Shut the Box Strategy: Close the Biggest Tile You Can
The big decision in Shut the Box is which tiles to close for your roll. The best plain answer is to close the biggest tile you can. Play that way and you shut the whole box about 1 game in 11. Close tiles at random and it's about 1 in 49.
1Close the biggest tile you can
Big tiles are the hard ones to get rid of. A 9 needs a roll of 9 or more. A 1 fits into almost any roll later on. So when a roll gives you a choice, spend it on the biggest tile it can close, and leave the small ones as change for later.
Some rolls don't give you a choice. A roll of 2 can only close the 2, so early on you'll sometimes have to use a small tile. That's fine: the tip is about the rolls that do give you a choice.
2Don't go out of your way to save the small tiles
You'll often hear "keep the 1, 2 and 3 for the end". Closing the biggest tile already does that. Trying to save the small tiles on purpose costs you, as the very first roll shows:
Play the whole game by "use as few of the 1, 2 and 3 as you can" and your average falls to 34.00, from 34.71.
3Wait on the one-die roll
In our version, once the 7, 8 and 9 are all shut you can choose to roll one die instead of two. It's tempting to take it straight away. Don't: roll one die only when the open tiles add up to 6 or less. Before that, two dice fit what's left more often.
How much it matters: closing the biggest tile but switching to one die as soon as you're allowed, you shut the box only 5.6% of the time, about 1 game in 18. Wait until 6 or less is left and it's 9.5%.
4How we know
A box of nine tiles can only be in 512 states, so we worked out the best possible play exactly, from our game's own rules: no simulation, no guessing. Here's how a perfect player compares with the tip and with two worse habits. "Left open" is the total of the tiles still up when the game ends:
| How you play | Average score | Box shut | Left open |
|---|---|---|---|
| Perfect play | 34.96 | 9.7% | 11.0 |
| The tip | 34.71 | 9.5% | 11.2 |
| Any tiles that fit, at random | 24.8 | 2.1% | 20.4 |
| Smallest tiles first | 20.9 | 1.1% | 24.2 |
The tip gets 99.3% of a perfect player's average score. Whenever a roll gives you a choice, it picks the best move 93% of the time. The rest of the gap is in positions too particular for any simple rule to capture.
Our scoring: you score the total of the tiles you shut, up to 45, plus 10 if you shut them all, so 55 at most. Online, every player plays their own box and the highest score wins.
Play Shut the Box