Shut the Box move helper
1. Tap the tiles to show which are open. Shut tiles go dark.
2. Choose your roll.
When one die is allowed, the helper also says whether to roll one die or two. The Shut the Box strategy guide explains when to switch.
Best first move for every roll
The best first move in Shut the Box is to shut the one tile that matches your roll, for any roll from 2 to 9. For the three rolls above 9, shut the 9 with the smallest tile that makes up the difference:
| First roll | Best move | Chance of that roll |
|---|---|---|
| 2 to 9 | Shut the tile with that number | 30 in 36 |
| 10 | Shut the 9 and 1 | 3 in 36 |
| 11 | Shut the 9 and 2 | 2 in 36 |
| 12 | Shut the 9 and 3 | 1 in 36 |
This is the same choice whether you are playing for the lowest score or only to shut the box.
When the usual rule gets it wrong
The usual rule, shut the fewest tiles and take the highest tile when you can, finds the best move about 19 times in 20. When it goes wrong, it is almost always a roll that needs two tiles, where the best pair is not the one with the highest tile. These are the cases you are most likely to meet, with best play up to that point:
| Tiles open | Roll | Best move | The rule's move |
|---|---|---|---|
| 1, 2, 3, 4, 6, 7, 8, 9 | 5 | 2 and 3 | 1 and 4 |
| 1, 2, 3, 4, 5, 8, 9 | 7 | 3 and 4 | 2 and 5 |
| 1, 2, 3, 5, 6, 7, 8, 9 | 10 | 2 and 8 | 1 and 9 |
| 1, 2, 3, 4, 5, 6, 9 | 8 | 3 and 5 | 2 and 6 |
| 1, 2, 3, 4, 5, 7, 9 | 8 | 3 and 5 | 1 and 7 |
| 1, 2, 3, 4, 5, 7, 9 | 6 | 2 and 4 | 1 and 5 |
| 1, 3, 4, 5, 6, 7, 8 | 10 | 4 and 6 | 3 and 7 |
In each case the best move keeps a tile the rule would spend, often the 1, so that more of the next rolls can still be matched. We also tested two other simple rules, "shut the closest pair" and "keep the 1". Both found the best move less often than the usual rule (85% and 89% of the time, against 95%).
How the helper chooses the best move
The helper looks at every group of open tiles that matches your roll. For each one, it works out the average final score you would get if you kept making the best choice on every later roll, over every way the dice could land. It shows the choice with the lowest average first. This is the same method our game uses for hints in practice games.
Playing for the lowest average score and playing only to shut the box almost always agree. Where they differ, the helper favours the lower average score. That is why best play for the lowest score shuts the box in 9.7% of games, just under the 9.8% you get by playing only to shut it. See the odds of shutting the box.