ADOM Guidebook
Appendix - Amulets of Order - Mechanics
AMULETS OF ORDER - MECHANICS BY MALTE HELMERT
1. What is alignment?
=====================
Each PC has an "alignment score", which can be queried by reading a
scroll of balance. It can be negative (if there are black stones on the
scale) or positive (if there are white stones on the scale), or zero (if
the scale is balanced). The number of stones on the scale determines the
absolute value of the alignment score, so 3000 black stones = -3000,
1000 white stones = +1000.
The score corresponds to alignments as follows:
C-: -10000 ... -5000
C : -4999 ... -1251
CN: -1250 ... -1000
NC: -999 ... -750
N-: -749 ... -126
N=: -125 ... +125
N+: +126 ... +749
NL: +750 ... +999
LN: +1000 ... +1250
L : +1251 ... +4999
L+: +5000 ... +6000
Scores lower than -10000 or higher than +6000 are not possible.
2. How do amulets of order work?
================================
Amulets of order, if equipped, add a random amount of points to the PC's
alignment score at regular intervals.
* Blessed amulets of order are activated every 10 turns (whenever the
turn counter is a multiple of 10).
* Uncursed amulets of order are activated every 20 turns (whenever the
turn counter is a multiple of 20).
* Cursed amulets of order are activated every 50 turns (whenever the
turn counter is a multiple of 50).
This is based on the *turn counter*, not on game time, so if you want
the alignment change to happen quickly, you'd better spend your turns
doing fast things (like walking around in a dungeon in blessed
seven-league boots) and not wait around on the wilderness map.
Specifically, this should give you a rough idea of how much time 1000
turns take for a PC with speed 100:
- ~10 hours if the PC is resting or walking without seven league boots
(not on the wilderness map).
- ~5 hours if the PC is walking (*not resting*) with blessed seven
league boots.
- ~1000 hours if the PC is resting or walking in the Wilderness without
seven league boots (more if terrain is difficult).
After the amulet has added points to the alignment score of the PC, a
message is displayed if the PC is not lawful (i.e. his *new* alignment
score is +999 or less). Note that this happens even when the amount
added to the alignment score is zero, so getting the message is not an
indication of the amulet being effective.
If the PC is now neutral, the message is:
"You notice an itching feeling around your neck."
If the PC is now chaotic, the message is:
"You feel a burning pain around your neck!"
In the latter case, the PC also loses 1d3 hit points.
To come up with this formula and verify it, I recorded the exact amount
of damage 1000 times for various PCs. In each case, the relative
frequencies of ones, twos and threes match a 1d3 roll:
uncursed amulet, Level 1, Raven: 1: 328, 2: 351, 3: 321
uncursed amulet, Level 50, Raven: 1: 343, 2: 321, 3: 336
uncursed amulet, Level 1, Unicorn: 1: 328, 2: 359, 3: 313
uncursed amulet, Level 1, Tree: 1: 354, 2: 350, 3: 296
blessed amulet, Level 1, Raven: 1: 340, 2: 334, 3: 326
cursed amulet, Level 1, Raven: 1: 335, 2: 343, 3: 322
The complicated thing, then, is determining by what amount the PC's
alignment score is changed upon activation of the amulet. This is the
topic of the next section.
3. By what amount do amulets of order change the PC's alignment?
================================================================
This is influenced by three factors: blessed/uncursed/cursed status of
the amulet, birth sign of the PC, and level of the PC. In
pre-experiments, I noticed that only the Tree birth sign behaves
differently from the norm, so only two birth signs were tested, Raven
for the baseline and Tree for the special case.
In total, there are 3 * 2 * 50 = 300 different combinations of those
features. For each of those, I repeated the following procedure a
thousand times, for a total of 300,000 data points:
1. Read a blessed scroll of balance.
2. Wait until the amulet is activated for the next time
(i.e. until the turn counter is a multiple of 10/20/50, depending
on the blessed/uncursed/cursed status of the amulet).
3. Read a blessed scroll of balance and record the change in the
alignment score.
