Recalling a five hero game against the Ennead in which the only damage my heroes took was 3 points of damage self-infliced by Legacy's Heroic Interception, I wondered what are the chances that the Ennead wouldn't do damage on their first turn in a five hero game?
Of the 25 Ennead non-character cards, only eight don't immediately deal damage: Two each of Rise To Power, Taste of Immortality, The Desert's Wrath, and The Grave Beckons.
Rise To Power plays another card, so from a probability standpoint, what it's really doing is decreasing the pool of cards to consider, from 25 to 23.
Taste of Immortality neither does damage nor triggers any of the three symbols: Green, Purple, or Red, so that's 2/23 chance of no damage.
The Desert's Wrath has a green symbol. There are five members of the Ennead that will deal damage if triggered by a green symbol, so there is no way to choose five members of the total nine that WON'T deal damage, so The Desert's Wrath will cause at least some damage to be done.
The Grave Beckons has a purple symbol. There are three members of the Ennead that will deal damage if triggered by a purple symbol, so it's possible for the starting members of the Ennead to not deal damage if triggered by a purple symbol: 6/9 * 5/8 * 4/7 * 3/6 * 2/5 = 1/21. The total probability of The Grave Beckons not leading to damage is therefore 2/23 * 1/21.
Adding these together gives 2/23 + (2/23 * 1/21) = 2/23 * (1 + 1/21) = 2/23 * 22/21 = 9.1%.
End result? Nearly a ten percent chance of the Ennead not dealing damage on their first turn in a five hero game. Quite surprising!