NAME
dicelab - roll and examine dice rolling schemes
SYNOPSIS
dicelab [options] [-f <file>]
OPTIONS
-h, --help, -?
print a help message
--version, -v
display version number
--print-tree, -p
print the parse tree (for debugging purposes)
--roll, -r
roll the dice as specified. This will also be used if no other
action is requested
--eval, -e
reroll many times and sum up the results to get a statistical
distribution of values
--count, -c
specify the number of rerolls for --eval, default it 10000
-f<file>
read the scheme description from file instead from stdin
DESCRIPTION
Dicelab reads a description of a dice rolling scheme from a file or
from stdin if no file is specified and then rolls or examines this
scheme.
QUICK START
Single die rolls may be made using the ’d’ operator, followed by the
number of faces on the die to be rolled. E.g., d6 will roll a single
six-sided die, and d2 will flip a coin. Expressions may be modified by
the standard arithmetic operators. d10-1 will yield a value between 0
and 9, inclusive. In order to roll multiple dice of the same type, use
the repetition operator ’#’. 2#d6 will roll two six-sided dice; this is
not the same as 2*d6, which rolls only a single die but multipies the
result by two, or 2d6 which will cause a syntax error. In order to get
the sum of two six-sided dice, do sum(2#d6).
FULL SYNTAX
<integer> ::=
-?[0-9]+
<variable> ::=
[A-Za-z]+
<scalar> ::=
<integer>
| <variable>
| ( <scalar> )
| - <scalar>
| <scalar> + <scalar>
| <scalar> - <scalar>
| <scalar> * <scalar>
| <scalar> / <scalar>
| <scalar> % <scalar>
| <scalar> ^ <scalar>
| <scalar> . <scalar>
| d<scalar>
| sum <expr>
| prod <expr>
| count <expr>
<list> ::=
<scalar> # <expr>
| ( <list> )
| <scalar> .. <scalar>
| <expr> , <expr>
| perm <expr>
| sort <expr>
| rev <expr>
| (drop|keep)? low <scalar> <expr>
| (drop|keep)? high <scalar> <expr>
| (drop|keep)? first <scalar> <expr>
| (drop|keep)? last <scalar> <expr>
| (drop|keep)? == <scalar> <expr>
| (drop|keep)? != <scalar> <expr>
| (drop|keep)? < <scalar> <expr>
| (drop|keep)? > <scalar> <expr>
| (drop|keep)? <= <scalar> <expr>
| (drop|keep)? >= <scalar> <expr>
| if <expr> then <expr> else <expr>
| let <variable> = <expr> in <expr>
| while <variable> = <expr> do <expr>
| foreach <variable> in <expr> do <expr>
<expr> ::=
<scalar>
<list>
<input> ::=
<expr>
| <expr> ; <expr>
Comments may be inserted by using double slashed (//) as in C.
SEMANTICS
+ - * / ^
These are the familiar binary arithmetic operators for addition,
subtraction, multiplication, division, and exponentiation.
Division rounds toward zero. Examples: 5+7, d6-1, 2^10
-
This is the unary minus operator. Examples: -1
%
This is the modulus operator. x % y gives the remainder of x
divided by y. Examples: 11%2, d6%3
.
This is the scalar concatenation operator. x . y gives xy, the
concatenation of x and y. Examples: -10.9, d6.d6
d
This is the die roll operator. dn gives the value of a single
roll of an n-sided die. Examples: d6, 2#d6
sum prod
These are the extended sum and product operators. If e is an
expression, sum e and prod e give the sum of the members of e
and the product of the members of e, respectively. Examples:
sum(1..100), prod(3#d6)
count
This is the list size operator. If e is an expression, then
count e gives the number of members of e. Examples:
count(1,2,3), count(== 6 10#d6)
#
This is the list repetition operator. If n is a nonnegative
scalar and e is an expression, then n#e is a list containing the
results of n evaluations of e. Examples: 10#8, 3#d10
..
This is the range operator. If x and y are scalars, then x..y is
a list consisting of the interval [x,y]. If x>y, then the
resulting list is empty. Examples: 1..10, 4..d10
,
This is the list concatenation operator. v,u gives the list
consisting of all of the members of v, followed by all of the
members of u. Examples: 1,2 4,(3#d6)
sort
This is the list sorting operator. sort e sorts the list e in
ascending order. Examples: sort(10#d6)
perm
This is the list permutation operator. sort e results in a
random permutation of the list e. Use perm to shuffle a list.
