Strategy puzzle

Can you bankrupt the larger army?

You are green, with 10 gold: enough for one Villager. Red has a Knight and a Spearman, and nothing you can buy beats either of them. One of the three marked hexes wins anyway. Which one?

A small hex island. Green holds the middle of the lower two rows, with its capital at the bottom. Red holds both ends and a one-hex-wide strip along the top that joins them, with its capital in the middle of the strip. Red’s Knight stands at the bottom-left corner and its Spearman at the top-right. Hex A is on the strip near the left end, hex B on the strip near the right end, and hex C on the right end, beside green’s land. — Green to move. A new Villager can take A, B, or C.

Red’s kingdom: 17 hexes, with 10 gold in its capital.
Red’s upkeep: 24 gold a turn: 18 for the Knight and 6 for the Spearman.
Your move: One 10-gold Villager, bought straight onto A, B, or C.

Each hex earns 1 gold a turn. When a kingdom splits, the side with the old capital keeps the gold and any other side starts at 0. A kingdom that can’t pay its upkeep at the start of its turn loses every unit. Need a refresher?

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The answer

A starves the Knight

Taking A cuts the Knight’s end off from the capital. That end becomes a kingdom of 6 hexes with a new capital and 0 gold. It earns 6 a turn and owes the Knight’s 18. At the start of red’s next turn, before it can move, the Knight becomes a grave.

Green’s Villager stands on A. The Knight’s end of red’s land is walled off as its own kingdom, labeled Earns 6, owes 18. — After the cut: 6 hexes can’t pay 18.

The same board at the start of red’s next turn. A grave stands where the Knight was. — Red’s next turn: the Knight starves.

The tempting one

B is a cut, but the Spearman can pay

B also splits red’s kingdom and strands a unit. But the Spearman’s end has 6 hexes, and a Spearman costs 6. The new kingdom pays exactly, with nothing left over, and the Spearman lives. The Knight stays on the capital’s side, where 10 hexes and 10 gold cover its 18.

Green’s Villager stands on B. The Spearman’s end of red’s land is walled off as its own kingdom, labeled Earns 6, owes 6. — 6 hexes pay a Spearman’s 6 exactly.

The safe one

C splits nothing

C takes a hex without cutting anything off. Red earns 16 a turn instead of 17, and with 10 gold saved it still covers all 24 of its upkeep.

Green’s Villager stands on C. All of red’s land is still one kingdom, labeled Earns 16 plus 10 gold, owes 24. — One kingdom, still paying its way.

Count the hexes on the far side of a cut, and compare them with what the units there cost.

This position is staged on a small island in the shipped game, and every outcome is checked by its rules engine.

Find the cut in a real match

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Read the split-and-starve guide