<!-- Generated by tools/Compare-Resolution.ps1. Do not edit by hand. -->
Resolution Scheme Comparison
Exhaustive enumeration of candidate roll-under schemes playable with one standard seven-piece dice set. Counts are exact, not simulated.
Edge steps are normalized (5 / 5 / 25) so every scheme tops out at 3 Edges and the Edge columns compare directly.
Candidates
| Scheme | Dice used | Range | Match rule |
|---|---|---|---|
| 2d10 | Both d10s | 2-20 | Doubles: d10 and percentile show the same digit |
| d20 | d20 only; both d10s freed | 1-20 | Natural 1 / natural 20 |
| d100 | Both d10s, as designed | 1-100 | Doubles: tens and units digits agree |
Modifier sensitivity — the decisive difference
+1 worth is how many percentage points one extra point of Target Number buys at that skill level. A player weighing a tactical tradeoff is really asking this question.
| Success rate | 2d10: +1 worth | d20: +1 worth | d100: +1 worth |
|---|---|---|---|
| ~25% | 8 pts (TN 8) | 5 pts (TN 5) | 1 pts (TN 25) |
| ~40% | 9 pts (TN 9) | 5 pts (TN 8) | 1 pts (TN 40) |
| ~50% | 10 pts (TN 10) | 5 pts (TN 10) | 1 pts (TN 50) |
| ~60% | 8 pts (TN 12) | 5 pts (TN 12) | 1 pts (TN 60) |
| ~75% | 7 pts (TN 13) | 5 pts (TN 15) | 1 pts (TN 75) |
| ~90% | 4 pts (TN 16) | 5 pts (TN 18) | 1 pts (TN 90) |
On 2d10 the same +1 swings between roughly 1 and 10 points depending on skill — a tenfold difference. On d20 it is 5 points everywhere; on d100, 1 point everywhere.
Edge generation at matched success rates
| Success rate | 2d10 >=1 Edge | d20 >=1 Edge | d100 >=1 Edge |
|---|---|---|---|
| ~25% | 3% | 0% | 0% |
| ~40% | 6% | 15% | 15% |
| ~50% | 10% | 25% | 25% |
| ~60% | 21% | 35% | 35% |
| ~75% | 28% | 50% | 50% |
| ~90% | 55% | 65% | 65% |
Margin distribution shape
Under one-roll resolution the Margin carries everything downstream — location control, penetration, and damage magnitude. So the shape of the Margin distribution is the shape of the damage curve.
Each successful roll's Margin is expressed as a fraction of the largest Margin achievable at that Target Number, then bucketed into quartiles. A flat scheme spreads mass evenly across all four. A bell scheme concentrates it low, producing a typical result with rare spikes — the behaviour multi-die damage would have given, which a one-set constraint otherwise forbids.
| Scheme | Low quarter | Mid-low | Mid-high | Top quarter |
|---|---|---|---|---|
| 2d10 (TN 13) | 38% | 33% | 21% | 8% |
| d20 (TN 15) | 27% | 20% | 27% | 27% |
| d100 (TN 75) | 25% | 24% | 25% | 25% |
Expected Margin per attempt
With Margin driving both damage and progress toward task thresholds, the expected Margin per attempt is the tuning constant for the whole game. Failures count as zero.
Rolls to 20 is how many attempts an average character needs to accumulate a 20-point task threshold. It converts a threshold directly into table time.
| Success rate | 2d10 E[Margin] | rolls to 20 | d20 E[Margin] | rolls to 20 | d100 E[Margin] | rolls to 20 |
|---|---|---|---|---|---|---|
| ~25% | 0.56 | 36 | 0.5 | 40 | 3 | 7 |
| ~50% | 1.2 | 17 | 2.25 | 9 | 12.25 | 2 |
| ~75% | 2.84 | 8 | 5.25 | 4 | 27.75 | 1 |
| ~90% | 5.2 | 4 | 7.65 | 3 | 40.05 | 1 |
Note that roll-under and roll-over are mathematically symmetric. Under roll-over, Margin is roll - Target Number and every distribution above is mirrored, so all of this analysis transfers unchanged.
