A mahjong board can look perfect and still have no solution. Here's how we stopped leaving that to chance — in three short clips.
+ +
+ loops
+ A tile is free when nothing covers it and a side is open. Match two free tiles of the same symbol and they leave the table.
+The crucial part: freeness depends only on where tiles sit — never on their symbols. And taking tiles away only ever frees more. Hold onto those two facts.
+The obvious method: scatter the symbols onto the layout at random and hope. Played as well as possible, a random board still strands tiles that can never be matched.
+
+ loops
+ Every move shown is forced and optimal, yet the last tiles have their partners buried or hemmed in on opposite ends. An exhaustive search confirms no sequence wins it.
++ Computed live, on the same 16-tile board as the clips (small enough to follow every move). On the full 144-tile table the odds of a dead deal are far worse. The verdict holds: with random fill, winning is partly luck of the draw — which quietly erases the player's skill. +
+Flip the problem around. Instead of dealing tiles and searching for a solution, build the solution first and lay the tiles onto it.
+
+ loops
+ + The symbols are still shuffled, so boards stay varied — only the possibility of an impossible deal is gone. +
+Some boards can't be won no matter how you play. A loss might be the deal's fault, not yours — and nothing can tell the difference.
+Every board has a winning line by construction. If you lose, it's a move you made. Now the timer and the leaderboard measure skill — the whole point.
+The whole guarantee rests on facts about freeness — the same rule the live game uses to decide what you can click.
+What can be taken depends only on layer / row / column and which tiles remain — never on the symbol. So any symbol assignment over a valid removal order is winnable.
+Taking a tile away can only free more tiles, never cover one back up. So peeling the layout pair-by-pair always reaches the empty table — the recorded order can't get stuck.
+The generator, in essence:
+// 1. Peel the fixed layout into a valid removal order (geometry only). +const pairs = peelLayout(random); // 72 pairs, each free when removed + +// 2. Lay matched token pairs onto that order. +const pairTokens = shuffle([...tokens, ...tokens]); // each symbol ×2 pairs +pairs.forEach(([a, b], i) => { + board[a] = board[b] = { token: pairTokens[i] }; // the pair matches +}); + +// Replaying `pairs` wins ⇒ solvable by construction, for every shuffle. +// Verified by re-solving 360 random deals in tests.+
Every board is now guaranteed solvable. This brief asks the next question: how hard should it be, and which lever do we pull to set that.
+ +Keep scatter as the default, and add a difficulty dial via the symbol-labeling knob we haven't touched yet.
We shipped scatter because it removed a visible artifact (matching pairs pre-stacked at the top of the pyramid — 100% of old-default boards). The trade-off, now measured: scatter is ~28% more forgiving than the previous default (9.6 vs 7.5 legal moves per step). That matches playtest feedback ("plays well, but a bit easier").
Crucially, difficulty today is an accidental side-effect of board shape. The deliberate lever — how a symbol's copies are spread out — is still random and identical across every strategy. That's the dial to add.
+Boards are built by recording a solution: peel the layout into a removal order, then lay matched symbol-pairs onto it. The peel policy used to cluster the top of the pyramid into ready-made matching pairs — "two matching pairs sitting right below the top tile," every game.
+| strategy | top-4 tiles self-paired | same-layer pairs |
|---|---|---|
| topDownRandom old default | 100% | 96% |
| bottomUpRandom | 100% | 46% |
| original | 0% | 47% |
| scatter default | 0% | 21% |
scatter pairs the highest free tile with the lowest, spreading matches across layers — so no layer becomes a self-contained giveaway. All strategies remain 100% solvable; scatter never falls back.
Geometry is fixed and symbol frequencies are fixed, so a board is fully determined by two choices — and they do different jobs.
+Which positions get paired. Controls the board's look and, as a side-effect, how many moves are open at once (branching). This is the knob we've been turning (topDown / bottomUp / scatter / original).
+ tuned +Which pairs get the same symbol. Controls how far apart a symbol's copies are in the solve — the deliberate difficulty lever. Currently pure-random and identical across all four strategies.
+ untouched ← the opportunity +We walked each board's guaranteed solution and, at every step, counted the legal moves available (free tiles that share a symbol). More moves per step = more forgiving. We also tracked how often a step is forced (exactly one move).
+ + + + + +| strategy | branching | forced % | opening moves | copy-spread |
|---|---|---|---|---|
| bottomUpRandom | 4.5 | 30.0% | 11.9 | 0.34 |
| topDownRandom old | 7.5 | 3.8% | 16.6 | 0.35 |
| scatter default | 9.6 | 3.4% | 15.1 | 0.33 |
| original | 9.7 | 3.8% | 18.4 | 0.34 |
bottomUp, is hard because it forces single moves 30% of the time — but it carries the 100% top-cluster artifact. We have no "hard and good-looking" strategy yet.Keep scatter's look; turn the labeling knob. A 0→1 dial spreads a symbol's copies from clustered (easy) to far-apart in the solve (hard). Can scale with level to offset grace tiles, which currently make late levels easier.
Generate ~20 candidate boards per deal (≈ms each), keep the one closest to a target difficulty score. Removes board-to-board variance — the cleanest way to stabilize highscores.
+balanced / ring / outward, for board character. Lower difficulty impact than labeling — mostly aesthetic variety.
+More approachable for new players, or do we want to restore the old default's challenge — or sit somewhere between?
Pick a branching range to aim for (e.g. hold ~6–8 moves/step), so the dial has a destination.
Today grace tiles make higher levels easier. A level-scaled dial would reverse that curve. Do we want a rising challenge?
Metric-driven deals make every board feel comparable; some randomness in difficulty can also feel more organic. Which do we want?
Figures are computed, not playtested — relative indicators of difficulty, not absolute. For each strategy we deal boards on the real 144-tile layout, then walk each board's guaranteed solution under the live selection rule (isSelectable), measuring at every step:
Artifact figures over 300 deals; difficulty figures over 20 deals each. Caveats: this walks one valid solution rather than modelling real player choices or running a full search, so treat the numbers as a consistent yardstick for comparing strategies, not as a calibrated difficulty score.
+