Ha, I remember that Battle! It was a Poison one and I thought I could protect my Magnor using the Zalran Efreet. However, the Efreet died before it could even us its cleansing effect, completely demolishing my strategy ;).

In my view, expensive decks can make a difference, but it is VERY ruleset dependent. For instance, very low mana battles tend to bias towards expensive decks (e.g. epic Beta summoners, Dice legendaries), while e.g. the Rise of the Commons battles naturally allow a good chance for the cheap decks :).