Different casinos (both live and online) endorse versions of blackjack played with either a single deck or multiple decks. At a single deck game there will only be one deck shuffled and played with, whereas at a multi-deck game eight decks are being played with simultaneously. It would seem that because the cards are still in the same proportions the odds would be the same, but this is not true. A single deck game has a 0.6% advantage over a multi-deck game and a 0.3% advantage over a double-deck. Although these differences seem minute, over time a small difference adds up. Disparities in house advantages can be narrowed down to several differences in your odds.
When you play blackjack online you can find out the shoe size (how many decks) if you look at the rules for the game.
Firstly, your chances of getting blackjack decrease with more decks. While a natural blackjack will occur once in every 20.7 hands in a single deck game, a natural will only occur once every 21.1 hands in a multi-hand game. Though your chance of getting blackjack decreases, the chance of the dealer getting blackjack when you do increases. This is due to the fact that the effect of removing your blackjack cards from the deck is smaller when there are more decks. In a single-deck game the odds of the dealer repeating your blackjack is once every 27.2 hands, but in a multi-deck game the chance of the dealer repeating your blackjack is once in every 21.9 hands.
Second, the odds when doubling down in beneficial circumstances are hurt. For example, if you have a 3 and an 8 in hand you would normally double down. However, the odds of getting a 10-card to complete your hand of 11 are worsened. In a single-deck game you have a 32.65% chance of getting a 10-card, but in a multi-deck game you have a 31.07% chance. Although the number of 10-cards in the deck remains proportional, the odds are decreased with more decks due to clones of the cards you are holding, i.e. there are more 3 of spades in a multi-deck than in a single-deck game.
Lastly, your rates of victory when standing with stiff hands (12 through 16) are worsened. This is due to the increase in small cards in the deck. Because house rules force dealers to hit more often than players, this increase leads to less dealer busts.
As you can see, more decks leads to worse and worse odds for the player and better odds for the house. The reduction of odds is due to a variety of causes including less naturals for the player and more pushes for the house, worse doubling down odds, and a lower frequency of dealer busts.