I first had a close look at a few data points and formulated a
hypothesis from looking at those. This hypothesis perfectly matched the
additional data I obtained later, so I think it is correct. The formula
is as follows:
1. Roll 1d3 for a cursed amulet, 1d6 for an uncursed amulet, 1d10 for
a blessed amulet.
2. If this value is greater than 1, subtract 1 if the PC was born under
the Tree birth sign. The Tree birth sign has no effect if the roll
already was 1.
3. Multiply this by (51 - level) / 50, rounding the result down.
This is the final amount which is added to the PC's alignment score.
Using this information, we can calculated by how many points the PC's
alignment is changed on average for a given combination of
blessed/uncursed/cursed status, birth sign, and PC level.
As an example, consider an uncursed amulet and a PC born under the Tree
birth sign with an experience level of 15.
If the initial roll is a 1 or 2, we get 1 * 36 / 50 rounded down = 0.
If the initial roll is a 3, we get 2 * 36 / 50 rounded down = 1.
If the initial roll is a 4, we get 3 * 36 / 50 rounded down = 2.
If the initial roll is a 5, we get 4 * 36 / 50 rounded down = 2.
If the initial roll is a 6, we get 5 * 36 / 50 rounded down = 3.
So we get 0 with probability 2/6, 1 with probability 1/6,
2 with probability 2/6, and 3 with probability 1/6, resulting in an
expected value of 8/6 or 4/3 = 1.3333... .
So blessed amulets are more effective than uncursed amulets (and even
more than cursed ones) on two accounts: They are activated more often,
and they result in a bigger change of alignment when activated.
The following tables show the expected change of alignment for the
different types of amulet, birth signs and player levels after 600 turns
have passed, so that both factors are taken into account. I chose 600
because it is the smallest number such that all quantities in the table
are integers.
[Note: These tables could be better presented as a single table by using
rows for the levels and columns for the six cases. If anybody wants, I
can prepare such a table after the weekend. Right now, I don't have the
time.]
Blessed amulet, any birth sign except Tree:
PC level: 1 2-6 7 8 9 10-11 12
Change in alignment: 330 270 258 252 246 240 228
PC level: 13 14-15 16 17 18-19 20-21 22
Change in alignment: 222 210 204 198 180 174 162
PC level: 23 24-26 27-28 29 30-31 32 33-34
Change in alignment: 156 150 120 114 108 96 90
PC level: 35-36 37-38 39 40-41 42 43 44
Change in alignment: 72 60 48 42 30 24 18
PC level: 45 46 47-50
Change in alignment: 12 6 0
So in this case, which is the most important one, the amulet stops
working at PC level 47. However, even at slightly lower levels its
effect is marginal, so that the amulet gets near useless somewhere in
the 40s. For example, at level 46 it would take 500,000 turns to get
from N= to L+.
Uncursed amulet, any birth sign except Tree:
PC level: 1 2-9 10-11 12-13 14-17 18-21 22-26
Change in alignment: 105 75 70 65 60 50 45
PC level: 27-31 32-34 35-38 39-41 42 43-50
Change in alignment: 30 25 15 10 5 0
Cursed amulet, any birth sign except Tree:
PC level: 1 2-17 18-26 27-34 35-50
Change in alignment: 24 12 8 4 0
Blessed amulet, Tree:
PC level: 1 2-6 7 8 9 10-11 12
Change in alignment: 276 216 210 204 198 192 186
PC level: 13 14-15 16-17 18-19 20-21 22 23
Change in alignment: 180 168 162 144 138 132 126
PC level: 24-26 27-28 29 30-31 32 33-34 35-36
Change in alignment: 120 96 90 84 78 72 54
PC level: 37-38 39 40-41 42 43 44 45
Change in alignment: 48 36 30 24 18 12 6
PC level: 46-50
Change in alignment: 0
Uncursed amulet, Tree:
PC level: 1 2-11 12-13 14-17 18-21 22-26 27-31
Change in alignment: 80 50 45 40 35 30 20
PC level: 32-34 35-38 39-41 42-50
Change in alignment: 15 10 5 0
Cursed amulet, Tree:
PC level: 1 2-26 27-50
Change in alignment: 16 4 0
4. The data
===========
If anybody feels like looking at the data and coming up with their own
hypotheses, here it is. The "avg." column doesn't list the actual
averages of the data points, but rather the "expected" average according
to the hypothesized formula.
