Amulets statistics

The PC had no amulets before this. The test was done on PC: 1 with an experience level
one PC who wished for the amulets 100 times.

The results were as follows:

   A - heap of 215 uncursed amulets of the cold heart {Ch-12}           645s
   B - heap of 26 blessed amulets of the cold heart {Ch-12}              78s
   C - heap of 2 uncursed amulets of the cold heart {Ch-14}               6s
   D - heap of 28 cursed amulets of the cold heart {Ch-12}               84s
   E - cursed amulet of the cold heart {Ch-10}                            3s
   F - heap of 10 uncursed amulets of the cold heart {Ch-11}             30s
   G - heap of 6 uncursed amulets of the cold heart {Ch-9}               18s
   H - heap of 3 blessed amulets of the cold heart {Ch-9}                 9s
   I - heap of 3 uncursed amulets of the cold heart {Ch-15}               9s
   J - heap of 6 uncursed rusty amulets of the cold heart {Ch-12}        18s
   K - heap of 4 uncursed amulets of the cold heart {Ch-10}              12s
   L - heap of 2 blessed amulets of the cold heart {Ch-10}                6s
   M - heap of 2 uncursed amulets of the cold heart {Ch-13}               6s
   N - blessed rusty amulet of the cold heart {Ch-12}                     3s

   A - heap of 212 uncursed amulets of defense +2                       636s
   B - heap of 36 cursed amulets of defense +2                          108s
   C - heap of 27 blessed amulets of defense +2                          81s
   D - amulet of defense +2                                               3s
   E - heap of 9 uncursed rusty amulets of defense +2                    27s
   F - heap of 4 uncursed amulets of defense +5                          12s
   G - heap of 2 uncursed amulets of defense +1                           6s
   H - blessed amulet of defense -1                                       3s
   I - heap of 2 uncursed amulets of defense +4                           6s
   J - blessed amulet of defense +5                                       3s
   K - heap of 2 amulets of defense +2                                    6s
   L - cursed amulet of defense +3                                        3s
   M - uncursed rusty amulet of defense +3                                3s
   N - heap of 2 uncursed amulets of defense +3                           6s
   O - heap of 2 uncursed amulets of defense +0                           6s
   L - uncursed amulet of defense -1                                      3s
   M - cursed amulet of defense +0                                        3s
   N - blessed amulet of defense +4                                       3s
   O - blessed amulet of defense +3                                       3s

The results may conceivably vary depending on the danger level of the dungeon
or the blessed/uncursed/cursed status of the wand of wishing. This will be
investigated in the future. The wand used for these tests was uncursed.

A couple of days after this was all figured out, a level 50 PC on D: 50 found
an amulet the cold heart {Ch-16}. It was dropped by a great wyrm. So it
seems that the +/- 3 is only a very good guide to amulets, not an ironclad rule.

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

Please note that this is an unofficial and unauthorised copy of Andy William's ADOM Guidebook. For further information on the legal and moral challenges raised against this Improved ADOM Guidebook please see rec.games.roguelike.adom.