> The race car gets to move any number of spaces vertically, horizontally, or in a circle
> It starts replacing the pawn front of the king
I genuinely wonder what the optimal strategy becomes – because I'm sure this invites a single dominant strategy.
You can't immediately checkmate, so I think the optimal strategy if you go first is to take the pawn in front of the queen, then take the car using your car.
Driving in circles is a weird one, because it seems like you don't have to be able to complete the circle (otherwise what would be the point, and can it be an ellipse?), so I wouldn't immediately know if it could be optimal to take out the queen if car got only one move. However, you definitely take the opposing car with its two moves.
Edit: Wait, okay, this is fucked. That checkmates you. If you take the queen, car checkmates; if you take the car, queen checkmates. This is very fucked.
Edit 2: WAIT. Car up one, right one, because that's part of a circle. Then up to take car. So you lose out on the pawn, but you take the opposing car. I don't know because this seemingly screws you over positionally a bit, but the car just seems too dangerous to be left alive (it controls the Senate and the courts).