Here's how I finally understood the problem intuitively: If your initial pick is correct, then switching loses 100% of the time. If your initial pick is incor

Here's how I finally understood the problem intuitively: If your initial pick is correct, then switching loses 100% of the time. If your initial pick is incorrect, then switching wins 100% of the time (because you picked wrong, and host will reveal the other incorrect door, leaving only the correct door to switch to). So switching always inverts your initial guess. Well what are the odds of picking incorrectly on your initial guess? 2/3. Switching wins 2/3 times.