Full tables
2d10 (d10 + percentile read as units)
| TN | Success | +1 worth | >=1 Edge | >=2 Edges | Match on hit |
|---|---|---|---|---|---|
| 2 | 1% | 2 pts | 0% | 0% | 1% |
| 3 | 3% | 3 pts | 0% | 0% | 1% |
| 4 | 6% | 4 pts | 0% | 0% | 2% |
| 5 | 10% | 5 pts | 0% | 0% | 2% |
| 6 | 15% | 6 pts | 0% | 0% | 3% |
| 7 | 21% | 7 pts | 1% | 0% | 3% |
| 8 | 28% | 8 pts | 3% | 0% | 4% |
| 9 | 36% | 9 pts | 6% | 0% | 4% |
| 10 | 45% | 10 pts | 10% | 0% | 5% |
| 11 | 55% | 9 pts | 15% | 0% | 5% |
| 12 | 64% | 8 pts | 21% | 1% | 6% |
| 13 | 72% | 7 pts | 28% | 3% | 6% |
| 14 | 79% | 6 pts | 36% | 6% | 7% |
| 15 | 85% | 5 pts | 45% | 10% | 7% |
| 16 | 90% | 4 pts | 55% | 15% | 8% |
| 17 | 94% | 3 pts | 64% | 21% | 8% |
| 18 | 97% | 2 pts | 72% | 28% | 9% |
| 19 | 99% | 1 pts | 79% | 36% | 9% |
| 20 | 100% | 0 pts | 85% | 45% | 10% |
d20
| TN | Success | +1 worth | >=1 Edge | >=2 Edges | Match on hit |
|---|---|---|---|---|---|
| 1 | 5% | 5 pts | 0% | 0% | 5% |
| 2 | 10% | 5 pts | 0% | 0% | 5% |
| 3 | 15% | 5 pts | 0% | 0% | 5% |
| 4 | 20% | 5 pts | 0% | 0% | 5% |
| 5 | 25% | 5 pts | 0% | 0% | 5% |
| 6 | 30% | 5 pts | 5% | 0% | 5% |
| 7 | 35% | 5 pts | 10% | 0% | 5% |
| 8 | 40% | 5 pts | 15% | 0% | 5% |
| 9 | 45% | 5 pts | 20% | 0% | 5% |
| 10 | 50% | 5 pts | 25% | 0% | 5% |
| 11 | 55% | 5 pts | 30% | 5% | 5% |
| 12 | 60% | 5 pts | 35% | 10% | 5% |
| 13 | 65% | 5 pts | 40% | 15% | 5% |
| 14 | 70% | 5 pts | 45% | 20% | 5% |
| 15 | 75% | 5 pts | 50% | 25% | 5% |
| 16 | 80% | 5 pts | 55% | 30% | 5% |
| 17 | 85% | 5 pts | 60% | 35% | 5% |
| 18 | 90% | 5 pts | 65% | 40% | 5% |
| 19 | 95% | 5 pts | 70% | 45% | 5% |
| 20 | 100% | 0 pts | 75% | 50% | 10% |
d100 (percentile, native reading)
| TN | Success | +1 worth | >=1 Edge | >=2 Edges | Match on hit |
|---|---|---|---|---|---|
| 1 | 1% | 1 pts | 0% | 0% | 0% |
| 2 | 2% | 1 pts | 0% | 0% | 0% |
| 3 | 3% | 1 pts | 0% | 0% | 0% |
| 4 | 4% | 1 pts | 0% | 0% | 0% |
| 5 | 5% | 1 pts | 0% | 0% | 0% |
| 6 | 6% | 1 pts | 0% | 0% | 0% |
| 7 | 7% | 1 pts | 0% | 0% | 0% |
| 8 | 8% | 1 pts | 0% | 0% | 0% |
| 9 | 9% | 1 pts | 0% | 0% | 0% |
| 10 | 10% | 1 pts | 0% | 0% | 0% |
| 11 | 11% | 1 pts | 0% | 0% | 1% |
| 12 | 12% | 1 pts | 0% | 0% | 1% |
| 13 | 13% | 1 pts | 0% | 0% | 1% |
| 14 | 14% | 1 pts | 0% | 0% | 1% |
| 15 | 15% | 1 pts | 0% | 0% | 1% |
| 16 | 16% | 1 pts | 0% | 0% | 1% |
| 17 | 17% | 1 pts | 0% | 0% | 1% |
| 18 | 18% | 1 pts | 0% | 0% | 1% |
| 19 | 19% | 1 pts | 0% | 0% | 1% |
| 20 | 20% | 1 pts | 0% | 0% | 1% |
| 21 | 21% | 1 pts | 0% | 0% | 1% |
| 22 | 22% | 1 pts | 0% | 0% | 2% |
| 23 | 23% | 1 pts | 0% | 0% | 2% |
| 24 | 24% | 1 pts | 0% | 0% | 2% |
| 25 | 25% | 1 pts | 0% | 0% | 2% |
| 26 | 26% | 1 pts | 1% | 0% | 2% |
| 27 | 27% | 1 pts | 2% | 0% | 2% |
