THE KNIGHT OF LODIS BIORHYTHM MECHANICS v1.00
======================================= =====

by Terence Fergusson <taf@university-of-murphy.freeserve.co.uk>

Tactics Ogre : The Knight of Lodis is copyright 2001 Nintendo of America, Co.
Ltd.  Tactics Ogre : The Knight of Lodis is also copyright 2001 Quest.

This document is entirely my work, and was written and is owned by me,
Terence Fergusson.  All copyrights and trademarks are acknowledged where not
specifically mentioned.  If you wish to reproduce this document AS IS, you
may do so without having to ask my permission, providing that the entire
document including this copyright notice is left intact, and preferably in
ASCII text format.

Please do not e-mail me asking questions about the Knight of Lodis.  If you
have found this file, you likely also have access to other FAQs on the
Knight of Lodis that could help you far more quickly than I check my mail,
and even if your question is regarding biorhythms, I do not have the time
to answer every little problem many people will have in understanding the
information contained inside.  Please direct any queries to the Knight of
Lodis GameFAQs Message Board.



=====================
== VERSION HISTORY ==
=====================
  v1.00 : 26/05/02 : Original Release



==============
== FOREWORD ==
==============
  Again, exhaustive research on an interesting field of an excellent game.
As I looked more and more into this, I was increasingly surprised at how
well the theory of biorhythms had gone into the Knight of Lodis.  Hence,
this document.

  I give you fair warning though.  This document is MATHS-INTENSIVE.  This
is not for the casual player, and I make no promises about dumbing down the
information included in here.  I will not answer e-mails requesting
clarification on any aspect of this document.



=======================
== TABLE OF CONTENTS ==
=======================

 Line
   62 : Overview on Biorhythm
  106 : Fortune
  298 : Fortune Calculations
  443 : Biorhythm Effects
  526 : Changes To Biorhythm
  543 : Alphonse's Starting Biorhythm



===========================
== OVERVIEW ON BIORHYTHM ==
===========================
  Your character has a hidden stat, that we shall call Luck.  Luck is used
in many of the random checks throughout a battle, but you will never be told
in advance what the effect is.  As such, it is often wise to attempt to keep
tabs on it.  This is because Luck changes, due to what is known as a
character's biorhythm.

  A biorhythm is a sine graph that starts moving when you are born.  When
you're on a high point of the sine graph, your attribute associated with
that biorhythm is strengthened.  When you're on a low point of the graph,
the associated attribute is weakened.  At midpoints, the attribute is at its
average value.

  The Knight of Lodis uses a biorhythm that is associated to your hidden
Luck attribute.  As such, this biorhythm has the following stats:
    Period
    Offset
    Altitude
    Amplitude

  A Biorhythm's Period is how long it takes to repeat itself.  It is
measured in days.

  The Offset is how many Days forward the Biorhythm has been moved.  This is
usually used to simulate it having started when you are born.  It is usually
a number between 0 and 364.

  The Altitude determines what the average value of the Biorhythm is.  A
high altitude continually gives you high luck, even on bad days.

  The Amplitude determines by how much your good and bad days vary by.  A
low amplitude means that your luck doesn't change much, so your good days
won't be *too* good, but your bad days won't be *too* bad.  A high amplitude
means the opposite; good days are *very* good, but bad days are *very* bad.


  Luck and your Biorhythm are hidden from you.  But you are given one piece
of information that helps you in determing what kind of Luck and Biorhythm
you have.  This piece of information is called your Fortune.



=============
== FORTUNE ==
=============
  Your Fortune is an estimate of both your current Luck and your actual
Biorhythm stats.  It is a rough approximation of everything that goes
together to create your Luck.

The various Fortunes are:
----------------------------------------------------------------------------
|       Vivacity        |       A clear mind      |      A strong will     |
|     Possibility       |        Enrichment       |         Luck(1)        | 
|      Discontent       |        Endurance        |       Anxiousness      |
|     Restlessness      |       Misjudgement      |          Slump         |
|-----------------------+-------------------------+------------------------|
|       Luck(2)         |        Prosperity       |       Tranquility      |
|      Enthusiasm       |        Stability        |        Confidence      |
|  Clouded judgement    |    Running Backwards    |        Hesitation      |
|       Idleness        |     Dissatisfaction     |       Irritations      |
|-----------------------+-------------------------+------------------------|
|      Liveliness       |       A warm heart      |      Enlightenment     |
|        Focus          |         Optimism        |       Coincidence      |
|   Misunderstanding    |      Overconfidence     |         Fatigue        |
|   Absentmindedness    |      Self-contempt      |    Sorry! ... Unlucky  |
----------------------------------------------------------------------------


  The Fortunes are collected in groups of 4.  Without changes to your
characters stats, these are the 4 Fortune states you will move through as
time goes on.  These are circular states; for example, 'A warm heart' will
lead to 'Optimism', which then leads to 'Overconfidence', 'Self-contempt'
and then back to 'A warm heart' once more.

