                         Statues and Spellbooks
                        ========================

            by Bryan Butler (butler@cluster.gps.caltech.edu)
                and Boudewijn Wayers (dedos4@win.tue.nl).


When you chop up a statue, with for example a pick-axe or a wand of
striking, you might find a spellbook in it. The probability of finding
one increases with increasing depth in the dungeon, and are as
follows:

Dungeon level  Probability
~~~~~~~~~~~~~  ~~~~~~~~~~~
 1, 2 and 3              0
    4 and 5           1/12
    6 and 7           2/13
    8 and 9           3/14
  10 and 11           4/15
  12 and 13           5/16
        ...            ...
  20 and 21           9/20
        ...            ...
  30 and 31          14/25
        ...            ...
  40 and 41          19/30
        ...            ...
  50 and 51          24/35
        ...            ...
  60 and 61          29/40

Please note that whether or not a statue contains a spellbook is being
determined when the statue is first created, so don't bother dragging
your statues deeper into the dungeon, just to increase your chance of
finding a spellbook in it: it won't work. A statue found at level three
will not contain a spellbook if chopped to pieces on level 40.

Note that the ORACLE is located somewhere between levels 5 and 10, so
the average chance on that level that a statue contains a spellbook is
about (1/12 + 2*2/13 + 2*3/14 + 4/15) / 6 = (35586/32760) / 6 = 0.181.

Since there are always eight statues on that level, the chance of
finding no spellbook there is about 0.2.  The cance of finding just one
is about 0.35. The chance of finding two is about 0.23. Chances of
finding more rapidly approach zero.

