The odds¶
Every possible roll in the game, worked out exactly. Your Skill die across the rows, the Narrator's Difficulty die across the columns.
| skill \ challenge | d4Easy | d6Moderate | d8Challenging | d12High difficulty | d20"Impossible" |
|---|---|---|---|---|---|
| d4 | 37.52537.5 | 2516.758.3 | 18.812.568.8 | 12.58.379.2 | 7.5587.5 |
| d6 | 58.316.725 | 41.716.741.7 | 31.312.556.3 | 20.88.370.8 | 12.5582.5 |
| d8 | 68.812.518.8 | 56.312.531.3 | 43.812.543.8 | 29.28.362.5 | 17.5577.5 |
| d12 | 79.28.312.5 | 70.88.320.8 | 62.58.329.2 | 45.88.345.8 | 27.5567.5 |
| d20 | 87.557.5 | 82.5512.5 | 77.5517.5 | 67.5527.5 | 47.5547.5 |
win tie lose — percentages, from the player's side, rounded to one decimal place. Each cell adds to 100 before rounding.
The tie is governed by the bigger die¶
There is a clean rule hiding in that grid, and it is exact rather than approximate:
The tie rule
A tie happens exactly 1 ÷ (the larger of the two dice) of the time.
d4 against d4 ties one roll in four. d20 against d20 ties one in twenty. It does not matter what the smaller die is.
Which means the most generous rule in the game — both sides get something — fires most often for beginners attempting easy things, and almost disappears at the top of the range.
A new player with a d4 Skill trying something Easy triggers it on a quarter of their rolls. Two experts in a d20 standoff trigger it on one roll in twenty. The game gets more decisive exactly as the stakes rise, and it is at its most collaborative exactly where new players are standing.
An even match is never a coin flip¶
Matched dice do not split 50/50, because the tie takes its share out of the middle first:
| Matched pair | Win | Tie | Lose |
|---|---|---|---|
| d4 vs d4 | 37.5% | 25% | 37.5% |
| d6 vs d6 | 41.7% | 16.7% | 41.7% |
| d8 vs d8 | 43.8% | 12.5% | 43.8% |
| d12 vs d12 | 45.8% | 8.3% | 45.8% |
| d20 vs d20 | 47.5% | 5% | 47.5% |
The tie is a real third outcome, not a rounding error. At the bottom of the range it is a quarter of all play.
Reading the grid¶
- Down a column — what a bigger Skill die buys you against a fixed challenge. Against a d12, moving from d4 to d20 takes you from 12.5% to 67.5%.
- Across a row — how fast a challenge outruns you. A d8 Skill is favoured against Easy and Moderate, level with Challenging, and outmatched above that.
- The diagonal — an even contest, where win and lose are exactly level.
How these were produced
Computed, not measured. Each cell enumerates all possible pairs of rolls and
counts them, so these are exact probabilities rather than the results of a
simulation. The generator is tools/generate-odds.py, and it asserts the
1 ÷ larger-die rule for all 25 pairings every time it runs.