Task: 100 prisoners

C: #include<stdbool.h>
#include<stdlib.h>
#include<stdio.h>
#include<time.h>

#define LIBERTY false
#define DEATH true

typedef struct{
	int cardNum;
	bool hasBeenOpened;
}drawer;

drawer *drawerSet;

void initialize(int prisoners){
	int i,j,card;
	bool unique;

	drawerSet = ((drawer*)malloc(prisoners * sizeof(drawer))) -1;

	card = rand()%prisoners + 1;
	drawerSet[1] = (drawer){.cardNum = card, .hasBeenOpened = false};

	for(i=1 + 1;i<prisoners + 1;i++){
		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){.cardNum = card, .hasBeenOpened = false};
	}

}

void closeAllDrawers(int prisoners){
	int i;
	for(i=1;i<prisoners + 1;i++)
		drawerSet[i].hasBeenOpened = false;
}

bool libertyOrDeathAtRandom(int prisoners,int chances){
	int i,j,chosenDrawer;

	for(i= 1;i<prisoners + 1;i++){
		bool foundCard = false;
		for(j=0;j<chances;j++){
			do{
				chosenDrawer = rand()%prisoners + 1;
			}while(drawerSet[chosenDrawer].hasBeenOpened==true);
			if(drawerSet[chosenDrawer].cardNum == i){
				foundCard = true;
				break;
			}
			drawerSet[chosenDrawer].hasBeenOpened = true;
		}
		closeAllDrawers(prisoners);
		if(foundCard == false)
			return DEATH;
	}

	return LIBERTY;
}

bool libertyOrDeathPlanned(int prisoners,int chances){
	int i,j,chosenDrawer;
	for(i=1;i<prisoners + 1;i++){
		chosenDrawer = i;
		bool foundCard = false;
		for(j=0;j<chances;j++){
			drawerSet[chosenDrawer].hasBeenOpened = true;

			if(drawerSet[chosenDrawer].cardNum == i){
				foundCard = true;
				break;
			}
			if(chosenDrawer == drawerSet[chosenDrawer].cardNum){
				do{
                    chosenDrawer = rand()%prisoners + 1;
				}while(drawerSet[chosenDrawer].hasBeenOpened==true);
			}
			else{
				chosenDrawer = drawerSet[chosenDrawer].cardNum;
			}

		}

		closeAllDrawers(prisoners);
		if(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;
}







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")