monty hall %50 - %50 - c

Question

i am trying to simulate monty hall problem. i didn't realized any problem but i recieve approximately %50 %50 output. i know that there are explanations but i couldnt understand these
please help me
#include <stdio.h>
#include <stdlib.h>
#include <time.h>
#define win 1
#define lose 0
#define yes 1
#define no 0
int main(){
//i assume that prize is behind the first door
srand(time(NULL));
int lose_counter = 0;
int win_counter = 0;
for(int i = 1;i <= 10000;i++){
int game_status;
int chosen_door = rand() % 3 + 1;
int choice;
//first step that i chose a door
if(chosen_door == 1){
game_status = win;
}
else if(chosen_door == 2){
game_status = lose;
}
else if(chosen_door == 3){
game_status = lose;
}
//host says "do you want to change your door"
choice = rand() % 2;
if(choice == yes){
if(chosen_door == 1 ){//this is the case i have chosen
//first door and change it after question
game_status = lose;
}
if(chosen_door == 2 ){
game_status = win;
}
if(chosen_door == 3 ){
game_status = win;
}
}
if(game_status == win){
win_counter++;
}
else if(game_status == lose){
lose_counter++;
}
}
printf("win: %d\nlose: %d\n",win_counter,lose_counter);
return 0;
}

Answer 1

The chances to win when not switching the doors are 1/3.
If you switch the chances increase to 2/3.
Your code takes samples of 50% switching and 50% not switching, hence the average of 1/3 and 2/3 comes up as 0.5.

Answer 2

The odds of winning are 2/3 if you switch.
Using
choice = 1; // Switch
results in win in about 2/3 of your trials as expected.
The odds of winning are 1/3 if you don't switch.
Using
choice = 0; // Keep
results in win in about 1/3 of your trials as expected.
If you randomly decide to switch or keep, the odds of winning are
( 1/2 * 2/3 ) + ( 1/2 * 1/3 ) = 1/2
Using
choice = rand() % 2;
results in win in about 1/2 of your trials as expected.
Fixed:
#include <stdio.h>
#include <stdlib.h>
#include <time.h>
int main(void) {
// I assume that prize is behind the first door
srand(time(NULL));
unsigned N = 10000;
unsigned win_if_keep_counter = 0;
unsigned win_if_switch_counter = 0;
for (unsigned i=N; i--; ) {
int chosen_door = rand() % 3 + 1;
if (chosen_door == 1) {
// Monte open door 2 or 3.
// You win if you keep door 1.
++win_if_keep_counter;
}
else if (chosen_door == 2) {
// Monte open door 3.
// You win if you switch to door 1.
++win_if_switch_counter;
}
else if (chosen_door == 3) {
// Monte open door 2.
// You win if you switch to door 1.
++win_if_switch_counter;
}
}
printf("win if keep: %.1f%%\n", ((double)win_if_keep_counter)/N*100);
printf("win if switch: %.1f%%\n", ((double)win_if_switch_counter)/N*100);
}