  The time it takes for this cycle to complete is the Biorhythm period.  For
the most part, the 1st and 3rd Fortunes in each group indicate medium luck,
while the 2nd is high luck and the 4th is bad luck.  In addition, the lower
the group is in the above 3x3 table, the lower your average luck is.  The
farther to the right the group is in the above table, the more your luck
varies over time.

  Each Fortune has its own description.  The 36 states, complete with
description, are as follows:


           === Low Amplitude, High Altitude ===

  Vivacity.
Many opportunities to use your talents.  Always do your best.

  Possibility.
Do things calmly, and be alert of others.

  Discontent.
Things may seem rather ordinary,
but your comrades will pull you through!

  Restlessness.
You're prone to error.  Think before you act.

  ---

          === Medium Amplitude, High Altitude ===

  A clear mind.
Be assertive, but mindful of others.

  Enrichment.
Mind the outcomes of your actions.
Be confident and challenge youself.
  
  Endurance.
Personal glory isn't everything.  Think about what's important.

  Misjudgement.
Your actions may be for naught.  Keep an eye on your enemies.

  ---

           === High Amplitude, High Altitude ===

  A strong will.
You will bear many hardships, but do not dwell on them.

  Luck(1).
You'll succeed in any endeavor.  Maintain a positive attitude.

  Anxiousness.
You may not be your usual self.  It won't hurt to rely on others.

  Slump.
Relax and think things over.  Sometimes it's better to wait.

  ---

          === Low Amplitude, Medium Altitude ===

  Luck(2).
Small mistakes won't hurt you.  Remember to help your friends.

  Enthusiasm.
Bold action could bring you luck.  Don't be stubborn.

  Clouded judgement.
Avoid foolish pursuits and dangerous places.

  Idleness.
Don't slack off too much.  Remember your original purpose.

  ---

         === Medium Amplitude, Medium Altitude ===

  Prosperity.
Never give up.  You will regain momentum.

  Stability.
You'll see satisfactory results if you don't miss your chance.

  Running Backwards.
It seems like good things are happening...to everyone else!

  Dissatisfaction.
It may seem like a hassle, but avoid taking the easy way out.

  ---

          === High Amplitude, Medium Altitude ===

  Tranquility.
Things will go more smoothly than you thought.  Just relax.

  Confidence.
Things will go your way, but don't be hasty!

  Hesitation.
Your actions may be inefficient.  Why not lend others a hand?

  Irritations.
If things don't go as planned, try looking at them from
a different perspective.

  ---

            === Low Amplitude, Low Altitude ===

  Liveliness.
Try something new.  Unexpected results may occur.

  Focus.
Concentrate on a single goal, and don't be distracted.

  Misunderstanding.
Be cautious.  Good intentions may be misinterpreted.

  Absentmindedness.
A small mistake can lead to big trouble.
It would be better to leave things to your comrades.

  ---

          === Medium Amplitude, Low Altitude ===

  A warm heart.
Forgive comrades' blunders.  You may make a mistake, too.

  Optimism.
You can push yourself a little harder, but know your limits.

  Overconfidence.
Don't overestimate yourself or you may get hurt.
Decide carefully.

  Self-contempt.
Ignore the small things.  Forget about your worries.

  ---

           === High Amplitude, Low Altitude ===

  Enlightenment.
You'll soon learn a shortcut to success, but don't get cocky!

  Coincidence.
You may have unexpected success.  Be aware of your surroundings.

  Fatigue.
Don't force yourself too much.  Wait for better luck.

  Sorry! ... Unlucky.
Everything seems to go wrong.  You better lay low.



==========================
== FORTUNE CALCULATIONS ==
==========================
  Your current Fortune is worked out according to both the current date and
your own stats.  While the following will tell you how to work out your
given Fortune, you should keep in mind that Fortune is only a *VERY* rough
approximation of your current luck.  There is a lot of room for differences
within each state, and even some overlap between different states.  This
overlap and guesses at the true value of your luck will be covered in more
detail in the next section.

