What simulated games show
We played 1,500 deals with each of these simple habits and no shuffling, to see how often each one cleared the whole board.
- Taking any open pair at random: 33%
- Always taking from the upper layers first: 26%
- Always taking from the longest rows first: 22%
- Always leaving the upper layers until last: 16%
- Taking the pair that leaves the most pairs open next: 42%
- The same, but taking a kind first when all four of its tiles are free: 52%
The surprise is that the familiar fixed rules did worse than picking at random. One rule applied blindly leaves other parts of the board locked. What worked best was looking at what each move opens up.
Count what a move opens
The line above the board shows how many pairs are open. A new deal starts with about 16, from about 32 free tiles. Before you take a pair, look at the tiles it will free. A pair that frees a match for something already free adds to your options. A pair that frees nothing just uses one up.
Three of a kind
This is the most common choice in the game. Say three Red Dragons are free and the fourth is buried. You can take only two now, and the third has to wait for the fourth. So choose the two that free the most, and leave the one that isn't holding anything back.
Watch where the fourth is, too. If it sits under the third one, or under tiles that can only come off after it, then taking the wrong pair can make the board impossible to clear.
All four of a kind
When all four tiles of a kind are free, you can clear them without any risk of stranding one. In the simulation, the habit worked well when combined with counting open pairs, but not by itself: taking these pairs first and picking at random otherwise won only 26%. So check whether another pair needs attention first.
Know what blocks what
- Rows open from the ends. A tile in the middle of a row can't move until one side is clear, so look for the end tile that holds a long row shut.
- Half-covered tiles still count as covered. On this board, the third layer sits between the rows below it, so each of its tiles blocks tiles in two rows.
- Watch stacked matches. Two matching tiles with one on top of the other can never be paired with each other. Each one needs another partner.
Using Hint, Undo and Shuffle
Hint uses the best habit from the list above, so it's a good guide, but it can't see all the way to the end. Undo has no limit, so you can back up a few moves from a dead end and try a different pair. Shuffle only appears when no pairs are left. It mixes the remaining tiles into an order that can be cleared, which rescues the game at the cost of the puzzle you were solving.