Spargo Puzzle #1

White to play. What is their best move and who will win?

Solution:  White should play a to win. This result is quite counterintuitive as Black has a strong group with two eyes, dominates most of the board, and outnumbers White's forces by more than 2:1.

Proof:  White has three legal moves: a, b and c (the top two empty holes would be illegal suicide moves). We consider each of these three options in turn.

Move a:  Move 1 (a) establishes two eyes for White. Black 2 threatens a connection to Black's main group but White 3 blocks it.

Black is now in serious trouble. They are forced to play an eye-filling move 4 which allows White to make a major capture with 5.
The remaining two Black pieces may survive for several further capture cycles, but White can eventually surround them to win.

Move b:  Move 1 (b) would provide a platform for Black to connect their isolated piece with their main group with move 2.
White would then be helpless to stop Black encroaching into their territory for an easy win.

Move c:  Move 1 (c) might look promising as it more or less forces Black into sacrificing a group at the bottom, but Black's move 4 stops White from forming two eyes.

The most likely continuation of play is shown below, with Black eventually winning the pile-up to connect across to their main group and win the game. Note that Black could have captured two White pieces by moving in the lower left hole with move 6, but White could then have immediately recaptured to set up a win. Capture is not always the best policy!

Move c (alternative):  The following figures show an alternative line of play for move 1 (c), with White move 3 pinning the vulnerable Black group rather than capturing it. This may seem like an odd choice but allows White to win the pile-up with move 5 and introduces a twist; Black cannot immediately recapture the White group! A move in the lower right corner looks promising for Black, but this would be an illegal suicide move as it would have no freedoms after its execution, due to the pinned White pieces.

Instead, Black is again forced to fill an eye with move 6 allowing White to capture the main Black group with move 7. However, this time Black has more surviving (pinned) pieces than White due to the recent pile-up, which tips the balance of the game. Black will win by a piece or two from this position, regardless of which player runs out of moves.

Move a is White's only winning move.

This puzzle demonstrates the cycles of capture and recapture that give Spargo its unique character, and shows that seemingly obvious positions can yield surprising outcomes that are non-trivial to analyse. This example also demonstrates the power of zombies.


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