I'm like 95% sure that the cards not played get put on the bottom of the deck, which helps you not draw them the very next turn, but since everything you play shuffles the deck it won't help for future turns. This also means that cards played in the current turn have a chance of being drawn the very next turn. i.e. don't play chickens if your deck is loaded with value.that's not how it works.
you play the chicken and a copy goes into your deck.
you don't play the chicken and it goes back into your deck when your hand shuffles back in at the end of the turn.
either way you have a chicken in your deck at the end of your turn.
if you time rewindered the chicken, or shadowstepped it or something then you would get more chickens in your deck.
Also, starting decklists are something like, 3 chickens, 2 coins, 1 attack part (2 if first player), 1 toughness part.
The only way to thin cards out of the deck is via discard, which makes fel reaver really good if you can drop him early and kill off your chickens. Mukla also nice if you have board control because you flood their deck with bananas and they're useless if they have nothing to buff.