[hathchip]

As the sibling comment explains, the system with the 35-bag has a nonrandom way of adding pieces to the bag when one is removed. But even without that, the size of a bag does make a big difference to what sequences can appear.

Suppose you have a 7-bag system and you draw 35 pieces from it. Each subsequence 0-6, 7-13, 14-20, etc must contain exactly one of each piece. On the other hand, 35 pieces from a 35-bag system have to contain 5 of each piece, but they can be jumbled up. So the sequence could start SSSSSZZZZZ, whereas with the 7-bag system you would have to get at least one I and one T before you could have a second S or Z. In Tetris, as in other games, this totally affects your chances of winning - if it takes longer for the pieces counts to 'average' out, you might have died waiting for an I before they do.

This is a little like the situation with card-counting in blackjack. Going from 1 deck to 6 decks shuffled together doesn't affect the odds for a player who isn't paying attention to the cards. But it makes the job of a card counter way, way harder, and increases the chance that she will run out of money during a long spell of unfavorable cards, before the inevitable regression to the mean eventually happens.