How Hard Is Mahjong Solitaire? Data From 80,000 Games
We had a bot play 80,000 games, 2,000 on every layout at every difficulty. The difference between levels is much larger than we expected, and how you pair tiles matters far more than the shape of the board.
Play Mahjong SolitaireWhat We Found
- The deal matters more than the board. On Pyramid, the same stack goes from 94.8% random-play wins on Easy to 1.3% on Expert, using exactly the same tiles. The only difference is where the tiles are placed.
- Every deal we measured can be won, yet random play usually loses. At Medium, the random bot wins between 26.5% and 64.5% of games, depending on the board. Those losses all come from choosing badly, since a winning order exists for each one.
- Among full 144-tile boards, shape shifts Medium win rates from 26.5% to 39.9%. Stairs is the hardest and Butterfly the easiest. That's a real gap, but it's far smaller than the gap between difficulty levels.
- Fewer starting moves goes along with lower win rates, but not perfectly. Stairs starts with only 9.8 free matches on average at Medium. Fortress starts with 26.9 and is still among the hardest, because it buries so many tiles.
Random-Play Win Rate by Layout and Difficulty
The share of games a random-playing bot won. Sorted from easiest to hardest at Medium.
| Layout | Tiles | Easy | Medium | Hard | Expert |
|---|---|---|---|---|---|
| Little Temple | 72 | 94% | 64.5% | 31.5% | 19.2% |
| Diamond | 136 | 91% | 49.7% | 9.3% | 2.4% |
| Butterfly | 144 | 91.1% | 39.9% | 4.8% | 1.8% |
| Pyramid | 144 | 94.8% | 39.8% | 4.3% | 1.3% |
| Turtle | 144 | 90.5% | 37.9% | 5.2% | 1.3% |
| Garden | 96 | 82.2% | 35.9% | 9.8% | 4.2% |
| Cross | 144 | 90.5% | 34.7% | 3.4% | 0.9% |
| Fortress | 136 | 57.1% | 27.8% | 2.1% | 0.2% |
| Bridge | 144 | 58.2% | 27.3% | 2.6% | 0.3% |
| Stairs | 144 | 91.9% | 26.5% | 2.9% | 0.8% |
Free Matches at the Start, and Tiles Left When Stuck
At Medium difficulty, averaged across all games.
| Layout | Layers | Free tiles at start | Free matches at start | Tiles left when stuck |
|---|---|---|---|---|
| Little Temple | 3 | 20 | 10.5 | 12 |
| Diamond | 4 | 44 | 26.7 | 24 |
| Butterfly | 3 | 40 | 22.5 | 33 |
| Pyramid | 4 | 38 | 20.5 | 35 |
| Turtle | 5 | 35 | 18 | 37 |
| Garden | 3 | 28 | 16.1 | 32 |
| Cross | 3 | 36 | 18.3 | 35 |
| Fortress | 4 | 44 | 26.9 | 31 |
| Bridge | 4 | 36 | 18.6 | 43 |
| Stairs | 3 | 24 | 9.8 | 49 |
How the Levels Are Built
Every deal starts the same way. We take the full board and repeatedly remove two tiles that are free at that moment, which gives a winning order. Then we decide which faces go on which tiles:
- Easy gives a face's two pairs to tiles that are all free at the same moment, so it rarely matters which two you pair.
- Medium assigns faces at random along the winning order.
- Hard sets up a trap for about 60% of faces when the board allows one: a pair whose tiles hold down a copy of the same face, while another copy lies free. See the strategy guide for how that plays out.
- Expert does the same wherever it can.
How We Measured This
For each layout and level, the bot played deal numbers 1 to 2,000. On each turn it found every legal pair, picked one at random, and continued until it won or had no pairs left. It didn't use undo, shuffles or hints.
What This Doesn't Tell You
- This isn't how often people win. A person looks ahead, and a random bot doesn't, so you'll do far better. Treat these as a measure of how forgiving a board is, not as a prediction of your score.
- These are Winnable Mode deals, on our boards. Turning that setting off gives fully random deals, which aren't measured here.
- These are our boards and our deal generator. Other sites build deals differently, so their numbers wouldn't match. Every deal here is winnable by construction, so these figures say nothing about fully random deals.
- Shuffles and highlights aren't counted. Hard and Expert also take away shuffles, and Expert takes away highlighting, so they're harder for people than these numbers alone suggest.
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