Task: 100 prisoners







Python: import random

def play_random(n):
    
    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):
    
    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")




Fortran: SUBROUTINE SHUFFLE_ARRAY(INT_ARRAY)
    
    
    IMPLICIT NONE

    INTEGER, DIMENSION(100), INTENT(INOUT) :: INT_ARRAY
    INTEGER, PARAMETER :: N_PASSES = 10
    

    INTEGER :: TEMP_1, TEMP_2   
    INTEGER :: I, J, PASS       
    REAL :: R                   

    CALL RANDOM_SEED()  

    DO PASS=1, N_PASSES
        DO I=1, SIZE(INT_ARRAY)

            
            CALL RANDOM_NUMBER(R)
            J = CEILING(R*SIZE(INT_ARRAY))

            
            
            DO WHILE (J > SIZE(INT_ARRAY))
                J = CEILING(R*SIZE(INT_ARRAY))
            END DO

            
            TEMP_1 = INT_ARRAY(I)
            TEMP_2 = INT_ARRAY(J)
            INT_ARRAY(I) = TEMP_2
            INT_ARRAY(J) = TEMP_1
        ENDDO
    ENDDO
END SUBROUTINE SHUFFLE_ARRAY

SUBROUTINE RUN_RANDOM(N_ROUNDS)
    
    
    IMPLICIT NONE

    INTEGER, INTENT(IN) :: N_ROUNDS 

    INTEGER :: ROUND, PRISONER, CHOICE, I       
    INTEGER :: N_SUCCESSES                      
    REAL(8) :: TOTAL                            
    LOGICAL :: NUM_FOUND = .FALSE.              

    INTEGER, DIMENSION(100) :: CARDS, CHOICES   
                                                

    
    
    
    
    CARDS = (/(I, I=1, 100, 1)/)
    CHOICES = (/(I, I=1, 100, 1)/)

    N_SUCCESSES = 0
    TOTAL = REAL(N_ROUNDS)

    
    
    
    
    ROUNDS_LOOP: DO ROUND=1, N_ROUNDS
        CALL SHUFFLE_ARRAY(CARDS)
        PRISONERS_LOOP: DO PRISONER=1, 100
            NUM_FOUND = .FALSE.
            CALL SHUFFLE_ARRAY(CHOICES)
            CHOICE_LOOP: DO CHOICE=1, 50
                IF(CARDS(CHOICE) == PRISONER) THEN
                    NUM_FOUND = .TRUE.
                    EXIT CHOICE_LOOP
                ENDIF
            ENDDO CHOICE_LOOP
            IF(.NOT. NUM_FOUND) THEN
                EXIT PRISONERS_LOOP
            ENDIF
        ENDDO PRISONERS_LOOP
        IF(NUM_FOUND) THEN
            N_SUCCESSES = N_SUCCESSES + 1
        ENDIF
    ENDDO ROUNDS_LOOP

    WRITE(*, '(A, F0.3, A)') "Random drawer selection method success rate: ", &
        100*N_SUCCESSES/TOTAL, "%"

END SUBROUTINE RUN_RANDOM

SUBROUTINE RUN_OPTIMAL(N_ROUNDS)
    
    
    
    
    IMPLICIT NONE

    INTEGER, INTENT(IN) :: N_ROUNDS

    INTEGER :: ROUND, PRISONER, CHOICE, I   
    INTEGER :: CURRENT_DRAW                 
    INTEGER :: N_SUCCESSES                  
    REAL(8) :: TOTAL                        
    LOGICAL :: NUM_FOUND = .FALSE.          
    INTEGER, DIMENSION(100) :: CARDS        

    
    
    CARDS = (/(I, I=1, 100, 1)/)

    N_SUCCESSES = 0
    TOTAL = REAL(N_ROUNDS)

    
    
    
    
    ROUNDS_LOOP: DO ROUND=1, N_ROUNDS
        CARDS = (/(I, I=1, 100, 1)/)
        CALL SHUFFLE_ARRAY(CARDS)
        PRISONERS_LOOP: DO PRISONER=1, 100
            CURRENT_DRAW = PRISONER
            NUM_FOUND = .FALSE.
            CHOICE_LOOP: DO CHOICE=1, 50
                IF(CARDS(CURRENT_DRAW) == PRISONER) THEN
                    NUM_FOUND = .TRUE.
                    EXIT CHOICE_LOOP
                ELSE
                    CURRENT_DRAW = CARDS(CURRENT_DRAW)
                ENDIF
            ENDDO CHOICE_LOOP
            IF(.NOT. NUM_FOUND) THEN
                EXIT PRISONERS_LOOP
            ENDIF
        ENDDO PRISONERS_LOOP
        IF(NUM_FOUND) THEN
            N_SUCCESSES = N_SUCCESSES + 1
        ENDIF
    ENDDO ROUNDS_LOOP
    WRITE(*, '(A, F0.3, A)') "Optimal drawer selection method success rate: ", &
        100*N_SUCCESSES/TOTAL, "%"

END SUBROUTINE RUN_OPTIMAL

PROGRAM HUNDRED_PRISONERS
    
    
    IMPLICIT NONE
    INTEGER, PARAMETER :: N_ROUNDS = 50000
    WRITE(*,'(A, I0, A)') "Running simulation for ", N_ROUNDS, " trials..."
    CALL RUN_RANDOM(N_ROUNDS)
    CALL RUN_OPTIMAL(N_ROUNDS)
END PROGRAM HUNDRED_PRISONERS