val = math.random([l [, u]]); val = random([l [, u]]);
The functions math.random and math.randomseed are interfaces to the simple random generator functions rand and srand that are provided by ANSI C.
When called without arguments, math.random returns a pseudo-random real number in the range [0,1).
When called with a number n, math.random returns a pseudo-random integer in the range [1,n].
When called with two arguments, l and u, math.random returns a pseudo-random integer in the range [l,u].
The math.randomseed function sets a "seed" for the pseudo-random generator: Equal seeds produce equal sequences of numbers.
On random number generator distribution and security
The ANSI C rand() function is a Linear Congruential Pseudo-Random Number Generator (LPCRNG). Statistically speaking, LCPRNGs have a fair distribution. However, from a security standpoint they are very weak.
If you depend on random numbers to keep something secret or someone out of something, they only need to see a handful of numbers to be able to guess the next one accurately. In fact, if you output large enough numbers, they only need to see a single number to determine the next one. This is the standard LCPRNG used by Microsoft (written in C):
rng = rng * 214013 + 2531011 return (rng>>16)&0x7fff;
> local x = math.random(); > = x 0.34534 [0 - 1]
> local x = math.random(100); > = x 53 [1 - 100]
> local x = math.random(50, 52); > = x 51 [50 - 52]
The range [0,1) of math.random is exclusive, meaning that you can never get 1.0 exactly. Note that the returned number is not an integer, except the special (very rare) case of 0.
The other ranges of the functions are inclusive, and will always return integers.
It should be noted that the reason math.random does not allow 1.0 to be returned has to do with code they implemented to avoid issues on SunOS systems. However, they "correct" this issue by using modulus division. This has a side-effect for all non-SunOS systems making 0.0 twice as likely to occur than any other randomly generated number. In other words, when it would normally roll a 1.0, Lua changes that to 0.0 - so both 0.0 and 1.0 return as 0.0.
It has been suggested that the game client might seed the RNG when it is started