random numbers

I was exploring Benford's Law thusly: (not very elegant but it works):

#!/bin/zsh

integer level=
integer a1=0
integer a2=0
integer a3=0
integer a4=0
integer a5=0
integer a6=0
integer a7=0
integer a8=0
integer a9=0

for ((level=1; level<=1000; level++)); do

#First tests:
var=$RANDOM

#Second tests:
#var=$(shuf -i 1-1000 -n 1)

     if [ ${var[1]} = '1' ]; then ((a1++)); fi
     if [ ${var[1]} = '2' ]; then ((a2++)); fi
     if [ ${var[1]} = '3' ]; then ((a3++)); fi
     if [ ${var[1]} = '4' ]; then ((a4++)); fi
     if [ ${var[1]} = '5' ]; then ((a5++)); fi
     if [ ${var[1]} = '6' ]; then ((a6++)); fi
     if [ ${var[1]} = '7' ]; then ((a7++)); fi
     if [ ${var[1]} = '8' ]; then ((a8++)); fi
     if [ ${var[1]} = '9' ]; then ((a9++)); fi
done

echo a1 is: $a1
echo a2 is: $a2
echo a3 is: $a3
echo a4 is: $a4
echo a5 is: $a5
echo a6 is: $a6
echo a7 is: $a7
echo a8 is: $a8
echo a9 is: $a9

---------------------------------------------------------------------------------

First tests give close to this:

5 /aWorking/Zsh/Source/Wk/Boneyard/Math 1 % . ./test1
a1 is: 339
a2 is: 336
a3 is: 134
a4 is: 27
a5 is: 31
a6 is: 25
a7 is: 28
a8 is: 40
a9 is: 40

Second tests close to this:

5 /aWorking/Zsh/Source/Wk/Boneyard/Math 1 % . ./test1
a1 is: 110
a2 is: 102
a3 is: 114
a4 is: 114
a5 is: 107
a6 is: 99
a7 is: 135
a8 is: 108
a9 is: 111

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I think i know why, it's because zsh's RANDOM tops out at 32,767, but 
this insures that the first digit of a string of random numbers isn't 
random but strongly weighted to 1 and 2, with 3 also weighted.  Is this 
worth worrying about?  I'd say so.  Perhaps it should max out at 10,000 
or 100,000 or even offer a user selectable range?  Or do we have other 
tricks for coping with this?  I find zsh to be quite competent 
mathematically so having to use an external utility to get really random 
numbers seems not up to snuff.