A card with a per turn cost can be played earlier thus having a higher resilience than its one time cost counterpart.
Assume you need 3 turns to get 10 for a dragon
In an average game of 10 turns, the dragon is in play for 7 turns.
so it is 1 for an average of 7 damage per turn throughout the whole game.
If the dragon only needs an upkeep cost but no playing cost , it can be played at the first turn.
so the dragon can be on field for 10 turns, and deal 10 damage per turn.
Hence 10/7 = [C]/1, and [C] = 1.42
So your theory is that the per turn cost [Z] is balanced when it equals Casting Cost / (Normal Duration + Turns required to obtain casting cost)
I think this a good theory. However it did not count the increased duration of Crimson Dragon towards the cost. As it turns out the increased value should be countered by having to pay the cost longer.
10/5 is balanced with 14/7
14/7 = [C]/1
[C] = 2
So we return to the theory that:
per turn cost [Z] is balanced when it equals Casting Cost / (Normal Duration)
How long is the Normal Duration [N] for a standard permanent like Shard of Gratitude?
Is it similar to 6 turns?
Unstable Hourglass:
Casting Cost [Y] / Normal Duration [N] = per turn cost [Z]
per turn cost [Z] * 2 = per 2 turns cost [Z
2]
per 2 turns cost [Z
2] -1 = quanta upkeep cost per 2 turns +1 card per 2 turns
9 / 6 = 1.5
1.5 * 2 = 3
3-1 = 2
+ 1 draw
Unstable Hourglass
Casting Cost: 1
+ 1 draw
Activation Cost: 1
You obviously will want to inflate the casting cost slightly to pay for the anti deckout. Currently antideckout costs 3
per turn.
Unstable Hourglass
Casting Cost: 4
+ 1 draw
Activation Cost: 1
Interesting coincidence. Your pretheoretical estimation was accurate. This is a good sign.