In the past I've toyed with playing games using dice numbered from 0 instead of 1.

So, for example, playing a d20 system game with 3d8, numbered 0 to 7, treating a roll of 21 as an automatic success and a 0 as critical failure.

What kind of dice notation would one use when writing about this?

What would you even call a die numbered from 0 to distinguish it from normal dice?


3 Answers 3


According to Wikipedia, this is called zero bias notation(retrieved Aug 31, 2010). You simply replace the “d” with a “z” and the old highest die value with the new one. So your example of three eight-sided dice marked 0–7 would be written as 3z7.

The only reference the Wikipedia article provided for this was an RPGnet post. I've never seen any signs that the notation caught on anywhere, but I do like it as a system.

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    \$\begingroup\$ in case anyone's looking for it, the zero bias notation part of that wikipedia entry was removed 3.5 years ago. :) en.wikipedia.org/w/… \$\endgroup\$ Commented Feb 18, 2014 at 18:57
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    \$\begingroup\$ It looks like this is now part of the cycle of citogenesis \$\endgroup\$
    – LeguRi
    Commented Mar 20, 2014 at 5:54
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    \$\begingroup\$ @RobStarling You might want to add that information to the answer directly. \$\endgroup\$ Commented Aug 4, 2014 at 5:23
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    \$\begingroup\$ It is worthy to note that the Troll programming language (for specifying die-rolls) had already implemented this notation in march 2009. This predates both the RPGnet post and the Wikipedia entry. It is possible, albeit unlikely, that Torben Mogensen (the maker of Troll) was the one to conceive this notation. Also, in modern parlance it seems to be more common to refer to these dice as zero-based rather than "zero biased". \$\endgroup\$
    – DarkAlf
    Commented Mar 30, 2018 at 23:22

If I had to design a notation from scratch, I wouldn't use the zero bias notation (3z8) at all. The "z" is a little arcane for my tastes.

I'd prefix the die size with a zero: 3d08.

ETA: But, you know, 3d8-3 also works.

Geeky stuff, in case you're looking to write a dice roller or something:

For more power, use a range operator: 3d[0-7].

For even more power, use a set operator: 3d{0,1,2,3,4,5,6,7}.

This lets you express all kinds of weird dice, like Fudge dice for example: 4d{+1,-1,0}.

More power, allow strings or strings-value pairs in the sets: 3d{CABBAGE:1, GOAT:3, WOLF:-3, BOAT:0, PERSON:9} or 1d{ADAM, BOBBY, CHRIS}.

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    \$\begingroup\$ I like the answer, but dice notation is to be read by normal people, not computers nor software developers. Using the set syntax... you might as well write it out in words! :P \$\endgroup\$
    – LeguRi
    Commented Aug 31, 2010 at 19:48
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    \$\begingroup\$ ... but I like 3d08 \$\endgroup\$
    – LeguRi
    Commented Aug 31, 2010 at 19:49
  • \$\begingroup\$ I wasn't sure if you were inventing notation for casual use, a game text, or a dice roller / dice stats program. \$\endgroup\$
    – Adam Dray
    Commented Aug 31, 2010 at 20:07
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    \$\begingroup\$ Added a note that 3d8-3 works fine, too. \$\endgroup\$
    – Adam Dray
    Commented Aug 31, 2010 at 20:09
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    \$\begingroup\$ @Adam Dray - Shhhhhhh... no one had noticed that yet... ;) \$\endgroup\$
    – LeguRi
    Commented Aug 31, 2010 at 20:21

The standard notation mode for this, using your 3d8, is 3d8-3, in the form NdX-N.

Zero-Bias notation (NzX) has never caught on, and would be presumed by many (including myself) to be a typographical error if seen without clear context. Worse, for dyslexics, including me, it can look very much like 3s8 or 328.

If your game uses only one size of die, and is always zero-biased, then using a letter code instead of the size might be a viable option.

For example, Fudge uses 4d3-8, written as 4dF, with 1dF = 1d3-2 (for a range of -1 to +1).

For example: the Stress Die in Ars Magica is sometimes fan-written 1dS, and is read specially - a 1 is "x2 and roll again" (Recursively), a 0 is a fail on an initial roll, or a 10 on a subsequent roll, while 2-9 are read as face value. In the editions I have, it's always written out as "stress die"...

1dA or 1dAv is a d6 marked 2, 3, 3, 4, 4, 5. It's used in a few older wargame sets, usually by approximation with standard d6's reading 1 as 3 and 6 as 4.

Note that dF is becoming fairly well known, but still puzzles many; dA are a historical footnote for RPGers.


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