bad interaction between "random" and "word"?

[Mick Collins]

Hello, everyone,
I was working on a project that involved randomness, which seemed to  
be a little off, so I did some testing.

I ran this handler from msgbox:
on tst2
    repeat with i = 2 to 10
       put i into randarg
       put "0 0 0 0 0 0 0 0 0 0" into theList
       put 10000 * i into nRepeats
       repeat nRepeats times
          add 1 to word random(randarg) of theList
       end repeat
       put nRepeats && randarg && theList into line i of fld "tmpFld"
    end repeat
end tst2

THE RESULTS:

20000 2 10027 10027 0 0 0 0 0 0 0 0
30000 3 9974 9973 9974 0 0 0 0 0 0 0
40000 4 10152 10153 10151 10150 0 0 0 0 0 0
50000 5 10144 10145 10142 10143 10142 0 0 0 0 0
60000 6 9981 9981 9979 9982 9979 9980 0 0 0 0
70000 7 10188 10193 10191 10187 10188 10192 10191 0 0 0
80000 8 10088 10089 10088 10089 10087 10086 10088 10087 0 0
90000 9 9984 9978 9976 9984 9983 9980 9980 9983 9983 0
100000 10 9998 9998 9997 9998 9999 9999 9998 9998 9998 9998

You can see the numbers of repeats are as expected, yet the sum of  
each line SHOULD be exactly the same as the number of repeats, but  
isn't (some above, some below) ... the individual numbers are all  
near to 10000 but even nearer to one another in a given line (but  
aren't all equal either).

HOWEVER, when I replace the line
          add 1 to word random(randarg) of theList
WITH
          put random(randarg) into tmp
          add 1 to word tmp of theList

THE RESULTS ARE:

20000 2 9825 10175 0 0 0 0 0 0 0 0
30000 3 9792 9994 10214 0 0 0 0 0 0 0
40000 4 10077 9955 9808 10160 0 0 0 0 0 0
50000 5 9926 10083 10078 9888 10025 0 0 0 0 0
60000 6 9964 10100 9922 9928 10019 10067 0 0 0 0
70000 7 9920 10094 9945 9823 9968 10079 10171 0 0 0
80000 8 10143 10129 10080 9809 10024 9948 9971 9896 0 0
90000 9 9764 10054 10094 9983 10038 10017 9991 10070 9989 0
100000 10 10029 9947 9910 9776 10252 10114 9935 9938 10006 10093

This appears correct ... the sum of each line is (the ones I've  
checked are and estimates of the others are close) the number of  
repeats and the numbers seem randomly sprinkled around 10000.

It seems to me that the replacement lines should do exactly the same  
thing as the line they replace.  Is this not working correctly or am  
I missing some knowledge of how it should be working?