Roll two dice and the totals aren’t equally likely — there’s only ONE way to make a 2 (1+1) but SIX ways to make a 7. That’s why 7 is the heart of craps and the pivot of every board game: the sums pile up into a neat triangle, peaking at seven. Slide to roll and watch the distribution fill in.
For two fair dice the number of ways to make a sum s is 6 − |s − 7| (for s = 2…12), so the 36 equally-likely ordered outcomes give a triangular distribution: P(7) = 6/36 ≈ 16.7% (the mode), P(2) = P(12) = 1/36. The ways sum to 36 and the distribution is symmetric about 7 — which is why 7 dominates craps and drives board-game movement. A fail-loud self-check throws unless the ways total 36 and 7 is the unique mode at 6/36. ◆ real probability, node-verified.
Exact for two FAIR, independent dice; loaded dice or non-standard dice change the shape. The triangle is the count of equally-likely outcomes, not a claim about any single roll.