이것은 기존 파판 랜드의 공식과 기본적으로 유사하나, 보다 더 정확한 정보라고

여겨집니다. 기존 공식과 달리 인터판 기준입니다. 전에, 여러번 실험하고 핵심내용을

제 사견을 섞어서 올렸는데 짤렸습니다. 그 짓 다시 하기 싫어서 그냥 복사해 놓은

부분만 올릴테니.. 참고하세요. 생각보다 양이 많습니다. 아래 제가 예제를

써놨으니 그것도 읽어보시면 참고가 될겁니다.


I. Introduction

Hello, and welcome to the Yojimbo Mathematics Guide (my first attempt at
writing a guide/FAQ document for a video game).  The purpose of this guide
is to explain the process of how the attacks of the optional aeon Yojimbo
are chosen.  Yojimbo's attacks are determined by a formula that is a bit
more complex than the basic attack damage formulae in Final Fantasy X (FFX).  
In addition to the Yojimbo formula itself, this guide has step-by-step
example scenarios and tips so that you might be able to use the mathematics
of Yojimbo to your advantage.  

There are two versions of the Yojimbo formula.  The first version is in the
North American and original Japanese releases of "Final Fantasy X".  
The second version is in "Final Fantasy X International" (both the Japanese
and Asian versions) and the PAL releases of "Final Fantasy X" (including
Platinum).  At this time, I do not know which formula is used in the
Japanese "Mega Hits" release of "Final Fantasy X".

After reading section II ("Important Information for ALL releases of FFX"),
those who have an International or PAL release should read section III.  
Those who have the North American or original Japanese release should skip
section III and go directly to section IV.  

          

II. Important Information for ALL releases of FFX
(Note: game quotes are based on English voice/text)

When you first meet Yojimbo's fayth, he says the following:    

"Summoner, I ask you.  What do you want of me?"

The answer you give is very important in the calculation of his attack.
Your choices are:

"To train as a summoner." (in this guide, this will be called "Option 1")
"To gain the power to destroy fiends." (Option 2)
"To defeat the most powerful of enemies." (Option 3)

Be careful, because you only get to choose your answer once per game
(you cannot change it).

Also, here are some short notes on the effects of Yojimbo's four attacks:

Daigoro - physical damage to one enemy (Power 10, Piercing),
          critical hit is possible  
Kozuka - physical damage to one enemy (Power 13, Piercing),
         critical hit is possible
Wakizashi - physical damage to one enemy OR all enemies (Power 18, Piercing),
            critical hits are possible
Zanmato - instantly kills all enemies (for boss battles in which the enemy
          has multiple "forms", the boss simply moves to the next "form").
          Like the Death spell or a successful [Deathstrike], Zanmato
          does not do numerical damage, so you cannot get Overkill(s)
          from it.


Finally, here are some key terms that you will see in the formula sections:

Compatibility -- How much Yojimbo "likes" you, represented as an integer
                 from 0 to 255.

Motivation -- Parameter that determines Yojimbo's paid attack.

Math:

(+) -- addition
(-) -- subtraction
(*) -- multiplication
(/) -- division (keep decimal remainder)

ln(x) -- natural logarithm function

[0..63] -- Random integer picked from the range of 0 to 63 (inclusive)

[x] -- floor function (greatest integer less than or equal to x)
       examples:  [1.0] = 1, [2.4] = 2, [2.9] = 2, [47/16] = 2,
       [-0.4] = -1 (there will be no negative values used here, though)
III. International/PAL section

A.  A few words on "Compatibility"

Compatibility is the measure of your relationship with Yojimbo.  
Assuming that everything else is equal, Yojimbo is more likely to use his best
attacks (Zanmato or Wakizashi) with a high Compatibility stat.

