Reversi Stable Discs — Permanent Territory You Can Never Lose

What Makes a Disc Stable?

A stable disc is one that can never be flipped for the remainder of the game — no sequence of legal moves by either player can reverse it. Once a disc becomes stable, it’s permanently locked to your color.

In a game where every disc on the board can potentially change sides multiple times, stability is the ultimate strategic prize. Stable discs are guaranteed points that cannot be taken away.

The Three Sources of Stability

A disc is stable if and only if it cannot be outflanked from any of the four line directions that pass through it (horizontal, vertical, and both diagonals). This happens when, for each direction, at least one of the following is true:

1. Edge protection: The disc sits on the edge of the board in that direction (no square exists beyond it on that line)
2. Filled line: Every square in that direction is occupied (no empty square exists to place a new disc)
3. Stable neighbor: The adjacent disc in that direction is itself stable and the same color

If all four directions are blocked by one of these conditions, the disc is stable.

Corner Stability: The Foundation

Corners are the simplest stable discs. A corner disc (a1, a8, h1, h8) satisfies the edge-protection condition in all four directions simultaneously — there are no squares beyond it in any direction.

This is why corners are so valuable: they’re automatically stable from the moment they’re placed. No calculation or surrounding support needed — the board geometry guarantees permanence.

Edge Stability: The First Cascade

The most important stability cascade runs along the edges from corners.

How It Works

Consider corner a1 owned by Black. Now Black plays b1. Is b1 stable?

Check the four directions from b1:

• Left (toward a1): a1 is Black and stable → stable in this direction
• Right (toward c1, d1, etc.): Unknown — depends on what’s there
• Up: b1 is on row 1, the top edge → edge-protected in this direction
• Diagonal to a2: a1 side is covered by stable corner; but this direction goes toward b2, c3, etc.

b1 is not yet stable just from having a1 — it needs protection in the rightward and diagonal directions too. But if the entire top row (a1 through h1) fills up with Black discs, each one anchored through the chain to a1, the entire row becomes stable.

The Full Edge Lock

When Black owns both corners on the same edge — say a1 and h1 — and fills the entire row 1, every single disc on that row is stable:

• a1: Corner (always stable)
• b1: Protected left by stable a1, right by stable c1 (which connects to h1), up by edge, diagonals eventually covered
• c1 through g1: Chain of stable neighbors connects to both corners
• h1: Corner (always stable)

Result: 8 permanently locked discs from two corner investments. This is one of the most powerful formations in competitive reversi.

Partial Edge Stability

You don’t need the full 8-square edge. If Black owns a1 and has discs on b1, c1, and d1 — all Black — those four discs are stable along the row direction (protected by a1 on the left and the board geometry). Whether they’re fully stable depends on the vertical and diagonal directions, which requires further analysis.

The key insight: stability grows outward from corners along edges. The more edge squares you own adjacent to your corners, the more stable territory you accumulate.

Deep Stability: Into the Interior

Stability doesn’t stop at the edges. It cascades inward from stable edge discs.

The Triangular Cascade

If Black owns the entire top row (a1 through h1, all stable), disc a2 can become stable if:

• Up (toward a1): a1 is stable and Black → covered
• Down (toward a3+): Depends on the column
• Left: a2 is on column a, the left edge → edge-protected
• Diagonals: The a1-side diagonal is covered by the stable corner

Similarly, b2 can become stable if a1, b1, a2, and the discs surrounding it are all stable. The stability frontier can creep inward from the edge, forming a triangular region of stable discs extending from the corner.

The Maximum Stability Region

In an extreme case, a player who owns all four corners and all four edges can have a massive block of stable discs covering most of the board. In practice, this level of dominance is rare — but even a triangular stable region of 10-15 discs anchored on one edge represents an enormous advantage.

Counting Stability: A Practical Approach

You don’t need to calculate exact stability during a game. Instead, use these quick assessment methods:

Corner Count

Each corner you own guarantees at least 1 stable disc. Two corners on the same edge can guarantee 8+ stable discs if the edge fills with your color. Corner count is the fastest stable disc proxy.

Edge Ownership Assessment

Look at each edge. If you own the corner and several adjacent edge squares, those are likely stable or becoming stable. Count visually: “I have 5 stable discs along the top edge, 3 along the left edge.”

The Stability Comparison

In the late midgame and endgame, compare your stable disc count to your opponent’s. A significant stability advantage (10+ more stable discs) is usually decisive — those discs cannot be reversed, and you only need 33 total to win.

Stability vs Disc Count

A fundamental reversi insight: stable disc count matters more than total disc count until the very end of the game.

Consider this scenario at move 50:

• Player A: 15 discs total, but 12 are stable (anchored to two corners)
• Player B: 35 discs total, but only 3 are stable

Player A is almost certainly winning despite having far fewer discs. Those 35 discs of Player B are mostly unstable — they can and will flip during the final 10 moves. Player A’s 12 stable discs are guaranteed, and the remaining moves will add more.

This is the endgame payoff for the mobility strategy: playing quietly and positionally in the midgame leads to corners, which lead to stable territory, which leads to an insurmountable endgame advantage.

Building Stable Territory: The Strategy

Step 1: Win Corners

Everything starts with corners. You cannot build significant stable territory without at least one corner (there are theoretical exceptions, but they’re negligible in practice).

Use mobility strategy to force your opponent onto X-squares, which gives you corner access.

Step 2: Extend Along the Edge

After securing a corner, prioritize placing discs along the connected edges. Each edge disc adjacent to your corner adds to your stable territory.

Don’t overextend — pushing too far along an edge without support can create unbalanced edge formations that your opponent can exploit with wedges.

Step 3: Protect the Expansion

As your stable territory grows, protect the frontier of the stable region. Opponent wedges and edge attacks target the boundary between your stable territory and the rest of the board.

Step 4: Lock Down in the Endgame

In the final 15 moves, your stable territory acts as a foundation. Play endgame strategy — use parity and disc maximization — to convert your stable base into a winning disc count.

Stability Traps and Pitfalls

False Stability

Beginners sometimes assume a disc is safe because it’s “surrounded.” But surrounded ≠ stable. A disc in the center with all 8 adjacent squares occupied can still be flipped if the surrounding discs themselves change color. True stability requires a chain back to the edge or a corner.

Over-Investing in One Edge

Putting all your effort into one edge while ignoring the rest of the board can backfire. If your opponent takes the other three corners, your one stable edge (even with 8 discs) won’t be enough.

Ignoring Wedge Vulnerability

A long line of your discs along an edge is only stable if connected to a corner. If an opponent places a wedge — a disc between two of your edge discs — it breaks the chain and can flip your supposedly “safe” edge discs. Always ensure corner protection before assuming edge stability.

Quick Reference

The path to winning reversi runs through stability: mobility → corners → stable edges → cascading interior stability → winning disc count.