Mathmatically, I think the odds of any given pick being a duplicate of the previous pick are ~1/6.45e+44, which is vanishingly unlikely. Obviously, the more you pick the more likely a duplicate, but given the starting odds, even if you are picking trillions they are still very unlikely.

Something like 1e12*2(*)/6.45e44 ~= 1/3.22e32. (For reference, that about a million times the number of grams in the entire Earth!)

((*) For the Birthday paradox)

Of course, it also depends somewhat upon the validity of your rand(), but even using the notoriously poor rand() built-in to Win32 perl, I didn't get a single dup in 1e7 picks:

undef %h; 
++$h{ join'', map $chars[ rand @chars ], 1 .. 25 }  for 1 .. 1e7; 
print scalar keys %h;;
10000000
[download]

You could use a better rand, like Math::Random::MT, but it is probably unnecessary unless you are picking trillions. It is also much slower than the built-in on my machine.

Finally, no matter how good your rand(), even with those vanishingly small odds, there are no guarantees that you won't get a duplicate. The odds may be very small against it happening, but it still can happen. You are very, very unlikely to see it happen twice in your lifetime though.