When you first acquire Yojimbo, his Compatibility is 128.  The minimum value
possible is 0, and the maximum value is 255.  It can change in the following
ways:

Action                                              |  Compatibility Change
----------------------------------------------------|----------------------
Yojimbo uses "Zanmato" attack           |          + 4
Yojimbo uses "Wakizashi" attack on all enemies          |          + 3
Yojimbo uses "Wakizashi" attack on one enemy           |          + 1
Yojimbo uses "Kozuka" attack                                    |            0
Yojimbo uses "Daigoro" attack                                    |          - 1
You Dismiss Yojimbo immediately after summoning him  |          - 3
Yojimbo is KO'ed                                                         |          -10
You pay Yojimbo 0 (zero) Gil                                         |          -20*

*-In addition to losing 20 points of Compatibility, Yojimbo automatically
Dismisses himself without attacking when paid 0 Gil.


~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

B.  CALCULATION OF YOJIMBO'S ATTACK

(The International/PAL Yojimbo attack formula originally appeared in the
FFX Ultimania Omega Guide (Digicube/Studio Bentstuff).  It was then posted
at the GameFAQs Secrets and Side Quests board by Olivier Hague.  I have
added explanations to all the steps and I have changed the order of some
things to make it easier to follow, and the result is what you see below.)

Step Zero:  Free Attack?

When Yojimbo's turn comes, he may attack immediately without asking for
payment.  The chance of this happening is (Compatibility/1024).  That
means when you first get Yojimbo, he has a 1 in 8 chance of attacking for
free, and if you max out his Compatibility, he has almost a 1 in 4 chance of
attacking for free.  If there is a free attack, the type of attack is chosen
like this:

F = [Compatibility/4] + [0..63]

Value of "F"  |          (Free) Attack used
--------------|--------------------------------------------
     80+      |    Zanmato OR Wakizashi against all enemies*
    64-79     |    Wakizashi against all enemies      
    48-63     |    Wakizashi against one enemy  
    32-47     |    Kozuka
     0-31     |    Daigoro

*-if the Zanmato Resistance Level (explanation in "Step Four") of the enemies
   is 1, then Yojimbo will use his "Zanmato" attack.  Otherwise, he will use
   his "Wakizashi" attack against all enemies.  

If Yojimbo attacks for free, his turn is over and the calculation stops here.

If Yojimbo does not attack for free, he will prompt you for payment.  From this
point, Yojimbo's attack will be determined by a parameter called "Motivation".
After you pay him, his Motivation is calculated and his attack is chosen.  
The following steps explain the process.

Motivation starts at zero, and it resets each turn.  

Step One: Motivation from payment

(Note:  The name "MotivationK" is used below to denote Yojimbo's Motivation
        after Step K ("Motivation2" is the Motivation after Step Two,
        for example).  The game itself might only use one Motivation parameter
        throughout the entire process, but I found it easier to write it
        this way.)

The amount of Motivation added based on how much you paid him:

Payment                     |      Motivation1
----------------------------|---------------------------------------
   0 Gil                    |   N/A (Yojimbo instantly Dismisses himself)
   1-3 Gil                  |           0          
   4-7 Gil                  |           4
   8-15 Gil                 |           8
   16-31 Gil                |          12
   32-63 Gil                |          16
   64-127 Gil               |          20
   128-255 Gil              |          24
   256-511 Gil              |          28
   512-1023 Gil             |          32
   1024-2047 Gil            |          36
   2048-4095 Gil            |          40
   4096-8191 Gil            |          44
   8192-16383 Gil           |          48
   16384-32767 Gil          |          52
   32768-65535 Gil          |          56
   65536-131071 Gil         |          60
   131072-262143 Gil        |          64
   262144-524287 Gil        |          68
   524288-1048575 Gil       |          72
   1048576-2097151 Gil      |          76
   2097152-4194303 Gil      |          80
   4194304-8388607 Gil      |          84
   8388608-16777215 Gil     |          88
   16777216-33554431 Gil    |          92
   33554432-67108863 Gil    |          96
   67108864-134217727 Gil   |          100
   134217728-268435455 Gil  |          104
   268435456-536870911 Gil  |          108
   536870912-999999999 Gil  |          112


