The guarantee is usually true. It is just not a promise about your game.
“Guaranteed solvable” is a claim about the deal. It means that when the tiles were laid out, at least one complete sequence of matches existed that would clear the board. Buried in that are two assumptions: that you can read every tile, and that you play a perfect line. Neither is usually true — so the guarantee can be entirely honest, and you can still be looking at a table you cannot finish.
Mahjong solitaire deals 144 tiles into a shape several layers deep. A tile can be taken only when nothing is resting on top of it and at least one of its long sides is clear. Match two free tiles that go together — identical for the suits, winds and dragons; any two of a family for the flowers and seasons — and both come off. Clear all 144 and you win.
To promise solvability, the deal is either built backwards — laying pairs down in an order that can be undone — or checked by a solver before you see it. Either way the promise is the same and it is narrow: a winning line exists. Not that you will find it, and not that it survives your next move.
This is the part that is rarely explained, and it is not bad luck. It is a specific, ordinary-looking mistake.
Almost every tile in the set has four identical copies — 136 of the 144. Over the game you will pair them up, and you decide which two go together. That choice is not free.
The exception is the eight flowers and seasons, which are four different faces that match anything in their own family. It makes no difference to what follows: four tiles, two pairs, and you still choose which goes with which.
Say the four Bamboo 3 tiles sit like this — two out in the open, two stacked one directly on top of the other:
A B [ C ]
[ D ]
Match A with B and you have just killed the board. C and D are all that remain of that tile, and C is sitting on D — they can never both be free at the same moment, so they can never be matched. That pair is dead.
Match A with C instead and everything is fine: D is uncovered and pairs with B later.
Nothing announces this. The board looks healthy, you keep playing, and twenty moves later you run out of legal matches for a reason you made long ago and had no way to see. The deal was solvable the entire time. It stopped being solvable when you touched it.
Now add the second problem: in a stack several layers deep, some of those tiles are underneath other tiles and you cannot read what they are. You are being asked to plan around information you have not been given.
It rearranges the tiles still on the table until matches exist again. Look at what that admits: the game can put you somewhere you cannot leave, and the fix is to rewrite the puzzle mid-solve.
It is also, very often, the moment the app asks for something — a countdown, an advert, a purchase. That is worth naming plainly: you are being sold the solution to a problem the design created. The dead end is not a difficulty setting. It is a consequence of hiding information and then not letting you take a move back.
Two things, and they only work together.
If you can see all four Bamboo 3 tiles and where they sit, the fatal pairing is visible before you make it rather than twenty moves after. The puzzle becomes one of planning instead of one of guessing, which is the game most people thought they were buying.
Perfect information does not stop you making the mistake. It makes the mistake yours, visible, and reversible — and reversible has to cost nothing, or it is just the shuffle button wearing a different hat.
There is a third thing worth having, which is honest difficulty. A board graded by how far ahead you must plan to avoid stranding a tile is telling you something real. A board graded by tile count or a countdown clock is telling you how long it takes, which is a different question.
Teahouse turns every tile face-up, certifies each board winnable before you see it, and has no shuffle button because it does not need one. Undo is unlimited and always free, and if you do strand the board it works back through your moves to find the one that did it and the pair you should have taken instead.
On a tangled position that search can run out of room before it is certain. When that happens the app says so rather than guessing: it reports the move as “at or before” rather than naming it exactly, and it may have no replacement pair to offer. That is the same principle as the rest of this page — an answer it cannot prove is reported as one it cannot prove.
It will still let you make the mistake above. That is the point — it is a logic puzzle, and a logic puzzle you cannot lose is not one. What it will not do is hide the information you needed, and then sell you the way out.
Written by the author of Teahouse, a mahjong solitaire app for iPhone and iPad. Free to play a fresh certified board every day; one optional unlock, paid once, opens unlimited boards. No ads in either version.