KrapkyLarge captures and game depth
Building a large loop takes many moves, but it captures everything inside at once, even what your opponent has already captured. Games last longer, and every mistake is costly.
A large capture
A single loop can capture many dots at once. Until the final link is added, a gap remains, and your opponent can extend their group through it by placing new dots. When building a large loop, watch every gap.
Twelve blue dots around five red ones. The last dot, at 5-6, closes the loop and captures all five red dots.
A capture within a capture
A larger loop captures everything inside it, including the opponent’s territory. The opponent then loses the points they previously scored there.
Red previously captured the blue dot at 7-7, making the score 0 : 1. Blue closes a larger loop around it, capturing four red dots. Red loses its point, and the score becomes 4 : 0.
A net of widely spaced dots
Strong players place dots not only side by side but also a few grid points apart, forming a net that marks out a large area in advance. The net is not yet a closed loop: its gaps let the opponent in, and the fight is for control of those gaps.
How deep the game is
We measured this using the game’s own neural network. Opponents included the engine at a low difficulty setting and generations of the network, from early versions to the strongest. They played one another in pairs, and each successive opponent on the ladder won at least 60% of its games against the previous one. We found over 30 such rungs (the estimated range is 24 to 40).
This is a lower bound: a complete beginner is below the first rung, and the network plays even better when it searches ahead. That is why you can spend years learning the dots game and still have room to improve.