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Strategy

Why Mahjong Boards Run Out of Moves

Why Mahjong Boards Run Out of Moves

A board with tiles left and no legal move is usually not bad luck. It is an accounting error made several minutes earlier. Every design in the set has four copies, every removal spends two of them, and the game is therefore a long sequence of decisions about which two. Get one of those decisions wrong and the board keeps letting you play for a while, then stops. Below are the shapes that failure takes, and the check that catches nearly all of them.

First, some boards were never solvable

Worth settling this before you blame yourself. A layout generator can work two ways: scatter tiles at random into the slots, or build the board backwards from a solution it already knows. The first method is cheaper and produces layouts that can be dead from the opening click. If a board stalls with more than half its tiles still standing and you made no obviously reckless match, that is the likely explanation. Stalls that arrive with ten or twelve tiles left are a different animal, and those are yours.

The wrong pair out of four

This is the commonest death in the game. Take a design with all four copies still on the table. Two of them are somewhere harmless, out in the open with free edges. The other two are in a mutual block: one lying on top of the other, or a pair of neighbours in a row whose only open sides face each other. Those two can never be matched together, because a match needs both tiles free on the same click and the lower or inner one never is. They are a locked unit, and the only keys are the two loose copies.

Pair the loose copies with each other and you have thrown both keys away. The locked unit stays on the table for the rest of the game, together with everything sitting beneath it. The correct pairing takes one loose copy with the top of the block, which frees the second, then the remaining loose copy with what was underneath.

The twin buried under its own copy

A special case that deserves its own name, because it is invisible from directly above. In a deep layout a tile can end up covered by an identical tile. On screen you see one three of bamboo where there are in fact two, and from then on your count of that design is wrong by one. Anyone tracking copies will pair the two visible ones somewhere else and never work out where the last pair went.

The tell is the tile count. When a design has four copies and only three can be found, the fourth is under something, and sometimes it is under one of the three. Look along the edge of the stack rather than straight down at it, since an identical tile underneath shows as a doubled outline at the corner.

Clearing one wing of a symmetrical layout

Most layouts are mirror-symmetric, and the deal usually scatters the four copies of a design across both halves. Clear one wing much faster than the other and you finish with a whole side of the board whose partners all left the table twenty moves ago. Nothing was buried, nothing was blocked, and the board is dead anyway, purely because both halves of every design went to the same side.

The fix costs nothing. Alternate sides: when two identical matches are on offer, take the one on the side you have been neglecting.

Spending the spare tiles

Free tiles that cover nothing are not clutter, they are the partners the buried tiles are going to need. A layout can deadlock while showing a dozen liftable tiles, none of which match each other, simply because everything they could have matched was cleared early for the sake of a tidy table. Deep tiles need partners from outside the stack, so leave some outside the stack. Mahjong Shanghai Dynasty is one of the layouts kept on this site.

Flowers and seasons are the safest tiles you own

Where a version matches flowers within their group and seasons within theirs, those eight tiles cannot suffer the wrong-pair failure at all: any of the four answers any other, so no choice among them is ever the wrong one. That makes them exactly the wrong tiles to spend first. They are the only pieces on the table that can be aimed at whichever awkward position turns up twenty moves later, and cashing a pair of them for a tidy early match converts a wildcard into an ordinary removal.

The exception is a flower buried under another flower. Group matching does not rescue a covered tile, and two of them stacked together are as locked as two identical dragons in the same position.

The three-question check

Before each match, run three questions. Where are the other two copies of this design. Can they still reach each other, or does one block the other. If they cannot, is the pair in front of you the key that would unlock them. The questions take about two seconds once the habit is in, and they prevent every failure above apart from the unsolvable deal. The removal order they belong to is set out in the solitaire order of play, and the wider case for it in the strategy pillar. The site’s own example of it is Mahjong China.

What a shuffle does and does not do

When a board really has stalled, a shuffle rearranges which face sits in which slot and leaves the geometry untouched. Positions that were mutually blocking are still mutually blocking, they merely hold different pictures now. That is why a shuffle sometimes buys two moves and then stalls again, and why it pays to read the board before spending one. Layouts differ in how well they recover: a wide flat solitaire layout usually does, while a tall stack often does not, and the tower boards are where that difference shows most clearly. Dense arrangements such as Mahjongg Alchemy pack tiles closely enough that mutual blocks appear early, which makes them good practice for spotting one. A layout of that kind in the catalogue here is Mah Jongg.