The official GemStone IV encyclopedia.
A chart used to determine the number of ranks required to attain a bonus, based on an incremental additive scale. It is used particularly for Lore bonuses in certain spells. To use the chart all you need to know is the number of skill ranks (not skill bonus) needed to first see a bonus. This value is known as the Seed.
Calculation
| X
|
Bonus
|
| Y
|
Seed
|
| Z
|
Ranks Needed
|
X = (sqrt(4Y^2 - 4Y + 8Z + 1) - 2Y + 1) / 2
Y = -(X^2 - X - 2Z) / 2X
Z = (X^2 - X) / 2 + XY
Summation Chart
| Bonus (X)
|
Seed (Y)
|
Ranks
Needed
(Z)
|
| 1
|
1
|
2
|
3
|
4
|
5
|
6
|
7
|
8
|
9
|
10
|
| 2
|
3
|
5
|
7
|
9
|
11
|
13
|
15
|
17
|
19
|
21
|
| 3
|
6
|
9
|
12
|
15
|
18
|
21
|
24
|
27
|
30
|
33
|
| 4
|
10
|
14
|
18
|
22
|
26
|
30
|
34
|
38
|
42
|
46
|
| 5
|
15
|
20
|
25
|
30
|
35
|
40
|
45
|
50
|
55
|
60
|
| 6
|
21
|
27
|
33
|
39
|
45
|
51
|
57
|
63
|
69
|
75
|
| 7
|
28
|
35
|
42
|
49
|
56
|
63
|
70
|
77
|
84
|
91
|
| 8
|
36
|
44
|
52
|
60
|
68
|
76
|
84
|
92
|
100
|
108
|
| 9
|
45
|
54
|
63
|
72
|
81
|
90
|
99
|
108
|
117
|
126
|
| 10
|
55
|
65
|
75
|
85
|
95
|
105
|
115
|
125
|
135
|
145
|
| 11
|
66
|
77
|
88
|
99
|
110
|
121
|
132
|
143
|
154
|
165
|
| 12
|
78
|
90
|
102
|
114
|
126
|
138
|
150
|
162
|
174
|
186
|
| 13
|
91
|
104
|
117
|
130
|
143
|
156
|
169
|
182
|
195
|
208
|
| 14
|
105
|
119
|
133
|
147
|
161
|
175
|
189
|
203
|
217
|
231
|
| 15
|
120
|
135
|
150
|
165
|
180
|
195
|
210
|
225
|
240
|
255
|
| 16
|
136
|
152
|
168
|
184
|
200
|
216
|
232
|
248
|
264
|
280
|
| 17
|
153
|
170
|
187
|
204
|
221
|
238
|
255
|
272
|
289
|
|
| 18
|
171
|
189
|
207
|
225
|
243
|
261
|
279
|
297
|
|
| 19
|
190
|
209
|
228
|
247
|
266
|
285
|
|
| 20
|
210
|
230
|
250
|
270
|
290
|
|
| 21
|
231
|
252
|
273
|
294
|
|
| 22
|
253
|
275
|
297
|
|
| 23
|
276
|
299
|
|
| 24
|
300
|
|
Resources
http://www.play.net/gs4/info/spells/lores.asp#Summation - The summation chart