Let's set aside the argument that computers have a pseudo-random number generator.
I'm interested in knowing if a lottery terminal generates each quick pick independently from all previous picks and draws each from an identical uniform distribution.
Why I'm doubtful of the above claim.
A colleague of mine relayed a story (I don't know his source) where he said that the lotteries are more interested in having multiple winners for a given jackpot prize than a single winner because it creates more publicity. So, people who ask for a quick pick are more likely to get numbers that were already picked.