A. blessed amulet of order
--------------------------
Amulet changes alignment every 10 turns.
Formula: 1d10 * (51 - level) / 50 (rounded down)
+0 +1 +2 +3 +4 +5 +6 +7 +8 +9 +10 "avg."
Level 1: 0 104 98 108 106 77 80 92 106 121 108 5.50
Level 2: 87 116 81 109 112 94 91 104 105 101 0 4.50
Level 3: 98 90 101 96 111 103 110 96 106 89 0 4.50
Level 4: 134 101 93 96 98 124 95 91 87 81 0 4.50
Level 5: 112 95 103 103 97 102 98 72 106 112 0 4.50
Level 6: 97 98 109 94 99 106 92 95 100 110 0 4.50
Level 7: 99 106 85 101 91 96 109 194 119 0 0 4.30
Level 8: 97 109 98 117 113 98 162 95 111 0 0 4.20
Level 9: 102 84 105 100 101 190 111 89 118 0 0 4.10
Level 10: 112 98 100 99 205 103 105 89 89 0 0 4.00
Level 11: 100 97 115 77 189 109 108 110 95 0 0 4.00
Level 12: 92 87 101 204 96 105 114 201 0 0 0 3.80
Level 13: 106 103 105 182 103 117 196 88 0 0 0 3.70
Level 14: 112 109 202 92 104 200 79 102 0 0 0 3.50
Level 15: 98 112 225 94 85 201 98 87 0 0 0 3.50
Level 16: 93 105 195 97 201 91 111 107 0 0 0 3.40
Level 17: 106 91 183 98 204 90 228 0 0 0 0 3.30
Level 18: 100 167 125 183 95 215 115 0 0 0 0 3.00
Level 19: 95 216 98 176 101 202 112 0 0 0 0 3.00
Level 20: 95 204 89 205 212 101 94 0 0 0 0 2.90
Level 21: 81 200 111 189 201 112 106 0 0 0 0 2.90
Level 22: 103 215 179 103 213 187 0 0 0 0 0 2.70
Level 23: 113 201 210 191 95 190 0 0 0 0 0 2.60
Level 24: 106 210 176 203 195 110 0 0 0 0 0 2.50
Level 25: 98 214 191 199 178 120 0 0 0 0 0 2.50
Level 26: 97 202 214 203 188 96 0 0 0 0 0 2.50
Level 27: 210 196 194 215 185 0 0 0 0 0 0 2.00
Level 28: 200 199 204 212 185 0 0 0 0 0 0 2.00
Level 29: 203 202 199 298 98 0 0 0 0 0 0 1.90
Level 30: 199 191 311 197 102 0 0 0 0 0 0 1.80
Level 31: 229 188 295 194 94 0 0 0 0 0 0 1.80
Level 32: 174 319 208 299 0 0 0 0 0 0 0 1.60
Level 33: 190 327 282 201 0 0 0 0 0 0 0 1.50
Level 34: 191 299 317 193 0 0 0 0 0 0 0 1.50
Level 35: 292 300 305 103 0 0 0 0 0 0 0 1.20
Level 36: 285 285 318 112 0 0 0 0 0 0 0 1.20
Level 37: 320 393 287 0 0 0 0 0 0 0 0 1.00
Level 38: 305 398 297 0 0 0 0 0 0 0 0 1.00
Level 39: 394 396 210 0 0 0 0 0 0 0 0 0.80
Level 40: 403 496 101 0 0 0 0 0 0 0 0 0.70
Level 41: 406 504 90 0 0 0 0 0 0 0 0 0.70
Level 42: 506 494 0 0 0 0 0 0 0 0 0 0.50
Level 43: 616 384 0 0 0 0 0 0 0 0 0 0.40
Level 44: 712 288 0 0 0 0 0 0 0 0 0 0.30
Level 45: 781 219 0 0 0 0 0 0 0 0 0 0.20
Level 46: 907 93 0 0 0 0 0 0 0 0 0 0.10
Level 47: 1000 0 0 0 0 0 0 0 0 0 0 0.00
Level 48: 1000 0 0 0 0 0 0 0 0 0 0 0.00
Level 49: 1000 0 0 0 0 0 0 0 0 0 0 0.00
Level 50: 1000 0 0 0 0 0 0 0 0 0 0 0.00
B. uncursed amulet of order
---------------------------
Amulet changes alignment every 20 turns.
