User:ABELIAN

An intermittent player of GemStone, with a majority of their play concentrated shortly after the de-ICEing.

Enchant page scratch

Marginal Enchant Difficulty Modifier Formula

The difficulty in enchanting an item to a target enchant value (e.g. from +25 to +26) is computed as the sum of the base difficulty determined by a Bardic Loresong and a marginal enchanting difficulty modifier (mED) that is a function of the target enchant value, i.e., base + mED(x). A wizard's skills are assessed against this composite difficulty. The marginal difficulty modifier makes it increasingly difficult to enchant an item to higher values.

For a given enchant value ${\textstyle 0\leq x\leq 50}$ define the Cumulative Enchant Difficulty (cED) to be

$$cED(x):={\biggl \lfloor }{\frac {(x-2)^{2}}{9}}{\biggr \rfloor },$$

i.e., the truncation of the quadratic $(1/9)\cdot (x-2)^{2}$.

Then the marginal Enchant Difficulty modifier mED(x) applied when enchanting to the target enchant value x from current enchant value (x-1) is given by

$$mED(x):=cED(x)-cED(x-1)={\biggr \lfloor }{\frac {(x-2)^{2}}{9}}{\biggr \rfloor }-{\biggr \lfloor }{\frac {(x-3)^{2}}{9}}{\biggr \rfloor }={\biggl \lfloor }{\frac {2x-5}{9}}{\biggl \rfloor }+{\begin{cases}1,&x\equiv 1,2,5,8\mod 9\\0,&{\text{otherwise.}}\end{cases}}$$

Note that since truncation is applied to the cumulative enchant difficulty, the marginal difficulty is not monotonically increasing. In particular, mED actually decreases when the target enchant $x\equiv 0,6\mod 9$.

Example

An item has a current enchant of +25. Then the marginal Enchant Difficulty to enchant to the target value +26 is

$$mED(26)={\biggl \lfloor }{\frac {(2\cdot 26)-5}{9}}{\biggr \rfloor }+1=\lfloor 47/9\rfloor +1=5+1=6.$$

as $26\equiv -1\equiv 8\mod 9$. We can also compute this directly from the definition via

$$mED(26):={\biggr \lfloor }{\frac {(26-2)^{2}}{9}}{\biggr \rfloor }-{\biggr \lfloor }{\frac {(25-2)^{2}}{9}}{\biggr \rfloor }=\lfloor 576/9\rfloor -\lfloor 529/9\rfloor =64-58=6.$$

Thus there is a +6 difficulty penalty modifier applied to the base diffuclty (as determined by a Loresong).

Enchant Difficulty Modifier Tables

Below we present the truncated linear estimates (first table) and exact marginal Enchant Difficulty modifier values for target enchant values ${\textstyle 0\leq x\leq 50}$.