Stuck in Mahjong Solitaire? Which Tiles to Remove First

By Nesim Razon, independent Android developer

Almost every Mahjong Solitaire player has stared at a board with no matching free tiles left. Most of the time the mistake was made many moves earlier. This guide shows how to choose between several possible pairs, how to handle four identical tiles, and what to do when you really are stuck.

Why do boards get stuck?

A tile can only be removed when it is free: nothing lies on top of it and its left side or right side is open. Two matching tiles must both be free at the same moment. A board gets stuck when the tiles that are still free have no twin among them, and the twins are buried under tiles that cannot go anywhere.

There is a common belief that a stuck board means the deal was impossible. In Tilelings that is not the case. Every Solitaire deal is built backward from an empty board, one pair at a time, so at least one complete solution always exists. But a solution existing does not mean every sequence of moves leads to it. Several choices are fine, and some quietly close the door. Your job is to avoid those.

Free tiles: a quick reminder

Check two things on every tile. Is anything stacked on it? Are both its left and right sides touching other tiles? If the answer to the first is no and the answer to the second is not yes, the tile is free. Blocked tiles look a little darker in the game. Before you tap anything, take a moment to find every free tile on the board, not just the first pair you see.

Which pair first? Use depth

When you have several pairs to choose from, rank them by how much they open up. The pairs worth taking first are the ones that:

• sit on top of tall stacks, because every layer you lift frees the tiles underneath
• sit at the end of a long row, because taking an end tile opens the next tile in the row
• hide the most tiles underneath or beside them, which means they are blocking the most future choices

The pairs worth leaving for later are the ones that open nothing: tiles on the outer edge, or on the bottom layer with no neighbors. They will stay available, and they make good spare moves when you need to wait.

Four copies of a tile: which pair?

Most tile pictures appear four times. Flowers also come as four tiles, and seasons as four, and any flower matches any other flower, any season any other season. When all four are available you must choose which two to remove, and that choice matters more than it seems.

The classic deadlock is a pair of twins where one lies directly on top of the other. The upper tile is free, the lower one can only become free after the upper one has gone, and the upper one has no partner left to leave with. Neither can be removed, and the board is stuck for good. Always check where the other two copies are before you take a pair. Prefer to remove the two copies that are in the deepest or most buried places, and keep the copies that are easy to reach. Never leave the last two copies in a stack.

Plan ahead with a three-move check

• Before tapping a pair, ask what it frees. Is a new free tile created? Is it one that matches something?
• Look at the twins of the tiles you are about to uncover. If the uncovered tile has a free twin, you have just made a new pair for later.
• Look at the twins of the tiles you are about to leave covered. If both copies are in the same column and one is on top of the other, rescue them now.
• Do not remove a pair only because it is easy. An easy pair can wait. A pair that opens a deep stack cannot always wait.

Common mistakes

• Taking the first pair you see. The first pair is often a shallow one that opens nothing.
• Digging only one stack. Opening several stacks a little gives you more free tiles than emptying one stack completely.
• Burying a rare picture. If only two copies of a picture are left and one lies under a tall stack, clear that stack soon.
• Removing the top tile of a pair of twins that sit in the same stack without checking what lies below.
• Using Shuffle too early. Shuffle is best kept for a board where no moves are left, not for a board where you simply cannot see a move. Take ten seconds to scan first.

Use the tools wisely

Undo takes back the last pair you removed, so you can recover from a mistake as soon as you notice it. Hint points to a pair that is part of a real solution. You have a few free hints per day, and you can earn more by watching a short video. Shuffle redeals the remaining tiles in a way that is still solvable. It clears your undo history, because the faces change. In a rare case, tiles can be stacked so that no shuffle can fix them. The game then tells you, and the answer is to undo or restart.

If you want three stars in relaxed mode, avoid hints and shuffles. Use Undo freely while learning, then try to rely on planning.

Difficulty changes the plan

The game has Easy, Normal and Hard deals. On Easy, more matching pairs are available at each step, so mistakes are cheaper. On Hard, the deal is chosen so that fewer pairs are available during the solution, and the two pairs of the same kind tend to be spread between the early and late part of the solution. That means identical tiles are far apart in time, and careless removals hurt more. If Hard feels unfair, play Normal for a while and practice the habits above.

A quick routine

Scan for all free tiles. List the pairs. Pick the pair that frees the most or sits highest. Check that you are not stranding the last two copies of any picture. Tap. Repeat. With this routine most boards become a calm series of small decisions, instead of a panic when the last moves run out. Tilelings lets you practice it with many layouts, from small to tall ones.