The release of Valley of the Ancients has reignited the DO discussion. I travelled through the flux and met the Ancient Gods, they instructed me the ways of the Offering. I am the prophet that brings you the true solution from the Gods themselves. But first we must lay out the implications of the current VotA and DO implementations.
The situation before the release of VotA involved 2 problems with DO
1. Missing without having another shrine to play on turn 1 likely game loss.
2. Missing loses you a card from hand.
VotA fixes one of these problems, and that is problem 2. So I believe that VotA is definitely a step in the right direction. Problem 1 is only half solved, however. In case of miss without other shrine, VotA reduces the penatly from having 1 less mana the entire game and 1 less card, to merely having 1 less card. (a normal shrine would have redrawn) There are special cases of decks that can use the neutral level (and thus not lose a card) but those decks will likely still suffer from a disrupted mana curve, as neutral levels aren't very useful early.
Another problem with VotA, is that it shuffles the deck upon DO miss, which disrupts deck manipulation strategies, where the player tries to use DO to move a certain card close to the top of the deck. Full deck shuffling exists only in SW to keep the idea alive that one day the game could become a physical card game. VotA shuffling is completely unnecessary considering we are in a digital space. Remove the shuffling, or just rework DO, so VotA is not needed.
Turn 1 is a special case when it comes to DO risk. It is the only turn where you didn't have a chance to DO earlier. It is thus also the only turn where there is an increased chance to not have a shrine played at the end of the turn. (If not using VotA) I present you a new DO/mulligan system that fixes both the discard problem, while also more completely fixing the turn 1 problem, all the while not involving the card counting disruption, nor disrupting other game aspects like the necessity to play a healthy number and distribution of shrines in a deck. A nice side effect is that it will stop people from adding cards to their deck as well, and thus unmilling themselves, without running cards for it. (How great is the wisdom of the Ancient Gods?)
Fixing the discard problem: Simple solution is to return the offered card.
Fixing the turn 1 problem: Create a DO step before the end of the mulligan phase.
The mulligan phase would look like this: You are presented 7 cards, and as normally, you must choose between keeping or redrawing. Next you may perform a DO. (Or not, if you don't want to). When both players finish these steps, the game continues normally by starting turn 1 of the first player.
This way, the player will always have 2 opportunities to DO before being mana screwed. One at the end of last turn, and one this turn. On turn 1, the DO of the mulligan step would be the DO of "last turn".
This drops the chance of being mana screwed on turn 1 from ~0.8% to ~0.065% for an 18 shrine deck, and from ~0.56% to ~0.04% for a 19 shrine deck.
Calculated using {(60-n)!/([60-n-k]!*k!)} / {60!/([60-k]!*k!)} Where n is the number of shrines, and k is 12 or 17, depending on DO system. (7 in starting hand + 5 from DO, or +10 from DO) Note that these odds are smaller for the 2nd player, who draws 1 extra card.
in short:
This maintains the need to play a good number of shrines in your deck, as you are still mana screwed by 2 consecutive misses, and multicolor decks must get a good balance of colors.
This almost entirely eliminates mana screw on turn 1.
This removes the discard problem.
This removes the player's ability to prevent deckout using DO.
If you really want to get rid of T1 screw completely, design VotA to interface with this new system.
VotA's text would be changed to "When you miss DO, instead of being returned your offered card, you may search a single copy of VotA from your deck, and place it in your hand instead. Shuffle your deck."
Not running VotA would be a viable option under the rules of this new system. The old rules make VotA a must include that disrupts deck manipulation strategies. The value of a single VotA in your deck that prevents you from discarding is incredible. Nobody will want to play without that. (well..)