The Concept of Probability Density

Level: Intermediate

Cells with more possible ship placements passing through them have a higher chance of being hit.

For each cell, count the number of ways a remaining ship could be placed to pass through it — the higher that count, the more likely a ship occupies that cell. This is the basic idea behind probability density.

The center of the grid has more room for ships to pass through both horizontally and vertically, so it has higher density, while the corners have lower density. That's why targeting high-density cells near the center favors the hunting phase.

As misses and sinkings rule out impossible placements, the density map keeps changing. Recalculating density after every shot always lets you pick the most promising cell.

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