While we're working out odds, my deck of the moment has 12/40 pillars, and I just had back-to-back games with no pillars in my opening 8. Woo! By my quick math, there is a 4% chance of having the first 8 cards with no pillars from that deck, so assuming two mulligans, that is a 1/374825 chance. (I probably did not get either mulligan, if I understand how that works, because the deck has upgraded Sundials.)