I always find it fascinating how poorly the brain conceptualises various problem spaces, specifically in math related fields. The Monty Hall problem is an excellent illustration and just shows how irrationally our minds operate.
And the lottery. We misestimate probabilities, particularly when they are extreme (near-certainty and near-impossibility). That gap between how likely an event 'seems' and its real probability explains the lottery, not wearing seatbelts, smoking, witchcraft, the monty hall problem...
