Section 01
Randomness
Curves, flat lines, and what each one feels like. Every entry is a mechanism examined on its own, with the arithmetic shown and the table consequence stated. No system is treated as canonical.
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001
Why 3d6 is not a d20
Same average, completely different game. The flat line versus the bell, what each does to a difficulty number, and why one produces heroic swings and the other produces competence.
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002
The flat line
A single die is uniform: every result equally likely. What that means for a system that leans on it, and why big modifiers matter more than they look.
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003
Adding dice narrows it
Two dice make a triangle, three make a bell. Each die added pulls results toward the middle and makes the extremes rarer than most tables expect.
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004
Advantage is a curve trick
Rolling twice and taking the better is not a flat bonus — it is worth most in the middle of the range and almost nothing at the ends.
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005
Exploding dice
A die that re-rolls on its maximum has no upper bound. What that does to the tail, and why it changes how a table feels about a long shot.
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006
Dice pools
Count successes rather than sum faces. How pool size and target number trade off, and why the pool degrades gracefully where a single die does not.
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007
The d100 illusion
Percentile dice read as precise because they are granular. Granularity is not the same as meaningful resolution.