The probability of an adversary succeeding at guessing your random numbers must be made acceptably low, depending on the particular application. The size of the space the adversary must search is related to the amount of key ``information'' present in the information theoretic sense [11].
This depends on the number of different secret values possible and the probability of each value as follows:
where i varies from 1 to the number of possible secret values and 
is the probability of the value numbered 
. (Since is
less than one, the log will be negative so each term in the sum will
be non-negative.) n is the number of bits of information.
If there are 
different values of equal probability, then n bits
of information are present and an adversary would, on the average,
have to try half of the values, or 
, before guessing the
secret quantity. If the probability of different values is unequal,
then there is less information present and fewer guesses will, on
average, be required by an adversary. In particular, any values that
the adversary can know are impossible, or are of low probability, can
be initially ignored by an adversary, who will search through the
more probable values first.
For example, consider a cryptographic system that uses 56 bit keys.
If these 56 bit keys are derived by using a fixed pseudo-random
number generator that is seeded with an 8 bit seed, then an adversary
needs to search through only 256 keys (by running the pseudo-random
number generator with every possible seed), not the 
keys that
may at first appear to be the case. Only 8 bits of ``information'' are
in these 56 bit keys.