6

Through this answer I learned of a game called Shut the Box.

A game of Shut the Box with 1, 4, 6, 7, 9 still open

The rules are very simple. The numbers 1 through 9 are "open". Two dice are rolled and numbers are shut that sum up to the number rolled. A player keeps rolling until no numbers can be shut, at which point that player's score is the sum of the numbers still open. The goal is to score as low as possible.

Luck is a big factor here, but is there a strategy to this game? Does the strategy change based on the numbers still open?

  • 1
    I think there's a further wrinkle to the rules. If one is the only tile still open, you only roll one die. – Gregory Nisbet Jun 3 '17 at 0:06
13

Any panels you close on a turn will, by rule, always have the same sum, so a given roll will always reduce your score by the same amount.

So all you can do is leave open as many possibilities as possible for future rolls. You do this by closing as few numbers as possible on each roll. Closing 5 is better than closing 2 and 3 because if you roll a 2 or a 3, the 5 won't help you, but the 2 and 3 together can serve any purpose the 5 could serve.

A table is available that shows which numbers are best to close given the currently closed numbers and the current dice roll.

  • This seems like a pretty solid strategy. However, I'm not sure it's optimal to close the 1 as early as possible. While 1 is open, its value is in letting you close doors when your roll isn't quite right. If you never use it, it's only a 1-point penalty. In fact, judging by the optimal strategies listed here, there's no concession for using the 1 earlier than you have to. – Samthere Jun 2 '17 at 8:59
  • On the optimal strategies listed in the link, the rules are changed to use one die after the game progresses. Creating a table like the links show for the rules described in the OP could probably yield a more comprehensive answer. – jejorda2 Jun 2 '17 at 11:38
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    There's a table for the 2-dice version listed as well. – Samthere Jun 2 '17 at 14:15
  • I missed that one. Looking at the table, it does look like it's better to always close fewer numbers, even when the 1 is available. I'll edit the answer. – jejorda2 Jun 2 '17 at 14:24

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