I'm a bit disappointed in not finishing April A-Z, but at least it gave me some ideas for blog topics. Hopefully I can keep things up in the coming weeks.
In the meantime, I have something that might be of use to the gaming public in general. I was looking to create a table for determining the level of magic-user and cleric spells on things like spell scrolls and items like a ring of spell storing. Specifically, I was looking for a table where the chance of getting a lower level spell was exponentially greater than getting a higher level one. Being a bit of a math geek, I actually came up with a mathematical formula for creating this kind of table:
For those not familiar with calculus; this formula is the sum of all iterations of x to the ith power, where i is all integers from 1 to n, with the sum equaling 100. The lowercase n represents the highest level of spell; nine for mages, seven for clerics. My goal was to use this formula to find the value of x, and develop my tables from there. The only drawback that I have with this is that I have to figure out the ranges in reverse, for a 1st level mage spell I use x to the 9th, not x to the 1st.
(Thanks to Gratuitous Saxon Violence for pointing out a slight error in my placement of i and n in my summation. It has been fixed.)
Now at this point, I realize that I have lost most of you. If I have learned anything from April A-Z is that most of my readers and followers are literary types. So I imagine that you are all reading this going, "David, what the hell are you talking about?" or "Get with the damn tables already!" All I can say is, trust me the math works! Here you go.
(I re-ran the calculations for the tables on a spreadsheet. The following should be a more accurate representation of
| Mage (x=1.476) | d% Roll | Cleric (x=1.708) |
| 01-33 34-56 57-71 72-81 82-88 89-93 94-96 97-99 100 | First Second Third Fourth Fifth Sixth Seventh Eighth Ninth | 01-42 43-67 68-82 83-90 91-95 96-98 99-100 |
I think you need to flip your i and n on the Sigma. Otherwise you have n=1, and x^n = 100; therefore x=100.
ReplyDeleteD'oh! You're right. In my defense, it has been seven years since I took Calculus II.
ReplyDeleteI'll get that fixed right away.