Shut the Box Strategy: Which Tiles to Shut
The best Shut the Box strategy is simple: shut the single highest tile you can (roll 9, shut the 9, not 5 + 4), and switch to one die once the open tiles add up to 6 or less. Big tiles are the hardest to shut later, and keeping many small tiles open gives you more ways to use every roll. With perfect play you shut the box in about 9.8% of games.
Shut the big tiles first
Only a few rolls can ever shut a 9 (a 9 itself, or a sum that includes it), and once the 7, 8 and 9 are gone everything gets easier. So when your roll matches an open tile, take that one tile rather than splitting it into small ones.
| You roll | Best move | Chance to shut the box after | Next best |
|---|---|---|---|
| 9 | shut 9 | 14.5% | 1 + 8: 6.5% |
| 8 | shut 8 | 11.9% | 3 + 5: 5.8% |
| 7 | shut 7 | 9.8% | 2 + 5: 4.8% |
| 6 | shut 6 | 9.0% | 1 + 5: 4.3% |
| 10 | 1 + 9 | 8.7% | 2 + 8: 7.4% |
| 12 | 3 + 9 | 10.7% | 4 + 8: 9.7% |
Splitting a 6 into 1 + 2 + 3 throws away your best small tiles: your chance drops from 9.0% to 1.5%.
When the roll is 10 or more
No single tile matches, so use the 9 (or the highest tile you have) plus the small tile that makes up the rest: 10 = 9 + 1, 11 = 9 + 2, 12 = 9 + 3. Clearing a big tile is still worth more than keeping a 1 or a 2.
One die or two?
Once 7, 8 and 9 are shut you may roll one die. Two dice can never roll a 1 and roll a 2 only 1 time in 36, so with small tiles left, one die wins.
| Tiles still open | Two dice | One die |
|---|---|---|
| 1, 2 | 6% | 22% |
| 1, 2, 3 | 19% | 33% |
| 1, 5 | 16% | 22% |
| 1, 2, 4 | 24% | 19% |
| 3, 4 | 19% | 6% |
The rule of thumb: one die when the open tiles total 6 or less, two dice when they total 7 or more.
How often can you shut the box?
With perfect choices every roll, about 1 game in 10 (9.8%). Most games end with a few small tiles open, so the real contest is keeping your score low: a finish with only the 1 and 2 open (3 points) beats almost everyone.
Practise against Hops in Shut the Box: press Teach me and he shows the best tiles for your roll and explains why.
Frequently asked questions
What is the best first move in Shut the Box?
Shut the tile that matches your roll exactly. For a 10, 11 or 12, shut the 9 plus the small tile that makes up the difference.
Should I roll one die or two?
One die when the open tiles add up to 6 or less, two dice when they add up to 7 or more.
What are the odds of shutting the box?
About 9.8% with perfect play and the one-die rule. Without the one-die option it's lower.
Is Shut the Box all luck?
The dice are luck, but your choices change your chances a lot: always splitting rolls into small tiles can cut your odds of shutting the box by more than half.