Formula: 1d6 * (51 - level) / 50 (rounded down)
+0 +1 +2 +3 +4 +5 +6 "avg."
Level 1: 0 171 150 176 151 172 180 3.50
Level 2: 174 158 172 159 175 162 0 2.50
Level 3: 190 177 167 160 143 163 0 2.50
Level 4: 174 159 181 153 164 169 0 2.50
Level 5: 187 146 152 169 170 176 0 2.50
Level 6: 171 158 174 163 160 174 0 2.50
Level 7: 179 169 158 150 165 179 0 2.50
Level 8: 164 147 186 160 163 180 0 2.50
Level 9: 200 144 184 148 174 150 0 2.50
Level 10: 163 148 167 174 348 0 0 2.33
Level 11: 160 181 160 157 342 0 0 2.33
Level 12: 180 172 158 307 183 0 0 2.17
Level 13: 164 185 151 337 163 0 0 2.17
Level 14: 138 166 351 166 179 0 0 2.00
Level 15: 163 183 341 163 150 0 0 2.00
Level 16: 152 178 356 142 172 0 0 2.00
Level 17: 156 168 337 161 178 0 0 2.00
Level 18: 159 343 161 337 0 0 0 1.67
Level 19: 160 348 174 318 0 0 0 1.67
Level 20: 151 347 163 339 0 0 0 1.67
Level 21: 192 322 158 328 0 0 0 1.67
Level 22: 151 336 334 177 0 0 0 1.50
Level 23: 180 353 292 175 0 0 0 1.50
Level 24: 182 344 316 158 0 0 0 1.50
Level 25: 172 319 337 172 0 0 0 1.50
Level 26: 174 302 349 175 0 0 0 1.50
Level 27: 337 340 323 0 0 0 0 1.00
Level 28: 353 302 345 0 0 0 0 1.00
Level 29: 363 319 318 0 0 0 0 1.00
Level 30: 321 342 337 0 0 0 0 1.00
Level 31: 362 318 320 0 0 0 0 1.00
Level 32: 317 523 160 0 0 0 0 0.83
Level 33: 319 521 160 0 0 0 0 0.83
Level 34: 345 481 174 0 0 0 0 0.83
Level 35: 479 521 0 0 0 0 0 0.50
Level 36: 499 501 0 0 0 0 0 0.50
Level 37: 494 506 0 0 0 0 0 0.50
Level 38: 501 499 0 0 0 0 0 0.50
Level 39: 647 353 0 0 0 0 0 0.33
Level 40: 645 355 0 0 0 0 0 0.33
Level 41: 647 353 0 0 0 0 0 0.33
Level 42: 833 167 0 0 0 0 0 0.17
Level 43: 1000 0 0 0 0 0 0 0.00
Level 44: 1000 0 0 0 0 0 0 0.00
Level 45: 1000 0 0 0 0 0 0 0.00
Level 46: 1000 0 0 0 0 0 0 0.00
Level 47: 1000 0 0 0 0 0 0 0.00
Level 48: 1000 0 0 0 0 0 0 0.00
Level 49: 1000 0 0 0 0 0 0 0.00
Level 50: 1000 0 0 0 0 0 0 0.00
C. cursed amulet of order
-------------------------
Amulet changes alignment every 20 turns.
