The Monty Hall problem is a popular thought experiment that exemplifies (in my view) the "strangeness" of statistics and conditional probability.
After reading
Steven Pinker's recent book, Rationality,
I finally understand why the probability of winning if you swap is 2/3, not 1/2.
The code itself demonstrates how it became clear to me.
If you run the code, you will see a result like this:
// Swapping will win ~66% of the time.
{
numWinsByStrategyConcise: { stay: 332538, swap: 667462 },
numWinsByStrategyVerbose: { stay: 334535, swap: 665465 }
}