Chronos, despite not meeting the above criterion, is still considered to be an NUA as well, due to the fact that its cost curve is identical to the other NUAs. (NUA cost curve is 2n, with n being equal to the next level.)
There are a total of 15 NUAs: 9 whose effects converge to a certain value, and 6 whose effects are linear.
The converging NUAs never theoretically reach their cap at a finite level. However, because of the fact that the game can only count a certain number of digits, these ancients reach their caps once the effect is within 1/254 (approximately 5.55×10-15%) of the maximum effect.
The value at which the ancient curves to is represented by the number infront of the parenthesis, or the horizontal asymptote. For example, Atman will effectively reach +75% chance of primal bosses when leveled up enough, but will never go above it. According to the formula, it will never reach +75%, but in the game, it will reach its cap, due to the fact that the game only records a certain amount of digits.
The 9 converging ancients are listed below, in order of rate of convergence, are listed below:
|Ancient Name||Image||Effect (n = level)||Level at which maximum effect is reached|
|Chronos||+30(1-e-0.034n) seconds to Boss Fight timers||1101|
|Vaagur||-75((1-e-0.026n)% skill cooldowns||1440|
|Atman||+75(1-e-0.013n)% Chance of Primal Bosses||2880|
|Dogcog||-99.99999999(1-e-0.01n)% Hero Hiring and Level-Up cost||3743|
|Revolc||+96(1-e-0.01n)% Chance of double rubies from clickable treasures,|
|Fortuna||+100(1-e-0.0025n)% Chance of 10× gold||14972|
|Kumawakamaru||-100(1-e-0.0025n) monsters required to advance to the next level (minimum 2 monsters per zone)|
|Bubos||-5(1-e-0.002nn) Monsters Worth of Boss Life (minimum 5 monsters)||18715|
|Dora||+9900(1-e-0.002n)% more Treasure Chests (maximum 9900%)|
The non-converging NUAs have no effect cap, but have a linear effect. All six NUAs are listed below. Note that each one of them adds to the duration of a certain skill, by +2 seconds per level..