Since I couldn't understand the Monty Hall Problem in abstract, I programmed it in Gamemaker and tested it. I get it now, and it does in fact work. First image is staying with your door, second image is switching. Successes is the top number, failures is the bottom number.
Math works!
![code comments:
//This cowboy is infected with nightmares that come real.
//He can teleport because he moves like in a dream
//most of what he sees is from his past in war, there were a lot of bullets
//weaponry spawns, explosions happen, all of which only damage the player
//[bad cowboy boss] survived and hates it, he lost all his friends
//the other cowboys in the world all look like him because they're figments of his imagination
//wearing their uniform hats, his old friends come back to aid him, and die all over again](https://cdn.bsky.app/img/feed_thumbnail/plain/did:plc:ctrsfzylbthymidawaafwklj/bafkreiaqhpuywx43i6b4lrh4kj3ltsnzl5ak5w5ywn3pcn4cokf5yhrzhq)
