Countcircle

Countcircle takes the old Josephus problem — a ring of people, a count that skips around it, one person removed each time it stops — and drops you into one of the seats. The first circle has eight places, yours among them. Every beat the count jumps a random number of seats ahead, and the seat it is about to hit is marked the instant the window opens, so nothing is hidden: if the ring is pulsing on you, you have a fraction of a second to swap with the neighbour on your left or right. Get out and somebody else goes instead. Outlast everyone and the round is won, and a new circle three seats bigger forms at once, with no pause in between. The swap is the whole game, and it cuts both ways — sidestepping the count by one seat can just as easily walk you straight into it, so you have to read where the target sits before you move rather than flinching on reflex. The window starts at roughly a second and a half and shrinks by a tick every four eliminations, so a run that begins calm turns frantic. Dodging when you really were the target earns a clutch bonus, and clearing a whole circle is worth a hundred points.