Mahjong Solitaire Strategy: 3 Rules We Tested on 3,000 Games

The Mahjong Solitaire strategy that works comes down to two rules and a tie-breaker. Never leave the last two tiles of a kind stacked on each other. Take the pair that frees the most new tiles. When two pairs are equally good, take the higher one. We had a computer play 3,000 deals with and without these rules, and together they lifted the share of games cleared from 38.9% to 61.2%, with no undo and no shuffles.

We also tested a tip you'll see often, "clear the tall stacks first", and it made things worse. Here are the results, the reasoning behind each rule, and how to use them in a real game. If you're new to the game, start with how to play Mahjong Solitaire.

How we tested

We dealt 3,000 games of the Turtle layout with Poozee's Mahjong Solitaire engine. Every one of those deals can be cleared. For each rule, a computer played all 3,000 deals, always choosing its pair by that rule and breaking ties at random. It never undid a move or shuffled. A game counted as cleared if all 144 tiles came off.

A computer following one rule strictly isn't a person. You'll look further ahead and use undo, so expect to do better than these numbers. What they show is which habits help and which hurt, measured on the same 3,000 deals.

Rule 1: never strand the last two of a kind

There are four tiles of each kind, so each kind comes off in two pairs. The danger is the second pair. If the last two tiles of a kind end up one on top of the other, the top one can never be matched: its only partner is underneath it. From that moment the game can't be won, even if it takes another twenty moves to find out.

So before you take a pair, find the other two tiles of that kind. If one lies on the other, don't take this pair. Match each free tile with one of the stacked ones instead, as they come free.

On its own, this rule lifted the share of games cleared from 38.9% to 46.5%. Our how to play guide walks through this exact situation, checked with the game's solver.

Pro tip: A stack can hide more than one tile of a kind. The check is the same: any time two tiles that must be matched together lie one on the other, that pairing is dead.

Rule 2: take the pair that frees the most tiles

Every pair you remove can free the tiles it was sitting on or beside. Some pairs free nothing new; others open up several tiles at once. On a full Turtle:

• The single top tile frees all four tiles under it.
• The lone tile at the far left end frees two, one in each of the two middle rows.
• The end tile of a long row frees one, its neighbor.

(We counted these with the game's code.)

More free tiles means more choices on your next turn, and more choices means fewer dead ends. Choosing the pair that frees the most tiles cleared 45.7% of games on its own. Combined with rule 1, it cleared 56.6%, more than either rule alone.

The tie-breaker: prefer higher tiles

Often two or three pairs free the same number of tiles. When that happened, taking the pair that sat higher in the stack raised the share of games cleared from 56.6% to 61.2%. Taking the lower pair instead dropped it to 47.6%.

A likely reason: the middle of the Turtle is five tiles deep, and tiles at the bottom of it can't come free until everything above them is gone. Working down from the top, when it costs you nothing, keeps those buried tiles from being left until last.

The tip that backfired: clear the tall stacks first

If height helps as a tie-breaker, you might expect "always take the highest pair" to be a great rule. It isn't. As the main rule it cleared only 29.3% of deals, worse than picking pairs at random. Always taking the lowest pair was worse still, at 19.5%.

Height on its own ignores what really matters: whether a pair opens anything up and whether it strands a kind. Treat "dig into the middle" as a tie-breaker, never as the plan.

What didn't matter: taking all four at once

When all four tiles of a kind are free at the same moment, you can take both pairs, and it can never hurt, because none of them depends on anything else. But as a strategy it made no difference in our test: 38.9%, the same as random play. It won 407 deals that random play lost, and lost 407 that random play won. It's a safe move, not a winning one. Do it when you see it, but don't go looking for it.

Putting it together in a real game

1. Scan the free tiles for pairs. Turn on Show free tiles in Poozee's game to dim everything you can't take yet.
2. Cross off any pair that strands its kind: the other two tiles of that kind lie one on the other.
3. Of the rest, pick the pair that frees the most tiles. Look at what each tile covers and what sits beside it.
4. If there's a tie, take the higher pair.
5. When you're unsure, try it and undo. A move that looked fine can show its problems a few turns later.

If you do get stuck, Poozee's Hint button searches for a way to clear the whole board and tells you when none is left, and Shuffle rearranges the remaining tiles into a position that can be cleared.

Keep playing

Put the rules to work in Mahjong Solitaire. If you like games where one careful choice decides everything, try FreeCell with our FreeCell strategy guide, or the empty-column tactics in our Spider Solitaire strategy guide.