Poison is an excellent card; in my opinion it is perfectly balanced, it needs neither a buff nor a nerf.
Deadly Poison, however, need a bit of help I think. For starters, I deal more damage by playing two Poisons in two turns than by playing 1 Deadly Poison in one turn (and using 2 Death quanta for both in the process). In the former case, I deal 2 + 2 + ... + 2 + 4 + 4 + ... + 4 damage = 2t + 4(x-t) damage = 4x - 2t damage in x turns, while I deal 3 + 3 + ... + 3 damage = 3x damage in the latter case in the same number of turns. Unless x is less than 2t, the former case accumulates more damage than the second. (I'm assuming t is the number of turns I take to play the second Poison card after I had played the first one.) All this for the same amount of quanta? No thanks, I'll pass.
The same exact argument works if I play 4 Poison versus 2 Deadly Poison and 6 Poison versus 3 Deadly Poison. So how do 6 Poison versus 6 Deadly Poison fare?
Suppose I happen to play 6 Poison in 6 turns, one in each turn. The poison damage accumulated would be 2 + 4 + 6 + 8 + 10 + 12 + 12 + 12 + ..., and all this for just 6 Death quanta. This is the function
P(t) = t^2 + t, if t<7
P(t) = 12t - 30, if t>6
If I happen to play 6 Deadly Poison in 6 turns, one in each turn, the poison damage accumulated would be 3 + 6 + 9 + 12 + 15 + 18 + 18 + 18 + ..., and this for 12 Death quanta. This is the function
D(t) = 1.5t^2 + 1.5t, if t<7
D(t) = 18t - 45, if t>6
Thus, for P(t), the ratio of poison damage per quanta used is
R1(t) = (t^2 + t) / t = t+1, if t<7
R1(t) = (12t - 30) / 6 = 2t - 5, if t>6
This is the sequence 2, 3, 4, 5, 6, 7, 9, 11, ...
For D(t), the ratio of poison damage per quanta used is
R2(t) = (1.5t^2 + 1.5t) / (2t) = 0.75(t+1), if t<7
R2(t) = (18t - 45) / 12 = 1.5t - 3.75, if t>6
This is the sequence 1.5, 2.25, 3, 3.75, 4.5, 5.25, 6.75, 8.25, ...
As you can see, the first sequence always contains larger numbers than the second one for any t. In fact, this will continue for even large values of t, because suppose there was a t such that 1.5t - 3.75 > 2t - 5. This would mean that 5 - 3.75 > 0.5t, or that t < 2.5, which is not possible in our case since the second case only happens when t>6 for both R1(t) and R2(t).
But there's another consideration. Deadly Poison deals more damage in the long run, so it stands to reason that games should be shorter when using it.
Playing against Elders, P(t) would need 11 turns to deal 100 damage, whereas D(t) would need 9 turns (2 less turns).
Playing against Half-Bloods, P(t) would need 15 turns to deal 150 damage, whereas D(t) would need 11 turns (4 less turns).
Playing against False Gods, P(t) would need 20 turns to deal 200 damage, whereas D(t) would need 14 turns (6 less turns).
Thus, in short, Deadly Poison does less poison damage per quanta than Poison does, but finishes the game quicker, especially against HBs and FGs.
Because of this, I think that Deadly Poison should be buffed so that the poison-to-quanta ratio is improved. This can obviously be done by making it require one quantum to cast instead of two, and leaving it to inflict 3 poison damage per turn.
So, what do you think?
(I cannot find the button to post a poll, however the question is simple anyway: do you want Deadly Poison to be buffed by making it cost 1 Death Quantum instead of two, or not?)
