but "proving" such a thing is 1) ridiculously complicated and 2) flies in the face of the empirical observations of myself and other players, so I can't help but look askance at this kind of declaration.)
Exactly, it is complicated. For a while I thought about the hypothetical advantages of Immortals and decided to run some numbers to check it out. What I did was plot damage done X turn X quanta generated X enemy shields (-0, -1 or -2 physical dmg reduction). To simplify I modelled pillar drawing as a real number, quanta/turn, which starts at turn 1 with an integer number [1,7]; I did not bother to plot all possible combinations of everything because after a couple of tests I saw the pattern and felt satisfied.
What I noticed as result was that a deck that only plays dragons instead of playing immortals will be even in damage at maximum after 11 turns. That's because in many scenarios of slow quanta starts, playing an early immortal 'speeds' you up, but unless you can win before 11 turns, phase dragons catch up. Actually phase dragons catch up most of the times by turn 5-6, depending on the opening, 11 turns is like a worst-case scenario
A typical game: you will have at least 6 quanta by the 3rd turn, but not 13 (let's say, end turn 1 with 4 pillars, draw a pillar, end turn, draw non-pillar); Therefore by turn 3 you could play an immortal, or you could save quanta and play a dragon later, at turn 4 or the 5; If you actually calculate you will see that it does more damage if you don't play the immortal and save for the phase dragon. Damage contribution of that single immortal played at turn 2 will be (0,0,4,4,4,4,4...) or 4*(n-2); If you delay 2 turns instead while you build quanta and play a Dragon, that dragon damage contribution will be (0,0,0,0,8,8,8,8...) or 8*(n-4), resolving 8n-32 >= 4n-8 ===> n >= 6; That means after turn 6 phase dragon is already doing more damage. After turn 6 the only way for immortals to catch up would be to play another Immortal, in which case balance starts to favor HEAVILY towards dragons because of card cost: the chance that you will draw lots of immortals in succession is small, and as quanta builds up you might as well play dragons instead. You can variate upon this scenario, and you will notice that the results doesn't change, slower starts will only increase that number to 8-11, depending on shields;
This game is statistical, which means it doesn't matter against whom you win a game, as long as your grand total of wins is a larger number. In my experience I found 3 situations where immortals have advantage, and here is why I don't bother
- Against boneyards: more cards, easier to break through, but honestly, its impractical to deck 6 immortals, the deck won't do damage, and decking only 1 or 2 immortals and hoping that them will appear early to help against the boneyard is just wishful thinking. If you want you can wishful think that your enemy will be unlucky on his draws, its the same thing. Also, even immortal is an expensive card compared to what other decks can do to break boneyard, and boneyard is balanced against them. I found to be best to build as solid base of 4-5 dragons and pack a huge punch of dmg when boneyard is down instead of relying on a quicker kill of the shield. And I have shields, so I can afford to wait.
- Against gravity shield: Don't bother losing some here. Against the AI I can win most of the times using a smart PU, but honestly, if the gravity guy is luck to drawn gravity shield early... I doubt even 2 early immortals would win you a game. An armagio alone can soak all your damage. Winning against gravity is either something you seriously plan your deck for or give up... 2 or 3 extra immortals in your deck is just hoping for the good luck to draw 6 pillars and 2 immortals in the first 8 cards... with luck like that you can do it without immortals as well.
- Against quanta denial: sometimes in the very beginning of games against denial decks you will have 6 quanta to play an immortal, but the enemy will soon start pulling out steals/EQ/devourers to keep you from ever reaching 13 to play a dragon. I recognize it would be good to have some immortals here, but honestly I think immortals slow you down so much overall that its better not work bothering for a general-purpose deck.
Where more dragons help, immensely
- Against poison: need DAMAGE
- Against FFQ+Empatic bond: need DAMAGE
- Against dissipation shield: need LOTS OF DAMAGE
lol actually that proof is not mathematical/complicated as you claim it to be
but I do agree that Phase dragons are better than Immortals except when versus gravity shield, FYI if ppl think immortals are better just let it be because it is their loss lol, there is no point of getting flamed by everybody when you are trying to help
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