Reversi — also sold as Othello — is a board game with rules you can learn in a minute and strategy that takes far longer. Place a disc so that it flanks a line of your opponent's discs between it and another of yours, and every disc in that line flips to your colour.
The counterintuitive part is that having more discs mid-game is usually bad. A large group is a large target, and the player with fewer pieces often has more options — which is why 'take the most discs' loses to 'take the corners'.
A disc in a corner can never be flanked, so it can never be flipped. It also anchors the edges leading away from it, which is why corner control usually decides the game.
No — that's the classic beginner mistake. A large group mid-game restricts your own options and hands your opponent flipping opportunities.
Effectively yes — Othello is the standardised commercial version of Reversi, with a fixed starting position.