Shut the Box: rules and a game to play here

How to play Shut the Box

What you need

A board has a row of hinged tiles numbered 1 to 9 and a tray to roll the dice in. Without one, write 1 to 9 on a sheet of paper and cross numbers out, or use the game above. Any number can play, one at a time.

A turn

Start with every tile open. Roll both dice and add them. Close one or more open tiles whose numbers add up to exactly that total. Then roll again and do the same. You choose which tiles to close each time, and that choice is the whole skill of the game.

Once the 7, 8 and 9 are all down, you may roll a single die instead. The highest roll you could still need is then 6 or less, and one die makes those small totals easier to hit.

End of a turn and scoring

Your turn ends when no combination of open tiles adds up to your roll. In the usual scoring the open tiles are added up: if 2, 3 and 5 are open when you roll a 1, you score 10. After everyone has had a turn, the lowest score wins. A player who closes every tile has shut the box and wins immediately.

Variations

All of these are in the game above under "Rule choices". The Wikipedia article lists them among many local versions.

• 12 tiles. A longer box, numbered 1 to 12, sold as "Full house" boxes. Twelve is still the highest two dice can roll, so nothing else changes, but shutting the box becomes rare.
• Scoring. Golf adds the open tiles (the usual way). Missionary counts how many tiles are open. Digital reads them as a number from left to right: 1, 2 and 5 open scores 125, which punishes leaving several small tiles.
• Thai style. Always roll two dice, and close just one tile: the number on either die or their total. With dice of 2 and 3 you may close the 2, the 3 or the 5.
• For young players. Close the tile for the total, or the tiles for one or both dice. With a 6 and a 2 you may close the 8, or the 6 and the 2, or only one of them. It is a counting game more than an adding one; first to shut the box wins.
• Tournament. Play rounds and keep a running total. Anyone whose total reaches 45 drops out, and the last player left wins.

Odds and strategy

Here is how often a player who always makes the best choice shuts the box, and the score they end with on average (Golf scoring), for each set of rules:

A check on the arithmetic: Wikipedia says a simple Thai-style strategy (use the total on a 7, 8 or 9 when you can, otherwise close the lowest tile you may) succeeds 7.9855% of the time. Our move generator, playing exactly that strategy, gives the same 7.9855%. Best play does very slightly better.

Which tiles to close on the first roll

Take a first roll of 9 with every tile open. The chance of shutting the box afterwards, for each way to make 9:

1. Close the big tiles first. Only a big roll can close the 9, but a small tile fits into dozens of totals. Closing the 9 alone on a 9 is worth more than twice any split.
2. Close fewer tiles when you can. One tile leaves more small tiles for later, and small tiles are what make awkward rolls workable.
3. Chasing a low score is different from chasing a shut box. Late in a turn, the move that keeps the most total value closed can differ from the one with the best chance of closing everything. Turn on "Show the odds" in the game to see both numbers for every choice.
4. One die or two: add up what is open. Once you may roll one die, roll one if your open tiles add up to 6 or less, and two if they add up to more. We checked all 63 ways the tiles 1 to 6 can stand, and that rule gives the better chance of shutting the box in every one of them.

Where tables differ

• Does shutting the box end the game? The common rule says it wins at once. In a round where everyone plays anyway, it is simply a score of 0. The game has a switch.
• The one-die rule. Most tables allow one die once 7, 8 and 9 are down. Some never allow it. On 12 tiles, the article does not say; we allow one die only once every tile from 7 to 12 is down.
• How many tiles per roll. The usual rule allows any number; some pub rules allow at most two.
• How long a game lasts. One round, a set number of rounds, or the 45 tournament. The article's tournament also mentions playing to a grand total of 100; we use the drop-out at 45, which decides a game on its own.

House rules in the game above: every switch except the standard rules is a house rule. Agree on them before the first roll. In English pubs the game was traditionally played for money; ours keeps points only.

Shut the Box questions

How do you play Shut the Box?

Roll two dice and add them up. Close any open tiles that add up to the total, then roll again. When no set of open tiles makes your roll, your turn ends and the tiles still open are your score. Lowest score wins, and closing every tile (shutting the box) wins at once.

When can you roll one die in Shut the Box?

Once the 7, 8 and 9 are all closed, you may choose to roll one die instead of two. Until then you must roll both. On a 12-tile box we use the same idea: one die only when every tile from 7 up is closed.

What are the odds of shutting the box?

With nine tiles and the one-die rule, a player who always makes the best choice shuts the box 9.8% of the time, about one turn in ten. With twelve tiles it drops below one in a hundred.

Which tiles should you close first?

Usually the highest ones. The 7, 8 and 9 can only be closed with big rolls, while small tiles fit into many totals. On a first roll of 9, closing the 9 alone gives you more than twice the chance of any other choice.

How do you score Shut the Box with several players?

Each player takes one turn and scores the tiles left open. In the usual Golf scoring you add them up; Missionary scoring counts how many are open; Digital reads them as one number, so 1, 2 and 5 open scores 125. For a longer game, play rounds, or the tournament where anyone who reaches 45 drops out.