for each strategy")
 
DispatchQueue.concurrentPerform(iterations: 2) {i in
let strat = i == 0 ? PrisonersGame.Strategy.random : .optimum
var numPardoned = 0
 
for _ in 0..<numGames {
let game = PrisonersGame(numPrisoners: 100, strategy: strat)
 
if game.play() {
numPardoned += 1
}
}
 
print("Probability of pardon with \(strat) strategy: \(Double(numPardoned) / Double(numGames))")
 
lock.wait()
done += 1
lock.signal()
 
if done == 2 {
exit(0)
}
}
 
dispatchMain()
Output:
Running 100000 games for each strategy
Probability of pardon with optimum strategy: 0.31099
Probability of pardon with random strategy: 0.0

VBA[edit]

Sub HundredPrisoners()
 
NumberOfPrisoners = Int(InputBox("Number of Prisoners", "Prisoners", 100))
Tries = Int(InputBox("Numer of Tries", "Tries", 1000))
Selections = Int(InputBox("Number of Selections", "Selections", NumberOfPrisoners / 2))
 
StartTime = Timer
 
AllFoundOptimal = 0
AllFoundRandom = 0
AllFoundRandomMem = 0
 
For i = 1 To Tries
OptimalCount = HundredPrisoners_Optimal(NumberOfPrisoners, Selections)
RandomCount = HundredPrisoners_Random(NumberOfPrisoners, Selections)
RandomMemCount = HundredPrisoners_Random_Mem(NumberOfPrisoners, Selections)
 
If OptimalCount = NumberOfPrisoners Then
AllFoundOptimal = AllFoundOptimal + 1
End If
If RandomCount = NumberOfPrisoners Then
AllFoundRandom = AllFoundRandom + 1
End If
If RandomMemCount = NumberOfPrisoners Then
AllFoundRandomMem = AllFoundRandomMem + 1
End If
Next i
 
 
ResultString = "Optimal: " & AllFoundOptimal & " of " & Tries & ": " & AllFoundOptimal / Tries * 100 & "%"
ResultString = ResultString & Chr(13) & "Random: " & AllFoundRandom & " of " & Tries & ": " & AllFoundRandom / Tries * 100 & "%"
ResultString = ResultString & Chr(13) & "RandomMem: " & AllFoundRandomMem & " of " & Tries & ": " & AllFoundRandomMem / Tries * 100 & "%"
 
EndTime = Timer
 
ResultString = ResultString & Chr(13) & "Elapsed Time: " & Round(EndTime - StartTime, 2) & " s"
ResultString = ResultString & Chr(13) & "Trials/sec: " & Tries / Round(EndTime - StartTime, 2)
 
MsgBox ResultString, vbOKOnly, "Results"
 
End Sub
 
Function HundredPrisoners_Optimal(ByVal NrPrisoners, ByVal NrSelections) As Long
Dim DrawerArray() As Long
 
ReDim DrawerArray(NrPrisoners - 1)
 
For Counter = LBound(DrawerArray) To UBound(DrawerArray)
DrawerArray(Counter) = Counter + 1
Next Counter
 
FisherYates DrawerArray
 
For i = 1 To NrPrisoners
NumberFromDrawer = DrawerArray(i - 1)
For j = 1 To NrSelections - 1
If NumberFromDrawer = i Then
FoundOwnNumber = FoundOwnNumber + 1
GoTo Finish
End If
NumberFromDrawer = DrawerArray(NumberFromDrawer - 1)
Next j
Finish:
Next i
HundredPrisoners_Optimal = FoundOwnNumber
End Function
 
Function HundredPrisoners_Random(ByVal NrPrisoners, ByVal NrSelections) As Long
Dim DrawerArray() As Long
ReDim DrawerArray(NrPrisoners - 1)
 
FoundOwnNumber = 0
 
For Counter = LBound(DrawerArray) To UBound(DrawerArray)
DrawerArray(Counter) = Counter + 1
Next Counter
 
FisherYates DrawerArray
 
 
For i = 1 To NrPrisoners
For j = 1 To NrSelections
RandomDrawer = Int(NrPrisoners * Rnd)
NumberFromDrawer = DrawerArray(RandomDrawer)
If NumberFromDrawer = i Then
FoundOwnNumber = FoundOwnNumber + 1
GoTo Finish
End If
Next j
Finish:
Next i
HundredPrisoners_Random = FoundOwnNumber
End Function
 
Function HundredPrisoners_Random_Mem(ByVal NrPrisoners, ByVal NrSelections) As Long
Dim DrawerArray() As Long
Dim SelectionArray() As Long
ReDim DrawerArray(NrPrisoners - 1)
ReDim SelectionArray(NrPrisoners - 1)
 
