>>Nigel>> What's more, adapting my code to your algorithm makes it even
faster.  :)
  
>   on shuffle(aList)
>     script o
>       property l : aList
>     end script
>     
>     repeat with i from (count aList) to 2 by -1
>       set j to (random number (i - 1)) + 1
>       set v to item i of o's l
>       set item i of o's l to item j of o's l
>       set item j of o's l to v
>     end repeat
>   end shuffle
 

Thanks Nigel and Mark, this thread has helped me speed and improve a little
something I've been working on, so here's a practical example tested against
Nigel's version that's a bit faster.

------------
 property listIndex : {}
set aDeck to {}
repeat with s in {" of H", " of C", " of S", " of D"}
    repeat with x from 1 to 13
        if x = 1 then
            set c to "A"
        else if x = 11 then
            set c to "J"
        else if x = 12 then
            set c to "Q"
        else if x = 12 then
            set c to "Q"
        else if x = 13 then
            set c to "K"
        else
            set c to x as string
        end if
        set the end of aDeck to c & s
    end repeat
end repeat
set listIndex to {}
repeat with x from 1 to count of aDeck
    set the end of listIndex to x
end repeat

set startTime to the ticks

ashuffle(aDeck)

set aShuffledDeck to the result
set midTime to the ticks
bshuffle(aDeck)

set bShuffledDeck to the result
set endTime to the ticks
return {midTime - startTime, endTime - midTime, aShuffledDeck,
bShuffledDeck}

on ashuffle(aList)
    --my tweak of Nigel's version
    script o
        property l : aList
    end script
    repeat with i from (count aList) to 2 by -1
        set j to (some item of listIndex)
        --doesn't require OSAX call, yet is random
        set v to item i of o's l
        set item i of o's l to item j of o's l
        set item j of o's l to v
    end repeat
    return o's l
end ashuffle

on bshuffle(aList)
--Nigel's version
    script o
        property l : aList
    end script
    repeat with i from (count aList) to 2 by -1
        set j to (random number (i - 1)) + 1
        set v to item i of o's l
        set item i of o's l to item j of o's l
        set item j of o's l to v
    end repeat
    return o's l
end bshuffle
-----

Good luck!

ES