Shut the Box Solver

Shut the box is small enough to solve completely and awkward enough that nobody does. Nine tiles give 512 positions, and because tiles only ever close, the chance of shutting the box from any position can be worked out exactly — no simulation, no sampling, just arithmetic from the empty box backwards.

Tiles in the box

What you rolled

The total on the dice.

One die allowed once the tiles left add to six or less

Tiles still open

Close 7 — it leaves a 9.8% chance of shutting the box

Close	Chance of shutting the box
7	9.82%
2 + 5	4.80%
3 + 4	4.69%
1 + 6	4.62%
1 + 2 + 4	1.87%

Before this roll the position was worth 9.76%. The tiles left add to 45, which is what you score if you cannot go.

✓ Every move sums to the roll, using open tiles only — 5 legal moves for a roll of 7
✓ No legal move is missing — 5 combinations found by testing every subset of the open tiles
✓ Every chance is re-derived from the empty box upwards — 512 positions solved exactly, with no simulation anywhere
✓ The empty box is a certain win — shutting every tile is the win condition, so it is worth exactly 1 by definition
✓ The moves are ranked by the chance they leave — best is 9.8%, worst 1.9%

What this generator does

Solves every position from the empty box upwards, then lists the moves available for your roll with the exact probability each one leaves.

How to use this tool

Set how many tiles the box has and which are still open.
Type the total you rolled.
Read every legal move, ranked by what it leaves you with.
A position with no legal move says so, and gives the score.

Understanding the controls

Tiles in the box: Nine is the traditional box; ten and twelve boxes exist and change the odds considerably — a full twelve-tile box is shut under one per cent of the time.
What you rolled: The total on the dice. With the one-die rule in play and few tiles left, this can be as low as one.
One die allowed: The common house rule that lets you throw a single die once the tiles left add to six or less. It is worth a great deal, and the solver accounts for it throughout rather than at the end.
Tiles still open: Tap a tile to open or close it. Everything is computed from this position, not from an assumed opening.

Common use cases

Settling an argument about which tiles to close
Learning why closing the big tile early is usually right
Seeing how much a bad roll actually costs you
Checking the odds before a house rule is agreed
Working out how often a full box is shut at all

How this generator works

Because tiles only close, the positions form a directed graph with no cycles, so each one can be evaluated from the positions it can reach. Working up from the empty box — worth exactly one — every position's value is the sum over the possible rolls of the probability of that roll times the best move available. That gives an exact answer for all 512 positions of a nine-tile box in a few milliseconds. The checker re-derives the whole table and compares every published figure against it, confirms each listed move really sums to the roll from tiles that are open, and confirms no legal move has been missed by testing every subset of the open tiles.

Randomness and fairness

Nothing here is random. The dice probabilities are exact distributions rather than samples, and the same position always gives the same answer.

For how randomness is produced across the whole site, see how Generate Random works.

Limitations and good to know

House rules vary: some boxes allow the single die only with the highest tiles shut, others not at all.
The solver plays to shut the box, which is not the same as playing to minimise your score when shutting is unlikely.
Games scored across several rounds may want a different objective on the last round.
Twelve-tile boxes are included, but shutting one is rare enough that the numbers get very small.

Privacy and your data

The position is solved in your browser. No games or positions are transmitted or stored.