Optimal play via exact backward induction

Dice Bingo,
solved exactly.

Fill a grid with dice sums. Roll two dice, mark a matching cell, race to complete a line. This solver computes the optimal strategy for any board — and the exact expected number of rolls to win — using rational arithmetic, no simulation.

⚀ The board

Label every cell

Each cell holds a value from 2 to 12 — a possible sum of two dice. Repeats are allowed.

⚂ The turn

Roll & mark

Roll 2d6. If a cell matches the sum and is unmarked, mark one. Ties are broken optimally.

⚄ The win

Complete a line

First full row, column, or main diagonal wins. The solver minimizes expected rolls to get there.

Set up the board

Enter a value (2–12) in each cell.

Win by completing any full row, column, or one of the two main diagonals (all four cells). Solving all 65,536 states takes a moment.

Set up the board

Enter a value (2–12) in each cell.

How much does each mark help? Enter a 3×3 board; the solver measures each open cell's value as the next move — how many rolls you'd save by marking it. Pre-mark some cells to see how the best next move shifts once a line is partly filled. Darker means a more valuable mark.

Enter a board

Enter a value (2–12) in each cell.

Two boards, same rolls, each played by its own optimal strategy. The solver returns exact win / loss / tie probabilities — not estimates.

Board 1
Board 2