Examples: perm(1..52)
rev
This is the list reversal operator. rev e results in a list with
the same members as the list e, but in reverse order. Examples:
rev(1..10), rev sort(10#d8)
low high
These operators act as filters by finding the least and greatest
values in lists. If n is a nonnegative scalar and e is an
expression, then low n e gives the n least members of e, and
high n e gives the n greatest members of e. Examples: high 3
5#d6
first last
These operators act as filters by finding initial and final
segments of lists. If n is a nonnegtive scalar and e is an
expression, then first n e gives the first n members of e, and
last n e gives the last n members of e. Examples: first 3
(1..10)
== != < > <= >=
These operators act as filters by finding values in lists which
meet given conditions. If x is a scalar and e is an expression,
then == x e gives the list of members of e equal to x; != x e
gives the list of members of e not equal to x; < x e gives the
list of members of e less than x; > x e gives the list of
members of e greater than x; <= x e gives the list of members of
e less than or equal to x; >= x e gives the list of members of e
greater than or equal to x. Examples: >= 3 5#d6
drop keep
These operators modify filters on lists. If fop is a filter
operation on an expression e, then keep fop e has the same
result as fop e and drop fop e evaluates to e less keep fop e.
In other words, drop negates filter conditions, and keep affirms
them. keep is never necessary and exists only for symmetry.
Examples: sum(drop low 1 4#d6)
let
This is the variable assignment and substitution operator. If x
is a variable and e and f are an expressions, then let x = e in
f gives the list which results from evaluating f with the value
of e substituted for every occurance of x in f. Evaluation of e
is done prior to substitution. Examples: let x = d6 in x*x
foreach
This is the bounded iteration operator. If x is a variable and e
and f are expressions, then foreach x in e do f gives the list
which results from assigning to x each of the members of e and
evaluating f. Examples: foreach x in c do x+1
while
This is the unbounded iteration operator. If x is a variable and
e and f are expressions, then while x = e do f is the list
v0,v1,...,vn, where v0 is the result of evaluating e and vi+1 is
the result of assigning vi to x and evaluating f, stopping at
the first vi which is empty. Examples: while x=d6 do ((count <6
x)#d6)
if
This is the branching operator. If e, f, and g are expressions,
then if e then f else g gives f if e is nonempty, and g
otherwise. Examples: if count(>4 2#d6) then 1 else 0
EXAMPLES
Count the number of dice greater than 7:
count >7 5#d10
Count the number of dice greater than 7 minus the number of dice equal
to 1:
let c=5#d10 in (count >7 c)-(count ==1 c)
Count the number of rolls until a 6 is rolled:
count (while x=d6 do ((count <6 x)#d6))
Count the number of rolls until a 6 is rolled, more efficiently:
count (while x=(d6/6) do ((count <1 x)#(d6/6)))
Roll attributes for a new D&D character:
6#sum(drop low 1 4#d6)
Roll on the 11..66 morale check table in The Gamers’ Civil War Brigade
Series:
d6.d6
Find the median of 3 d20s:
high 1 low 2 3#d20
3d6 with rerolls on 6s:
sum(while x=3#d6 do ((count ==6 x)#d6))
Roll 7 d10 and find the largest sum of identical dice:
let x = 7#d10 in high 1 (foreach y in 1..10 do sum (==y x))
The Fibonacci sequence is defined by Fn = Fn-1 + Fn-2, with F1 = F2 =
1. Calculate the first twenty Fibonacci numbers:
let n = 20 in
let f = (1,1) in
foreach i in 1..n do
let f = (f,sum(high 2 f)) in
if ==n i then f else ()
Risk has battles where the attacker rolls 3d6 and the defender rolls
2d6. The highest attacker die is matched with the highest defender die
and the second highest attacker die to the second highest defender die.
For both matches, the highest wins, with ties going to the defender.
The number of attacker wins:
let a = 3#d6 in
let b = 2#d6 in
count( (<(high 1 a) high 1 b),
(<(high 1 low 2 a) low 1 b))
Storyteller die roll with target number 8 and botches indicated at -1:
let c=5#d10 in
let succs = count >7 c in
let ones = count ==1 c in
if >0 succs then high 1 (0,succs-ones)
else if >0 ones then -1 else 0
Combat in Silent Death is rather complex. Three dice are rolled. If
their sum is above a target, the roll is a hit. To calculate damage,
the same dice are sorted. If all three are equal, all are summed to
yield the damage. If the least two are equal, but the third is higher,
the high die is the damage. If the two highest are equal, but the
third is lower, the two high dice are summed to yield the damage. If
all three dice are different, the middle die is the damage. This
example assumes that the dice are two d8s and a d10, with a target
number of 15:
let x = 2#d8,d10 in
(count >15 sum x)#
let a = low 1 x in // low die
let b = high 1 low 2 x in // middle die
let c = high 1 x in // high die
if ==a ==b c then a+b+c // all equal
else if ==a <c b then c // two low equal
else if >a ==c b then b+c // two high equal
else b // all different
CREDITS
Dicelab is based on the excellent work "roll" by Torben Mogensen
(http://www.diku.dk/~torbenm/Dice.zip). Without his work and comments,
this would hardly ever have happened.
The current language specification and the extensions to the original
language are derived from the work of Joel Uckelman
(http://dice.nomic.net/bones.html), most of the documentation is stolen
from him as well.
This code was written by Robert Lemmen <robertle@semistable.com> who
would be glad to hear your questions and remarks.