The reason it's counterintuitive is because, in the game, you don't know that the two numbers are random. In fact, they are chosen by an adversary. You flip a

The reason it's counterintuitive is because, in the game, you don't know that the two numbers are random. In fact, they are chosen by an adversary. You flip a 2: do you think this is most likely the lower number, or do you think the other player picked 1 and 2 just to mess with you? That's the point of picking a random pivot: it reduces your opponent's ability to influence the situation to only placing their numbers as close to each other as possible.