Formula: 1d3 * (51 - level) / 50 (rounded down)
+0 +1 +2 +3 "avg."
Level 1: 0 338 308 354 2.00
Level 2: 316 352 332 0 1.00
Level 3: 325 331 344 0 1.00
Level 4: 322 368 310 0 1.00
Level 5: 336 323 341 0 1.00
Level 6: 349 334 317 0 1.00
Level 7: 330 355 315 0 1.00
Level 8: 343 324 333 0 1.00
Level 9: 325 346 329 0 1.00
Level 10: 317 340 343 0 1.00
Level 11: 319 335 346 0 1.00
Level 12: 336 315 349 0 1.00
Level 13: 310 348 342 0 1.00
Level 14: 325 326 349 0 1.00
Level 15: 364 309 327 0 1.00
Level 16: 357 339 304 0 1.00
Level 17: 341 340 319 0 1.00
Level 18: 367 633 0 0 0.67
Level 19: 336 664 0 0 0.67
Level 20: 333 667 0 0 0.67
Level 21: 327 673 0 0 0.67
Level 22: 317 683 0 0 0.67
Level 23: 335 665 0 0 0.67
Level 24: 324 676 0 0 0.67
Level 25: 351 649 0 0 0.67
Level 26: 355 645 0 0 0.67
Level 27: 659 341 0 0 0.33
Level 28: 690 310 0 0 0.33
Level 29: 665 335 0 0 0.33
Level 30: 671 329 0 0 0.33
Level 31: 645 355 0 0 0.33
Level 32: 659 341 0 0 0.33
Level 33: 660 340 0 0 0.33
Level 34: 716 284 0 0 0.33
Level 35: 1000 0 0 0 0.00
Level 36: 1000 0 0 0 0.00
Level 37: 1000 0 0 0 0.00
Level 38: 1000 0 0 0 0.00
Level 39: 1000 0 0 0 0.00
Level 40: 1000 0 0 0 0.00
Level 41: 1000 0 0 0 0.00
Level 42: 1000 0 0 0 0.00
Level 43: 1000 0 0 0 0.00
Level 44: 1000 0 0 0 0.00
Level 45: 1000 0 0 0 0.00
Level 46: 1000 0 0 0 0.00
Level 47: 1000 0 0 0 0.00
Level 48: 1000 0 0 0 0.00
Level 49: 1000 0 0 0 0.00
Level 50: 1000 0 0 0 0.00
D. blessed amulet of order, Tree birth sign
-------------------------------------------
Amulet changes alignment every 10 turns.
Formula: max(1, 1d10-1) * (51 - level) / 50 (rounded down)
+0 +1 +2 +3 +4 +5 +6 +7 +8 +9 "avg."
