Thankfully, the Monty Hall example here is explained well. Oftentimes it is explained in a way to make you think just the opposite. If you assume the House kn

Thankfully, the Monty Hall example here is explained well. Oftentimes it is explained in a way to make you think just the opposite. If you assume the House knows where the prize is, they'd have picked it (and won) when they reveal the door. So you'd be a sucker to switch. They went out of their way in this example to say that the host always opens a door without the prize rather than trying to win themselves, which gets you to the "surprising" answer that you should always switch. Maybe if you were familiar with the format of the show (I am not), you'd understand. But the question usually just states that the host knows where the prize is and you are expected to come to the unintuitive conclusion that they don't actually want to win. The gamblers fallacy is also amusing in that it is almost the exact opposite of what people often think it should be. If you have an extremely unlikely string of "red" on the roulette wheel, rather than think that "black" is due, you should start to consider that the wheel isn't fair. So a gambler who thinks he is due for a win is far more likely to be just getting scammed. Another way of looking at regression to the mean is basically the law of big numbers... infinity+1 is still infinity so no matter what the starting offset is (streak of improbable events), given enough rolls, it'll be irrelevant and you'll end up with the statistical probability.