HundredPrisoners_Random_Mem = 0
FoundOwnNumberMem = 0
 
For Counter = LBound(DrawerArray) To UBound(DrawerArray)
DrawerArray(Counter) = Counter + 1
Next Counter
 
For Counter = LBound(SelectionArray) To UBound(SelectionArray)
SelectionArray(Counter) = Counter + 1
Next Counter
 
FisherYates DrawerArray
 
For i = 1 To NrPrisoners
FisherYates SelectionArray
For j = 1 To NrSelections
NumberFromDrawer = DrawerArray(SelectionArray(j - 1) - 1)
If NumberFromDrawer = i Then
FoundOwnNumberMem = FoundOwnNumberMem + 1
GoTo Finish2
End If
Next j
Finish2:
Next i
HundredPrisoners_Random_Mem = FoundOwnNumberMem
End Function
 
Sub FisherYates(ByRef InputArray() As Long)
 
Dim Temp As Long
Dim PosRandom As Long
Dim Counter As Long
Dim Upper As Long
Dim Lower As Long
 
Lower = LBound(InputArray)
Upper = UBound(InputArray)
 
Randomize
 
For Counter = Upper To (Lower + 1) Step -1
PosRandom = CLng(Int((Counter - Lower + 1) * Rnd + Lower))
Temp = InputArray(Counter)
InputArray(Counter) = InputArray(PosRandom)
InputArray(PosRandom) = Temp
Next Counter
 
End Sub
Output:
Optimal: 29090 of 100000: 29.09%
Random: 0 of 100000: 0%
RandomMem: 0 of 100000: 0%
Elapsed Time: 388.41 s

Visual Basic .NET[edit]

Translation of: C#
Module Module1
 
Function PlayOptimal() As Boolean
Dim secrets = Enumerable.Range(0, 100).OrderBy(Function(a) Guid.NewGuid).ToList
 
For p = 1 To 100
Dim success = False
 
Dim choice = p - 1
For i = 1 To 50
If secrets(choice) = p - 1 Then
success = True
Exit For
End If
choice = secrets(choice)
Next
 
If Not success Then
Return False
End If
Next
 
Return True
End Function
 
Function PlayRandom() As Boolean
Dim secrets = Enumerable.Range(0, 100).OrderBy(Function(a) Guid.NewGuid).ToList
 
For p = 1 To 100
Dim choices = Enumerable.Range(0, 100).OrderBy(Function(a) Guid.NewGuid).ToList
 
Dim success = False
For i = 1 To 50
If choices(i - 1) = p Then
success = True
Exit For
End If
Next
 
If Not success Then
Return False
End If
Next
 
Return True
End Function
 
Function Exec(n As UInteger, play As Func(Of Boolean))
Dim success As UInteger = 0
For i As UInteger = 1 To n
If play() Then
success += 1
End If
Next
Return 100.0 * success / n
End Function
 
Sub Main()
Dim N = 1_000_000
Console.WriteLine("# of executions: {0}", N)
Console.WriteLine("Optimal play success rate: {0:0.00000000000}%", Exec(N, AddressOf PlayOptimal))
Console.WriteLine(" Random play success rate: {0:0.00000000000}%", Exec(N, AddressOf PlayRandom))
End Sub
 
End Module
Output:
# of executions: 1000000
Optimal play success rate: 31.12990000000%
 Random play success rate: 0.00000000000%

zkl[edit]

const SLOTS=100, PRISONERS=100, TRIES=50, N=10_000;
fcn oneHundredJDI{ // just do it strategy
cupboard,picks := [0..SLOTS-1].walk().shuffle(), cupboard.copy();
// if this prisoner can't find their number in TRIES, all fail
foreach p in (PRISONERS){ if(picks.shuffle().find(p)>=TRIES) return(False); }
True // all found their number
}
fcn oneHundredO{ // Optimal strategy
cupboard := [0..SLOTS-1].walk().shuffle();
foreach p in (PRISONERS){
d:=p;
do(TRIES){ if((d=cupboard[d]) == p) continue(2) } // found my number
return(False); // this prisoner failed to find their number, all fail
}
True // all found their number
}
s:=N.pump(Ref(0).incN,oneHundredJDI).value.toFloat()/N*100;
println("Just do it strategy (%,d simulatations): %.2f%%".fmt(N,s));
 
s:=N.pump(Ref(0).incN,oneHundredO).value.toFloat()/N*100;
println("Optimal strategy (%,d simulatations): %.2f%%".fmt(N,s));
Output:
Just do it strategy (10,000 simulatations): 0.00%
Optimal strategy    (10,000 simulatations): 31.16%

And a sanity check (from the Raku entry):

const SLOTS=100, PRISONERS=10, TRIES=50, N=100_000;
Output:
Just do it strategy (100,000 simulatations): 0.09%
Optimal strategy    (100,000 simulatations): 31.13%