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-// Copyright 2018 Developers of the Rand project.
-// Copyright 2013-2018 The Rust Project Developers.
-//
-// Licensed under the Apache License, Version 2.0 <LICENSE-APACHE or
-// https://www.apache.org/licenses/LICENSE-2.0> or the MIT license
-// <LICENSE-MIT or https://opensource.org/licenses/MIT>, at your
-// option. This file may not be copied, modified, or distributed
-// except according to those terms.
-
-//! ## Monty Hall Problem
-//!
-//! This is a simulation of the [Monty Hall Problem][]:
-//!
-//! > Suppose you're on a game show, and you're given the choice of three doors:
-//! > Behind one door is a car; behind the others, goats. You pick a door, say
-//! > No. 1, and the host, who knows what's behind the doors, opens another
-//! > door, say No. 3, which has a goat. He then says to you, "Do you want to
-//! > pick door No. 2?" Is it to your advantage to switch your choice?
-//!
-//! The rather unintuitive answer is that you will have a 2/3 chance of winning
-//! if you switch and a 1/3 chance of winning if you don't, so it's better to
-//! switch.
-//!
-//! This program will simulate the game show and with large enough simulation
-//! steps it will indeed confirm that it is better to switch.
-//!
-//! [Monty Hall Problem]: https://en.wikipedia.org/wiki/Monty_Hall_problem
-
-#![cfg(feature = "std")]
-
-use rand::distributions::{Distribution, Uniform};
-use rand::Rng;
-
-struct SimulationResult {
- win: bool,
- switch: bool,
-}
-
-// Run a single simulation of the Monty Hall problem.
-fn simulate<R: Rng>(random_door: &Uniform<u32>, rng: &mut R) -> SimulationResult {
- let car = random_door.sample(rng);
-
- // This is our initial choice
- let mut choice = random_door.sample(rng);
-
- // The game host opens a door
- let open = game_host_open(car, choice, rng);
-
- // Shall we switch?
- let switch = rng.gen();
- if switch {
- choice = switch_door(choice, open);
- }
-
- SimulationResult { win: choice == car, switch }
-}
-
-// Returns the door the game host opens given our choice and knowledge of
-// where the car is. The game host will never open the door with the car.
-fn game_host_open<R: Rng>(car: u32, choice: u32, rng: &mut R) -> u32 {
- use rand::seq::SliceRandom;
- *free_doors(&[car, choice]).choose(rng).unwrap()
-}
-
-// Returns the door we switch to, given our current choice and
-// the open door. There will only be one valid door.
-fn switch_door(choice: u32, open: u32) -> u32 {
- free_doors(&[choice, open])[0]
-}
-
-fn free_doors(blocked: &[u32]) -> Vec<u32> {
- (0..3).filter(|x| !blocked.contains(x)).collect()
-}
-
-fn main() {
- // The estimation will be more accurate with more simulations
- let num_simulations = 10000;
-
- let mut rng = rand::thread_rng();
- let random_door = Uniform::new(0u32, 3);
-
- let (mut switch_wins, mut switch_losses) = (0, 0);
- let (mut keep_wins, mut keep_losses) = (0, 0);
-
- println!("Running {} simulations...", num_simulations);
- for _ in 0..num_simulations {
- let result = simulate(&random_door, &mut rng);
-
- match (result.win, result.switch) {
- (true, true) => switch_wins += 1,
- (true, false) => keep_wins += 1,
- (false, true) => switch_losses += 1,
- (false, false) => keep_losses += 1,
- }
- }
-
- let total_switches = switch_wins + switch_losses;
- let total_keeps = keep_wins + keep_losses;
-
- println!("Switched door {} times with {} wins and {} losses",
- total_switches, switch_wins, switch_losses);
-
- println!("Kept our choice {} times with {} wins and {} losses",
- total_keeps, keep_wins, keep_losses);
-
- // With a large number of simulations, the values should converge to
- // 0.667 and 0.333 respectively.
- println!("Estimated chance to win if we switch: {}",
- switch_wins as f32 / total_switches as f32);
- println!("Estimated chance to win if we don't: {}",
- keep_wins as f32 / total_keeps as f32);
-}