| 28 | 28% | 1 pts | 3% | 0% | 2% |
| 29 | 29% | 1 pts | 4% | 0% | 2% |
| 30 | 30% | 1 pts | 5% | 0% | 2% |
| 31 | 31% | 1 pts | 6% | 0% | 2% |
| 32 | 32% | 1 pts | 7% | 0% | 2% |
| 33 | 33% | 1 pts | 8% | 0% | 3% |
| 34 | 34% | 1 pts | 9% | 0% | 3% |
| 35 | 35% | 1 pts | 10% | 0% | 3% |
| 36 | 36% | 1 pts | 11% | 0% | 3% |
| 37 | 37% | 1 pts | 12% | 0% | 3% |
| 38 | 38% | 1 pts | 13% | 0% | 3% |
| 39 | 39% | 1 pts | 14% | 0% | 3% |
| 40 | 40% | 1 pts | 15% | 0% | 3% |
| 41 | 41% | 1 pts | 16% | 0% | 3% |
| 42 | 42% | 1 pts | 17% | 0% | 3% |
| 43 | 43% | 1 pts | 18% | 0% | 3% |
| 44 | 44% | 1 pts | 19% | 0% | 4% |
| 45 | 45% | 1 pts | 20% | 0% | 4% |
| 46 | 46% | 1 pts | 21% | 0% | 4% |
| 47 | 47% | 1 pts | 22% | 0% | 4% |
| 48 | 48% | 1 pts | 23% | 0% | 4% |
| 49 | 49% | 1 pts | 24% | 0% | 4% |
| 50 | 50% | 1 pts | 25% | 0% | 4% |
| 51 | 51% | 1 pts | 26% | 1% | 4% |
| 52 | 52% | 1 pts | 27% | 2% | 4% |
| 53 | 53% | 1 pts | 28% | 3% | 4% |
| 54 | 54% | 1 pts | 29% | 4% | 4% |
| 55 | 55% | 1 pts | 30% | 5% | 5% |
| 56 | 56% | 1 pts | 31% | 6% | 5% |
| 57 | 57% | 1 pts | 32% | 7% | 5% |
| 58 | 58% | 1 pts | 33% | 8% | 5% |
| 59 | 59% | 1 pts | 34% | 9% | 5% |
| 60 | 60% | 1 pts | 35% | 10% | 5% |
| 61 | 61% | 1 pts | 36% | 11% | 5% |
| 62 | 62% | 1 pts | 37% | 12% | 5% |
| 63 | 63% | 1 pts | 38% | 13% | 5% |
| 64 | 64% | 1 pts | 39% | 14% | 5% |
| 65 | 65% | 1 pts | 40% | 15% | 5% |
| 66 | 66% | 1 pts | 41% | 16% | 6% |
| 67 | 67% | 1 pts | 42% | 17% | 6% |
| 68 | 68% | 1 pts | 43% | 18% | 6% |
| 69 | 69% | 1 pts | 44% | 19% | 6% |
| 70 | 70% | 1 pts | 45% | 20% | 6% |
| 71 | 71% | 1 pts | 46% | 21% | 6% |
| 72 | 72% | 1 pts | 47% | 22% | 6% |
| 73 | 73% | 1 pts | 48% | 23% | 6% |
| 74 | 74% | 1 pts | 49% | 24% | 6% |
| 75 | 75% | 1 pts | 50% | 25% | 6% |
| 76 | 76% | 1 pts | 51% | 26% | 6% |
| 77 | 77% | 1 pts | 52% | 27% | 7% |
| 78 | 78% | 1 pts | 53% | 28% | 7% |
| 79 | 79% | 1 pts | 54% | 29% | 7% |
| 80 | 80% | 1 pts | 55% | 30% | 7% |
| 81 | 81% | 1 pts | 56% | 31% | 7% |
| 82 | 82% | 1 pts | 57% | 32% | 7% |
| 83 | 83% | 1 pts | 58% | 33% | 7% |
| 84 | 84% | 1 pts | 59% | 34% | 7% |
| 85 | 85% | 1 pts | 60% | 35% | 7% |
| 86 | 86% | 1 pts | 61% | 36% | 7% |
| 87 | 87% | 1 pts | 62% | 37% | 7% |
| 88 | 88% | 1 pts | 63% | 38% | 8% |
| 89 | 89% | 1 pts | 64% | 39% | 8% |
| 90 | 90% | 1 pts | 65% | 40% | 8% |
| 91 | 91% | 1 pts | 66% | 41% | 8% |
| 92 | 92% | 1 pts | 67% | 42% | 8% |
| 93 | 93% | 1 pts | 68% | 43% | 8% |
| 94 | 94% | 1 pts | 69% | 44% | 8% |
| 95 | 95% | 1 pts | 70% | 45% | 8% |
| 96 | 96% | 1 pts | 71% | 46% | 8% |
| 97 | 97% | 1 pts | 72% | 47% | 8% |
| 98 | 98% | 1 pts | 73% | 48% | 8% |
| 99 | 99% | 1 pts | 74% | 49% | 9% |
| 100 | 100% | 0 pts | 75% | 50% | 10% |