  First, the current date must be transformed into a number that the game can
use.  The day/month sequence is as such:
    Deus 1 -   Deus 24 = Day 246 - 269
  Tierra 1 - Tierra 25 = Day 270 - 294
    Agua 1 -   Agua 23 = Day 295 - 317
  Sombra 1 - Sombra 24 = Day 318 - 341
  Branca 1 - Branca 25 = Day 342 - 365, Day 0
   Flama 1 -  Flama 24 = Day   2 -  25
   Vento 1 -  Vento 24 = Day  26 -  49
    Ouro 1 -   Ouro 25 = Day  50 -  74
  Trueno 1 - Trueno 24 = Day  75 -  98
  Trevas 1 - Trevas 24 = Day  99 - 122
  Oceano 1 - Oceano 25 = Day 123 - 147
   Preta 1 -  Preta 24 = Day 148 - 171
   Gemeo 1 -  Gemeo 24 = Day 172 - 195
    Fogo 1 -   Fogo 25 = Day 196 - 220
    Raio 1 -   Raio 25 = Day 221 - 245

  As you can see, the year actually 'starts' on the 25th of Branca.  This is
the way KoL works out Biorhythm, so be sure to take note of it.  In
addition, due to an apparent bug, there is no Day 1; Branca 25 is Day 0 and
Flama 1 is Day 2.


  Once we have the correct 'day' of the year, we must use the five stats
that a character has to work out their exact Biorhythm.

  The primary stats are the Period and Offset values.  We use these to work
out your basic state.  First, we apply them to the Day:

     Day = (Day + Offset) Mod Period

  (Note: A quick explaination of the Mod function is necessary.  When you do
x Mod y, what we're really doing is working out what the remainder is when
we divide x by y.  So, 3 Mod 2 would be 1, because 3 divided by 2 gives a
remainder of 1)


  Next, we must transform our current Day value into the Luck value, which is
a number between 0 and 256.  The formula we use is as follows:

     Luck = (Day * 256 / Period)
  
  If Luck is greater than 222, then we subtract 256 from the total.  Note
that it must be *greater* than 222; 222.5 would become -33.5, but 222.0
would stay as 222.

  We then add 34 to Luck and remove the fractional portion of the value; 0.5
would become 34, 16.7 would become 50 and 222.0 would become 256, as
examples.


  Now, we look up the Luck value in the following table.  The values are
spread out as such:
      Luck    State
      0- 69     1
     70-128     2
    129-197     3
    198-256     4


  After all this, we now have a State value which corresponds to one fortune
out of a series of four.  However, we still don't know which table to look
up.  Thus, we use the final two Biorhythm stats: Altitude and Amplitude.

  Using the following table, we get a Table value:

                              
 \Amplitude   0- 5    6-10   11+
Altitude\
 60-99         1       2       3
 41-59         4       5       6
  0-40         7       8       9


  Using the table that was printed in the previous section, we shall now
demonstrate how your resulting Fortune is worked out:

----------------------------------------------------------------------------
| 1     Vivacity        | 2     A clear mind      | 3    A strong will     |
|     Possibility       |        Enrichment       |         Luck(1)        | 
|      Discontent       |        Endurance        |       Anxiousness      |
|     Restlessness      |       Misjudgement      |          Slump         |
|-----------------------+-------------------------+------------------------|
| 4     Luck(2)         | 5      Prosperity       | 6     Tranquility      |
|      Enthusiasm       |        Stability        |        Confidence      |
|  Clouded judgement    |    Running Backwards    |        Hesitation      |
|       Idleness        |     Dissatisfaction     |       Irritations      |
|-----------------------+-------------------------+------------------------|
| 7    Liveliness       | 8     A warm heart      | 9    Enlightenment     |
|        Focus          |         Optimism        |       Coincidence      |
|   Misunderstanding    |      Overconfidence     |         Fatigue        |
|   Absentmindedness    |      Self-contempt      |    Sorry! ... Unlucky  |
----------------------------------------------------------------------------

  As you can see, the 9 possible Table values equate to the nine 4-fortune
tables shown above.  The State value determines which of the four fortunes
you get; State 1 is the topmost fortune and State 4 is the bottommost.


  An example is likely necessary at this point.  Let us use one.


  Alphonse's current Biorhythm in this example game has an Amplitude of 10
and an Altitude of 50.  After looking both these up, we see that we must use
Table 5 (Prosperity, Stability, Running Backwards, Dissatisfaction) to
discover our Fortune.

  His primary Biorhythm stats are 40 Period and 319 Offset.  It is currently
the 7th of Tierra.

  The 7th of Tierra equates to Day 276.  From that, we do the following:

     Day = (Day + Offset) Mod Period
         = (276 +   319 ) Mod   40
         = 595 Mod 40
         = 35


  Then:

     Luck = (Day * 256 / Period)
          = ( 35 * 256 /   40  )
          = 224


  Because Luck is greater than 224, we subtract 256 from it to get -32.  We
then add 34 to it as we'd do with any Luck value to get a final value of 2.

