Notes
- The mean of the six kept scores (grey line) is equal to picking one of those six scores uniformly at
random.
- The six ranked dice are not independent; for example, if you roll a 14 as your highest score, you
certainly can't have rolled a 15 as your second-highest score.
- Pathfinder point values are mostly equal to 2 less than D&D 5e (per score); however,
even beyond this, the references I used assign different values to scores below 8. References: D&D, Pathfinder
.
- Spikes are normal in the D&D 5e and Pathfinder total point values, especially at the
high end;
this is because costs jump more than one point at a time, so some totals may have more or less
possible/likely combinations of ability scores that add up to that total.
In particular, this calculator uses a direct calculation; the spikes are real and not due to any
sort of sample size phenomenon.
- If you specify to keep more dice than were rolled, the excess kept dice don't count.
- The highest possible number on a die will never be rerolled, since you can't hope for a better result.
How does it work?
I built this using Pyodide, Chart.js,
and of course, my own Icepool Python library.
A polynomial-time
algorithm for keep-highest
allows this calculator to deliver precise results at an interactive rate. It runs in your own browser, not
requiring a server once loaded.
Compare previous AnyDice
and Monte
Carlo approaches.
If you want to play with Icepool more directly, try this
example JupyterLite notebook,
which computes the distributions of the total ability scores generated by the four Advanced Dungeons
& Dragons 1st Edition methods.
Questions, comments, or suggestions? Find me on Reddit or Twitter.
Icepool