Level 1: 0 187 91 115 106 122 103 90 92 94 4.60
Level 2: 216 91 104 106 101 96 83 113 90 0 3.60
Level 3: 219 92 107 93 85 114 90 102 98 0 3.60
Level 4: 189 106 96 107 101 104 117 95 85 0 3.60
Level 5: 197 101 100 108 87 101 94 121 91 0 3.60
Level 6: 194 107 105 119 95 95 101 91 93 0 3.60
Level 7: 197 107 98 100 101 77 103 217 0 0 3.50
Level 8: 201 99 100 90 93 117 211 89 0 0 3.40
Level 9: 173 95 117 120 115 199 92 89 0 0 3.30
Level 10: 197 102 104 93 194 105 95 110 0 0 3.20
Level 11: 186 86 107 141 188 99 88 105 0 0 3.20
Level 12: 191 97 92 214 102 112 103 89 0 0 3.10
Level 13: 194 87 109 191 117 108 194 0 0 0 3.00
Level 14: 217 97 211 98 101 185 91 0 0 0 2.80
Level 15: 192 94 200 102 106 208 98 0 0 0 2.80
Level 16: 210 80 222 96 204 94 94 0 0 0 2.70
Level 17: 178 90 220 113 206 95 98 0 0 0 2.70
Level 18: 214 202 98 200 98 188 0 0 0 0 2.40
Level 19: 194 215 98 182 93 218 0 0 0 0 2.40
Level 20: 209 184 91 210 208 98 0 0 0 0 2.30
Level 21: 184 225 103 207 182 99 0 0 0 0 2.30
Level 22: 208 206 172 107 199 108 0 0 0 0 2.20
Level 23: 196 195 192 199 101 117 0 0 0 0 2.10
Level 24: 183 205 218 195 199 0 0 0 0 0 2.00
Level 25: 190 170 203 221 216 0 0 0 0 0 2.00
Level 26: 204 204 203 204 185 0 0 0 0 0 2.00
Level 27: 292 209 200 189 110 0 0 0 0 0 1.60
Level 28: 308 186 214 196 96 0 0 0 0 0 1.60
Level 29: 300 204 199 297 0 0 0 0 0 0 1.50
Level 30: 306 201 296 197 0 0 0 0 0 0 1.40
Level 31: 293 211 294 202 0 0 0 0 0 0 1.40
Level 32: 298 306 194 202 0 0 0 0 0 0 1.30
Level 33: 280 298 314 108 0 0 0 0 0 0 1.20
Level 34: 330 274 269 127 0 0 0 0 0 0 1.20
Level 35: 416 281 303 0 0 0 0 0 0 0 0.90
Level 36: 371 298 331 0 0 0 0 0 0 0 0.90
Level 37: 393 396 211 0 0 0 0 0 0 0 0.80
Level 38: 416 371 213 0 0 0 0 0 0 0 0.80
Level 39: 486 417 97 0 0 0 0 0 0 0 0.60
Level 40: 495 505 0 0 0 0 0 0 0 0 0.50
Level 41: 503 497 0 0 0 0 0 0 0 0 0.50
Level 42: 596 404 0 0 0 0 0 0 0 0 0.40
Level 43: 709 291 0 0 0 0 0 0 0 0 0.30
Level 44: 796 204 0 0 0 0 0 0 0 0 0.20
Level 45: 910 90 0 0 0 0 0 0 0 0 0.10
Level 46: 1000 0 0 0 0 0 0 0 0 0 0.00
Level 47: 1000 0 0 0 0 0 0 0 0 0 0.00
Level 48: 1000 0 0 0 0 0 0 0 0 0 0.00
Level 49: 1000 0 0 0 0 0 0 0 0 0 0.00
Level 50: 1000 0 0 0 0 0 0 0 0 0 0.00
E. uncursed amulet of order, Tree birth sign
--------------------------------------------
Amulet changes alignment every 20 turns.
Formula: max(1, 1d6-1) * (51 - level) / 50 (rounded down)
+0 +1 +2 +3 +4 +5 "avg."
