Spargo Puzzle #2 Question: Who will win from this position, regardless of who plays next? Solution:  Whoever's turn it is not to play will win. This is unexpected as Black only has a single-eyed group, which appears totally dominated by White's strong two-eyed group. But the zombies make the difference. Proof:  Every legal move by Black leads to a loss, and every legal move by White leads to a loss. This is an example of a very cold board position. We consider each player's possible moves in turn.

Black to Move: Black has two legal moves, a and b, as shown below. Note that the board position is symmetrical about the diagonal, so these two moves are equivalent.

If Black plays at a then White can play at b to win (below). Black now has no legal moves, which ends the game, which White wins by 9 balls to 8.

If Black plays at b then White can play the reverse move a to win. Black therefore loses if they move first.

White to Move: White has five legal moves labelled a, b, c, d and e (again, a and b are equivalent).

White move c: White's obvious move is c, which threatens to capture Black's single-eye group. But observe what happens if White makes this move; only two (unpinned) black pieces are actually captured, while the others are zombies that survive capture and remain on the board.

The white ball would have no freedom after the move, hence c is not a legal move. This is a case of zombies protecting a single eye.

White moves d and e: Either White move d or e would reduce White's group to a single eye, allowing Black to capture every white ball next turn for an easy win.

White must therefore play either a or its equivalent b.

White move a: If White plays at a, then Black must play at b as that would be their only legal move (and vice versa).

White must now follow up with d or e (move c would still be illegal due to the zombies).

If White follows up with d then Black can play at e to capture all but the two pinned (zombie) white pieces. Black can then easily absorb any remaining white moves to win, despite the two white zombies.

Similarly, if White plays at e then Black can play at d to create an unbeatable position.

Hence White also loses if they move first. Every possible line of play leads to defeat for the player to move, therefore the winner must be the player whose turn it is not to move.

This example demonstrates how zombies can have a surprising and devastating impact on a game. They are in fact the single most important factor in deciding most games.