  Looking up Luck 2 in the Luck/State table, we see that Alphonse's
Biorhythm is in State 1.  He must therefore currently be under Prosperity.



=======================
== BIORHYTHM EFFECTS ==
=======================
  Your luck, unlike your fortune which is merely an indicator of your luck,
is a number from 0 to 100.  It is worked out slightly differently from
Fortune because this time, both Altitude and Amplitude are factored into the
number, rather than just giving you a different series of tables.

  The formula to work out luck is as follows.  First, we calculate the Luck
value like we did in the previous section, but with a few differences:

     First, work out what Day of the year it is.  Then...

     Day = (Day + Offset) Mod Period

     Luck = Day * 360 / Period


  We thus have a value from 0 to 360, which starts its period at 0.  Using
this revised Luck value, we perform the following calculation:

    Luck = [Altitude + Amplitude * Sin(Luck)]


  And this gives us the final Luck value.  Keep in mind that Sin is indeed
the triogmetric function (I did warn you in the forward that this was
maths-intensive), and uses degrees, not radians.  Also, the [] brackets
means that we take the integer portion of this number.  For example, [36.5]
is 36.


  As a small example, we shall again the Alphonse from the previous section.
As you may recall, it was Day 276 of the year, and Alphonse's Biorhythm
stats were Period 40, Offset 319, Altitude 50, Amplitude 10.

  Thus:

     Day = (Day + Offset) Mod Period
         = (276 +  319  ) Mod   40
         = 595 Mod 40
         = 35


  Then:

     Luck = (Day * 360 / Period)
          = ( 35 * 360 /   40  )
          = 315


  Finally:

     Luck = [Altitude + Amplitude * Sin(Luck)]
          = [   50    +     10    * Sin(315 )]
          = [   50    +     10    * -0.707106]
          = [   50    +       -7.07106       ]
          = [42.92894]
          = 42


  Therefore, Alphonse's current Luck is 42.


============================================================================
  WARNING!  There are still errors in this formula, but this is a very good
approximation of the true formula.  Because of the way computers work and
the fact that a Sine formula is used, it is impossible to be sure where any
rounding errors may crop up.  The true Luck value may be off by 1 or 2
points in either direction.  The only values that are for sure are when
the Sine part of the equation works out to either 1, 0 or -1.
============================================================================


  You may wonder what this Luck value affects.  One of the easiest things
to demonstrate Luck having an effect is in buried treasure.  A lot of the
buried treasure you find in the game is selected from three groups of random
lists, where the group you get depends on which treasure spot you've found.
However, these lists are further subdivided into three more groups, and the
group you get depends on your Luck.

  If your Luck is 40 or less, you get the 'bad' group.

  If your Luck is between 41 and 60 inclusive, you get the 'medium' group.

  If your Luck is 61 or more, you get the 'good' group.



  Returning to your Fortune, we can see that it is very much a *very* rough
approximation of your Luck.  Because of this, we shall not try to determine
what values of Luck goes with each Fortune, since any attempt to do so would
be misleading.



==========================
== CHANGES TO BIORHYTHM ==
==========================
  Currently, the following events are known to have a distinct effect on
your Biorhythm.  More will be added to this section once their exact
workings are figured out.


  Berserk Emblem:       Adds 10 to your Biorhythm Period.
  Broken Heart Emblem:  Resets your Biorhythm Period to 30.

  (Note: If you get Berserk then Broken Heart, your Biorhythm Period will be
         30.  But if you get Broken Heart then Berserk, your Biorhythm
         Period will be 40.)



===================================
== ALPHONSE'S STARTING BIORHYTHM ==
===================================
  While the system used to determine Alphonse's starting biorhythm has yet
to be determined, several things can be said about the biorhythm you start
off with.

  Depending on the birthdate you select for Alphonse, your biorhythm stats
will fluctuate between certain values:

    Period will either be 30, 45 or 90.
    Amplitude will either be 5, 10 or 15.
    Altitude will fluctuate between about 43 and 51 inclusive.

    Offset is determined *precisely* by your birthdate, being a number
  between 364 and 0.  It starts at 364 for the 1st of January (or 1st of
  Deus) and counts down to 0 for the 31st of December (or 25th of Raio).



  This section may be updated in the future with biorhythms of special
characters and hired characters, as well as more precise methods of working
out Alphonse's starting biorhythm... but don't count on all that anytime
soon.

=============================================================================





The Knight of Lodis Biorhythm Mechanics, copyright 2002 Terence Fergusson