Shut the Box: How to Play, the Real Odds of Winning, and a Free Game
Quick answer
In Shut the Box you roll two dice and flip down any tiles from 1 to 9 that add up to your roll. Keep going until no open tiles can make your total; your score is the sum of the tiles left standing, and lower is better. Shutting every tile is rare: with perfect play it happens in about 9.8% of games.
| Players | 1 or more |
|---|---|
| Equipment | A box with tiles 1–9 and two dice |
| Goal | Flip down every tile (or leave the lowest total) |
| Chance of shutting the box (perfect play) | 9.76% with the one-die rule, 7.14% always rolling two |
| Most common roll | 7 (16.67%) |
Shut the Box is a simple dice game with a surprisingly cruel streak: you can play every turn perfectly and still lose nine times out of ten. Here are the rules, a free online version you can play right now, and the exact odds of shutting the box.
How to play Shut the Box
- Start with all nine tiles up, numbered 1 to 9.
- Roll two dice and add them up.
- Flip down any open tiles that add up to the total. Roll a 9 and you could flip the 9, or 8 + 1, or 2 + 3 + 4, and so on.
- Keep rolling until you roll a total that no combination of open tiles can make.
- Score: add up the tiles still standing. Lower is better. If you flip every tile, you've shut the box and win outright.
Under the most common rule, once the 7, 8 and 9 are all down you may roll one die instead of two. With several players, each takes a turn and the lowest score wins.
Play Shut the Box online
Shut the Box
What are the odds of shutting the box?
We solved the game exactly: for every one of the 512 possible sets of open tiles, we calculated the move that gives the best chance of eventually shutting the box, then worked back to the start. No simulation is involved.
| Rule | Chance of shutting the box with perfect play |
|---|---|
| Roll one die once 7, 8 and 9 are down | 9.76% (about 1 game in 10.2) |
| Always roll two dice | 7.14% (about 1 game in 14.0) |
So even a flawless player shuts the box only about one game in ten. Real players make the occasional suboptimal choice, so their rate is lower.
Two-dice odds: why 7 is your friend
Every move starts with a roll of two dice, so the totals you can expect matter:
| Roll | Ways (of 36) | Chance |
|---|---|---|
| 2 | 1 | 2.78% |
| 3 | 2 | 5.56% |
| 4 | 3 | 8.33% |
| 5 | 4 | 11.11% |
| 6 | 5 | 13.89% |
| 7 | 6 | 16.67% |
| 8 | 5 | 13.89% |
| 9 | 4 | 11.11% |
| 10 | 3 | 8.33% |
| 11 | 2 | 5.56% |
| 12 | 1 | 2.78% |
Totals of 6, 7 and 8 come up 44% of the time between them, while 2 and 12 each appear only once in 36 rolls. With two dice you can never roll a 1, so a lone 1 tile can only be cleared with the one-die rule, and a lone 9 needs one of just four combinations out of 36.
Shut the Box strategy
- Clear 7, 8 and 9 early. They can only be cleared by mid-to-high rolls. Once they're gone, you're allowed to roll one die (under the common rule), which makes small totals reachable.
- Use as few tiles as possible. In our solved game, in every one of the 1,774 situations where you have a real choice, at least one best move flips the smallest possible number of tiles. Flipping the 9 for a roll of 9 keeps 1, 2, 3 and 4 available for awkward small totals later.
- When in doubt, include your highest tile. A best move uses the largest tile you could use in about 89% of those situations.
- Keep a spread of small tiles. Having 1, 2 and 3 still up gives you many ways to make low totals with one die.
- Accept the odds. Even with perfect choices, most games end with tiles standing. A score under 10 is a good game.
More dice games
- Farkle: rules, scoring chart and a score calculator
- Yahtzee odds: your chance of a Yahtzee in one turn
- Liar's dice: when to call a bluff
- Online dice roller
Frequently asked questions
What are the odds of shutting the box?
With perfect play, about 9.76% if you're allowed to roll one die once 7, 8 and 9 are down, and about 7.14% if you must always roll two dice. We worked this out exactly by checking every possible position and choosing the best move each time.
When can you roll one die in Shut the Box?
Under the most common rule, once the 7, 8 and 9 tiles are all down you may choose to roll a single die. It helps: small totals become possible, and the chance of shutting the box with perfect play rises from about 7.1% to about 9.8%.
Which tiles should you flip first?
A good rule of thumb is to flip the high tiles first when you have a choice, especially 7, 8 and 9. They're the hardest to clear later, because once you're down to one die or a few low tiles, big totals become impossible.
How is Shut the Box scored?
When you can't move, add up the tiles still standing; that's your score and lower is better. Some players read the standing tiles as a number instead (1, 2 and 4 left = 124). Shutting every tile is an instant win.
Sources
- Shut the box — Wikipedia