Puzzle: a gap in White's edge, ten squares from the end
Published · By TG, the site operator
Ten squares left, Black to move, under this site's rules (see the guide). The idea behind the answer has a name, given after the solution.
The position
In the diagram, columns run a to h from the left and rows 1 to 8 from the bottom, the names the site's move list prints in capitals. The board can be turned, so go by the names.
8 ○ ○ ○ ○ ● ○ · ·
7 ○ ○ ○ ○ ○ ○ · ●
6 · ○ ● ● ○ ○ ○ ·
5 ○ ● ○ ○ ● ○ ○ ○
4 ○ ● ○ ● ○ ● ○ ·
3 ○ ○ ● ○ ● ● ● ·
2 ○ · ● ● ○ ● ● ●
1 · · ● ○ ● ● ● ●
a b c d e f g h
● Black, ○ White, · empty. Black (23): e8, h7, c6, d6, b5, e5, b4, d4, f4, c3, e3–g3, c2, d2, f2–h2, c1, e1–h1. White (31): a8–d8, f8, a7–f7, b6, e6–g6, a5, c5, d5, f5–h5, a4, c4, e4, g4, a3, b3, d3, a2, e2, d1. Empty: g8, h8, g7, a6, h6, h4, h3, b2, a1, b1.
Black to move. The legal moves are g8, g7, a6, h6, h4 and b2. Only one wins whatever White does. Which?
Show the solution
a6. It turns one disc, b6, but look at the a-file. White holds a8 to a2 except a6, and a1 is empty, so Black cannot play a1 in the diagram. With a Black disc on a6, a1 becomes a Black move that turns a2 to a5.
White wants the same square. After each of Black's other moves, White's strongest answer is a6, closing the file from a8 to a2, and with best play Black loses by 8 (h4, b2), 14 (h6), 16 (g8) or 18 (g7). The biggest flips, g7 and h6 (four discs each), are among the worst.
After a6 every White reply loses: by 18 after h3, 10 after b1 and 2 after b2, the toughest, which flips five. Against b2 only a1 wins. One best line: a6, b2, a1, b1, g7, h6, g8, h8; Black has no move and the site passes the turn; h4, h3. Black wins 33 to 31, owning a6 to a1.
An edge disc can only be trapped along its edge, and with White on a7 and a5 there is no square from which to trap a6. The search found it still Black in all 10,410 positions that can follow.
The idea: a gap is a target
The British Othello Federation's edge-play chapter, adapted from Brian Rose's book, has a word for a move like a6: a wedge, glossed as “play between two discs of the opposite color”. In the chapter's example, too, the wedge leads to a corner. It also prefers a two-square gap, or none, to a one-square gap in your own edge, noting many cases where an opponent exploits one by playing into it.
To be legal, a wedge must still trap a line in another direction, as a6 does through b6; the site highlights a gap square only when that is so.
How the answer was checked
A script loaded the site's own rules file and played every continuation to the end, without pruning: 81,563 move sequences through 42,665 distinct positions, each scored by final disc count. An independent move generator agreed with the engine at every position, and the diagram was reached by legal moves from the site's start. In our test the site's computer also chose a6, on Normal and on Hard.
Try it on the site
The site has no position editor, but in your own games, check the computer's edges near the end. If one has a single empty square between two of its discs and that square is highlighted for you, try it, watch the corner beyond, then press Undo and compare the biggest flip. Start a game.
Sources
- Chapter 5: Basic edge play — British Othello Federation (adapted from Brian Rose's book)
Written by the operator of this site from the sources listed above. Spotted a mistake? Email warmeve.label@gmail.com and it will be corrected.