The dice notebook
Shut the Box Dice Probability: Totals and Next-Roll Odds
With two fair, independent six-sided dice, 7 is the most likely total: six of the 36 ordered outcomes make it. That is a single-roll probability, not the chance of winning a whole game of Shut the Box.
Count outcomes rather than distinct totals
Each face of the first die can pair with six faces of the second, giving 6 × 6 = 36 ordered outcomes. The results 1+6 and 6+1 are separate outcomes even though both total 7. By contrast, a total of 2 has only the outcome 1+1.
The following table is an exact enumeration under fair, independent dice. It does not use observed player data or a simulation. Percentages are rounded to two decimal places; fractions show the exact values.
| Total | Outcomes | Probability |
|---|---|---|
| 2 | 1 | 1/36 = 2.78% |
| 3 | 2 | 2/36 = 5.56% |
| 4 | 3 | 3/36 = 8.33% |
| 5 | 4 | 4/36 = 11.11% |
| 6 | 5 | 5/36 = 13.89% |
| 7 | 6 | 6/36 = 16.67% |
| 8 | 5 | 5/36 = 13.89% |
| 9 | 4 | 4/36 = 11.11% |
| 10 | 3 | 3/36 = 8.33% |
| 11 | 2 | 2/36 = 5.56% |
| 12 | 1 | 1/36 = 2.78% |
| First / second | 1 | 2 | 3 | 4 | 5 | 6 |
|---|---|---|---|---|---|---|
| 1 | 2 | 3 | 4 | 5 | 6 | 7 |
| 2 | 3 | 4 | 5 | 6 | 7 | 8 |
| 3 | 4 | 5 | 6 | 7 | 8 | 9 |
| 4 | 5 | 6 | 7 | 8 | 9 | 10 |
| 5 | 6 | 7 | 8 | 9 | 10 | 11 |
| 6 | 7 | 8 | 9 | 10 | 11 | 12 |
Calculate a specific next-roll chance
With only 7 and 8 open, this site uses two dice because high tiles remain. Legal next totals are 7 and 8. Their combined outcome count is 6+5=11, so the chance of having a legal move on the next roll is 11/36, or about 30.56%.
The sum of the two open tiles is 15, beyond the maximum two-dice total. It adds no extra successful outcome. Surviving that next roll also does not guarantee closing the remaining tile afterwards.
Avoid double-counting combinations
An open board might offer several ways to close a roll of 7. That does not make 7 more likely to appear. You still have six dice outcomes that total 7, however many legal tile combinations exist for that target.
Count each successful dice result once. The five combinations for a roll of 7 describe choices after the roll. They are not five independent chances to roll that number.
Recalculate when the game switches to one die
With 1 and 2 open, our automatic rule uses one die. Rolling 1, 2 or 3 offers a legal move, so the immediate survival chance is 3/6, or 50%. A roll of 3 closes both tiles, giving an immediate clear-board chance of 1/6 from that position.
Those are different events. A roll of 1 or 2 lets you continue but leaves a tile to close on a later roll. Use the one-die guide to check which dice apply before calculating any probabilities.
Separate a position from a whole game
A complete-game success rate depends on board size, scoring rules, dice choices and which legal move you select at every decision. A number calculated for another variant should not be presented as this website’s win rate.
Our strategy page gives practical heuristics and clearly labels the hints as legal combinations. An exact overall figure would require a documented solver for these rules. Until then, these small, auditable next-roll calculations are the appropriate claims to make.
Rules scope: The Little Dice Club rules. Sources and calculation methods. Probability examples are not overall game win rates.