Ree & Plus_minus
Ree Ree
Plus_minus Plus_minus
Plus_minus Plus_minus
Hey, I’ve been pondering the minimum move count for a two‑rook versus king mate—there seems to be a neat pattern if you treat it like a simple equation. Curious to see if you’d find that interesting too?
Ree Ree
Indeed, there’s a neat formula once you strip it down. Let d be the king’s distance from the nearest edge. The minimal forced mate with two rooks is 2 + d moves, so a king in the corner is mated in two, one step away in three, and the worst case from the centre is sixteen. It’s a tidy linear pattern that pops up if you look closely.
Plus_minus Plus_minus
That’s a clean linear insight; it reminds me how a simple variable can capture a complex game. If we treat each extra square as a “unit of pressure,” the two rooks act like a balanced force field tightening the king’s options step by step. I wonder what the exact constant would be if we added a third rook—would it stay linear or bend into a curve?
Ree Ree
A third rook just shortens the corridor, so the slope drops but the relationship stays linear – each extra step still costs a move, only that the constant term shrinks. The king can be trapped in about 2 + d moves with two rooks, but with a third you shave off roughly a move per rank or file, giving something like 3 + ⌊d/2⌋ in the worst case. Still a tidy line, just with a smaller slope.
Plus_minus Plus_minus
Interesting, so adding that extra rook essentially halves the cost per step once you’re past the center. It’s like having a more efficient system where the redundancy shifts the balance. Makes me think about how in real life, more resources can compress the distance to a goal, but you still pay a linear price in the remaining variable. Nice observation.
Ree Ree
Exactly, more pieces give you tighter control, but the king still has to move out one square at a time. It’s the same principle in life—extra tools shrink the distance, yet you still pay a linear cost for each remaining step.
Plus_minus Plus_minus
That’s the elegance of it—more tools, but the underlying rhythm stays the same. Keeps the math tidy and the life analogy alive.
Ree Ree
It’s a satisfying symmetry, isn’t it? The extra rook just tightens the rhythm without breaking the pattern.