One Stone Changes Everything: 4×4 Go Solved

Read ~5 min · Updated July 2026 · Part of: Learn Go

Most Go advice is fuzzy: "play shape," "think about influence," "don't play on the edge." That vagueness comes from the 19×19 board — it is too large to ever fully solve. But on a 4×4 board, every possible position can be computed exactly. brainGO has done that computation. The result is a strange and beautiful fact: a single stone is often the difference between a forced win and a dead draw.

The board is small enough to be perfect

A 4×4 Go board has only 16 points, and each point is empty, Black, or White. After removing illegal positions, there are roughly 43 million reachable states. That is large for a human but trivial for a computer. Using retrograde analysis — working backward from every terminal position where a group is captured — brainGO has solved the game completely.

This means we do not guess whether a position is winning. We know. And once you know the exact answer for every position, you can ask a question that is impossible on 19×19: what changes if I add or remove just one stone?

One stone, opposite answer

Take this position (Black to move). The engine's exact verdict: Black wins in 1 move.

W W B .
. B . .
. . . .
. . . .

Now add a single White stone at (1,1). The verdict flips: draw — Black can no longer force a capture.

W W B .
. B W .
. . . .
. . . .

Same shape, one stone added, answer flipped from WIN to DRAW. This is not an opinion — it is the exact value computed from the full game tree.

You can explore the live version of this position on the one-stone variations page for cap-012.

Ko positions are even more fragile

When a position involves a ko (a capturing race where the answer depends on repetition), the one-stone sensitivity is extreme. Take the ko position cap-125: Black wins in 7 moves. But change any one of several stones — remove a Black stone, remove a White stone, or add a White stone in the center — and the position collapses into a draw.

This is why ko is hard for humans: the answer hides behind a single liberty, and the "correct" move depends on stone counts you cannot easily recount under time pressure. On 4×4, the computer has counted them all. See the cap-125 variation breakdown.

Why this matters for learning

If you are learning Go — especially as a child or a senior — the 4×4 board is the right place to build intuition, because the feedback is exact. When you play a move and the position flips from winning to drawing, you can see which stone caused it. That is a lesson about liberties, shape, and counting that scales directly to larger boards.

Browse the full variation set

brainGO has scanned all 205 base puzzles and generated every meaningful ±1-stone variation — over 1,300 positions where one stone flips the result, and over 1,200 where one stone shifts the difficulty.

Browse all one-stone variations

Each entry shows the base position and every one-stone change beside it, with the exact win/draw value and move count. It is, as far as we know, the first publicly browsable "one-stone sensitivity map" for any Go board size.

The takeaway

On a small, solved board, Go stops being mysterious and becomes measurable. One stone is not a footnote — it is often the whole answer. Play the capture puzzles to feel it, then study the variations to see it.