Take a simple example of one hand in a 1-deck game vs. a 6-deck game.
If you are holding 5-6 with the dealer showing a 5, regardless of what you draw, the dealer is going to need a 2-6 to make his hand. With a one-deck game, there are 5x4=20 cards that can make his hand. However, you and the dealer are holding three of them, so there are 17/20 of the original amount available to make his hand. In a 6-deck game, there are 5x4x6=120 cards that can make his hand. Given that three of the cards are in your hand and the dealers hand, there are now 117/120 of the original amount available to make his hand. Which is almost no effect at all.
The Casino's were forced to start using multiple decks because of the successful onslaught of counters back in the 60's...I don't think they realized at the time that it would also give them a greater edge...If they had, I think they would have done it before.
In a one deck game, and assuming that no face cards are showing, if you have an Ace in front of you and, for purposes of easy fractions, there were 50 cards left in the deck, your chances of getting a blackjack would be 16/50 which is 32%.
With a six deck shoe if there are 310 cards left in the deck, your chances are 96/310 which is 30.96%...This type of favorable condition for the Casino also applies to double down situations...These are part of the reason that a 6 or 8 deck game is more difficult to beat.
For a non counter, and if the tables are slow enough to allow you to do so, you should only play for the last three or four hands before the cut card...That might reduce the Casino's edge down to 0.20%, but that reduction is really just an educated [hopefully] guess on my part.
While less decks have less edge for the house (assuming the same rules), there are some other apects which also help the non-counter. 1 and 2 deck games are usually more crowded, hence the player will receive less hands per hour and therefore lose less. Also, the pitch games are hand shuffled where as more and more shoe games use an automatic shuffler. This also slows down the game for the player. Finally, decks are replaced MUCH more frequently in pitch games (often every hour). All these factors help slow the game down for the non-counter and they will lose less. This is exactly what a non-counter wants--particularly when a generic comp formula is used.