- Polyhedral dice provide varied discrete probability distributions useful for game mechanics, player choices, and flavor. Common types: d4, d6, d8, d10, d12, d20, plus percentile pairs (d100).
Gameplay uses
- Resolution mechanic: Single-die checks (e.g., roll a d20 + modifier vs. target) for pass/fail outcomes.
- Damage and resource rolls: d6/d8/d10 for damage or resource gains to control expected values and variance.
- Percentile systems: Two d10s (00–90 + 0–9) or a d100 for fine-grained probabilities.
- Skill/ability scaling: Use larger dice for higher-power effects (e.g., 1d6 → 1d8 → 1d10) to show growth without changing success mechanics.
- Success counting/thresholds: Roll multiple identical dice (e.g., 3d6, roll-and-count successes) to create bell-shaped distributions and predictable outcomes.
- Exploding/compounding: Reroll max faces and add to create long-tailed distributions and heroic variability.
- Advantage/disadvantage and min/max mechanics: Roll multiple dice and take best/worst to skew distribution without changing die size.
- Random tables & encounters: Dice with more faces give more varied tables (d20 vs d6).
Design considerations
- Granularity vs variance: Larger dice give larger steps; multiple smaller dice produce smoother (more predictable) distributions.
- Expected value: E(dN) = (N+1)/2 for a single fair dN. Use this to balance damage, costs, and rewards.
- Distribution shape: 1dN = uniform; ndN (n>1) approximates a normal distribution (less variance relative to mean).
- Player feel: d20s are associated with “high-stakes” checks; many players find sets of polyhedral dice tactile and satisfying.
- Complexity: Combining many different die types increases bookkeeping; prefer a small, consistent set for accessibility.
- Randomness transparency: Use visible dice rolls to build trust and drama; percentile or dice pools can obscure exact probabilities—document them.
Practical examples
- D20 check system: 1d20 + skill vs DC — wide range, high drama, easy modifiers.
- Damage progression: low-level spells 1d6, mid 2d6 or 1d8, high 3d8 — increases expected damage and variance smoothly.
- Skill test with degrees of success: Roll 2d6; 6–8 = partial, 9+ = full success (bell curve produces most middling results).
- Resource generation: d4/d6 to control average resource gain and cap extremes.
Teaching and hobby uses
- Teach probability, expected value, and distributions.
- Dice as collectibles, customization (colors, materials) and accessibility (large-print dice, apps for visually impaired).
Quick probability reminder
- Single fair dN: each face = 1/N probability; mean = (N+1)/2.
- 2d6: probabilities peak at 7 (most likely), creating a central tendency vs 1d12’s uniform spread.
If you want, I can:
- Convert a mechanic you have into a dice-based resolution and show probabilities; or
- Generate probability tables/graphs for specific dice combinations.