Butterfly Mahjong

Butterfly is our own layout for Mahjong solitaire: two wide wings that meet at a narrow body, a smaller pair of wings on top, and the body raised along the middle. You clear it by taking the 144 tiles off two at a time, each pair the same tile, and only tiles that are free. A tile is free when nothing lies on it and its left or right side is open. Flowers pair with any flower and seasons with any season.

The tiles, the controls and Shuffle work as on the turtle; the Mahjong Solitaire page explains each tile.

The lower wings lie on the ground, 84 tiles spread wide on both sides of a narrow waist. A smaller pair of wings, 48 tiles, rests on top of them, and the body, 12 tiles, runs along the middle on the top layer.

The two halves mirror each other, so most rows are short and many tiles sit at a row end. That is why 52 tiles are free at the start, more than on any of our other layouts.

• With so many free tiles, the risk is pairing too fast. Before you take a pair, look for a third tile of the same kind that is buried, and keep the free one that covers nothing.
• The body on top covers the middle of both wings. Clear its ends first to open the long middle rows of the lower wings.
• The same kind of tile often sits in the same place on both wings. Plan pairs across the wings, so one side does not run out of moves.
• The wing tips are free from the start. Save a few of them: they are the easiest way to match a tile that opens late.

We built 1,009 Butterfly deals, each from a way to clear it. Our solver had to find its own way through each one; it cleared 1,000 within its search limit, and those are the deals you play here.

Across 300 of these deals, the first position offers on average 16.8 kinds of tile with a free pair (12 at the fewest, 21 at the most), against 10.8 on the turtle. It is the most open start we have.