Level 1: 0 349 163 161 170 157 2.67
Level 2: 332 165 173 167 163 0 1.67
Level 3: 325 192 147 160 176 0 1.67
Level 4: 328 173 159 174 166 0 1.67
Level 5: 353 143 151 193 160 0 1.67
Level 6: 334 145 190 174 157 0 1.67
Level 7: 352 171 149 164 164 0 1.67
Level 8: 331 161 155 169 184 0 1.67
Level 9: 320 173 178 149 180 0 1.67
Level 10: 362 169 174 150 145 0 1.67
Level 11: 340 169 171 158 162 0 1.67
Level 12: 335 183 153 329 0 0 1.50
Level 13: 356 164 155 325 0 0 1.50
Level 14: 357 146 320 177 0 0 1.33
Level 15: 345 161 339 155 0 0 1.33
Level 16: 360 184 312 144 0 0 1.33
Level 17: 345 157 338 160 0 0 1.33
Level 18: 342 322 161 175 0 0 1.17
Level 19: 326 324 180 170 0 0 1.17
Level 20: 333 336 164 167 0 0 1.17
Level 21: 348 317 174 161 0 0 1.17
Level 22: 346 318 336 0 0 0 1.00
Level 23: 355 344 301 0 0 0 1.00
Level 24: 345 333 322 0 0 0 1.00
Level 25: 343 329 328 0 0 0 1.00
Level 26: 363 302 335 0 0 0 1.00
Level 27: 476 349 175 0 0 0 0.67
Level 28: 498 321 181 0 0 0 0.67
Level 29: 479 334 187 0 0 0 0.67
Level 30: 505 317 178 0 0 0 0.67
Level 31: 495 317 188 0 0 0 0.67
Level 32: 506 494 0 0 0 0 0.50
Level 33: 480 520 0 0 0 0 0.50
Level 34: 495 505 0 0 0 0 0.50
Level 35: 657 343 0 0 0 0 0.33
Level 36: 676 324 0 0 0 0 0.33
Level 37: 689 311 0 0 0 0 0.33
Level 38: 670 330 0 0 0 0 0.33
Level 39: 842 158 0 0 0 0 0.17
Level 40: 842 158 0 0 0 0 0.17
Level 41: 836 164 0 0 0 0 0.17
Level 42: 1000 0 0 0 0 0 0.00
Level 43: 1000 0 0 0 0 0 0.00
Level 44: 1000 0 0 0 0 0 0.00
Level 45: 1000 0 0 0 0 0 0.00
Level 46: 1000 0 0 0 0 0 0.00
Level 47: 1000 0 0 0 0 0 0.00
Level 48: 1000 0 0 0 0 0 0.00
Level 49: 1000 0 0 0 0 0 0.00
Level 50: 1000 0 0 0 0 0 0.00
F. cursed amulet of order, Tree birth sign
------------------------------------------
Amulet changes alignment every 50 turns.
Formula: max(1, 1d3-1) * (51 - level) / 50 (rounded down)
+0 +1 +2 "avg."
Level 1: 0 681 319 1.33
Level 2: 666 334 0 0.33
Level 3: 639 361 0 0.33
Level 4: 653 347 0 0.33
Level 5: 671 329 0 0.33
Level 6: 690 310 0 0.33
Level 7: 663 337 0 0.33
Level 8: 671 329 0 0.33
Level 9: 678 322 0 0.33
Level 10: 685 315 0 0.33
Level 11: 655 345 0 0.33
Level 12: 641 359 0 0.33
Level 13: 664 336 0 0.33
Level 14: 663 337 0 0.33
Level 15: 678 322 0 0.33
Level 16: 697 303 0 0.33
Level 17: 655 345 0 0.33
Level 18: 686 314 0 0.33
Level 19: 650 350 0 0.33
Level 20: 665 335 0 0.33
Level 21: 673 327 0 0.33
Level 22: 675 325 0 0.33
Level 23: 664 336 0 0.33
Level 24: 658 342 0 0.33
Level 25: 636 364 0 0.33
Level 26: 661 339 0 0.33
Level 27: 1000 0 0 0.00
Level 28: 1000 0 0 0.00
Level 29: 1000 0 0 0.00
Level 30: 1000 0 0 0.00
Level 31: 1000 0 0 0.00
Level 32: 1000 0 0 0.00
Level 33: 1000 0 0 0.00
Level 34: 1000 0 0 0.00
Level 35: 1000 0 0 0.00
Level 36: 1000 0 0 0.00
Level 37: 1000 0 0 0.00
Level 38: 1000 0 0 0.00
Level 39: 1000 0 0 0.00
Level 40: 1000 0 0 0.00
Level 41: 1000 0 0 0.00
Level 42: 1000 0 0 0.00
Level 43: 1000 0 0 0.00
Level 44: 1000 0 0 0.00
Level 45: 1000 0 0 0.00
Level 46: 1000 0 0 0.00
Level 47: 1000 0 0 0.00
Level 48: 1000 0 0 0.00
Level 49: 1000 0 0 0.00
Level 50: 1000 0 0 0.00
Updated July 8th, 2009