Step Two:  Motivation from Compatibility

Next, an amount is added to Motivation based on the value of his
Compatibility when you paid him:

Motivation2 = Motivation1 + [Compatibility/4]


Step Three:  Your choice at the cave

If you chose Option 1, then the game will make an extra adjustment
to Motivation based on the percentage of your total Gil that you paid
on this turn.  The adjustment is this:

     Motivation3 = [Motivation2 * (0.75 + (Payment * 0.5 / TotalGil))]

If you did not choose Option 1, then Motivation3 = Motivation2.


Step Four: Zanmato Resistance Level and You

Every enemy in FFX has a Zanmato Resistance Level (actually, it's just called
"Zanmato Level" by official publications).  It is a stat that they have, just
like Strength or Evasion.  There are many enemies in the game against which
cannot use Yojimbo, but they all have Zanmato Levels, too.

This step takes into account the Zanmato Level of the enemy
(Zanmato Levels range from 1 to 6) in order to adjust Motivation.

If you picked either Option 1 or Option 2, this is how Motivation
changes (depending on the enemy's Zanmato Level):

    Enemy's Zanmato Level  |           Motivation4
    -----------------------|---------------------------------------------
          1                |      [Motivation3 * 1] (there is no change)
          2                |      [Motivation3 * 0.5]
          3                |      [Motivation3 * 0.33]
          4                |      [Motivation3 * 0.25]
          5                |      [Motivation3 * 0.2]
          6                |      [Motivation3 * 0.16]


If you picked Option 3, one of two possible changes will happen:

  If the enemy's Zanmato Level is 3 or less, then
  Motivation4 = [Motivation3 * 0.8]

  If the enemy's Zanmato Level is 4 or greater, then
  Motivation4 = [Motivation3 * 0.4]


Step Five:  Overdrive

If Yojimbo's Overdrive meter is full, then Motivation5 = Motivation4 + 20.
Otherwise, Motivation5 = Motivation4.


Step Six:  Random

A random number between 0 and 63 (inclusive) is added to Motivation.

Motivation6 = Motivation5 + [0..63]


Step Seven:  Which attack?

If Motivation6 is greater than or equal to 80, then Yojimbo will use Zanmato
(end of turn, and the battle, unless the enemy has multiple forms).  

If not, then Motivation is reset to zero and recalculated.  Steps One through
Six are repeated, except that the enemy's Zanmato Resistance Level is
considered to be 1 in Step Three (regardless of the enemy's actual Resistance
Level), and the resultant Motivation determines Yojimbo's attack.

  Motivation1b = Motivation1 (the payment is the same)
  Motivation2b = Motivation2 (the Compatibility is the same)
  Motivation3b = Motivation3 (the Option chosen is the same)

  If Option 1 or Option 2, then Motivation4b = Motivation3b.
(If Option 3, then Motivation4b = [Motivation3b * 0.8])

  If Overdrive is full, Motivation5b = Motivation4b + 20.
  (Otherwise, Motivation5b = Motivation4b)

  Motivation6b = Motivation5b + [0..63]

  Motivation6b |        Attack
  -------------|----------------------------------  
      64+      |    Wakizashi against all enemies      
    48-63      |    Wakizashi against one enemy  
    32-47      |    Kozuka
     0-31      |    Daigoro

END OF CALCULATION

C.  The Zanmato Level List

Below is the list of the Zanmato Levels of all the enemies in FFX.  This
monster data is taken (with permission) from Christine Bomke's FFX Monster
Encyclopedia, so look there to find out where the various "types" of some
enemies appear (in most cases, there is only one type against which you can
use Yojimbo anyway).  Any corrections/additions to the data from the Monster
Encyclopedia that appear here are noted in the Credits section.

This list includes boss names, so watch out for spoilers.

ZANMATO LEVEL 1

Achelous
Aerouge
Ahriman
Alcyone
Anacondaur
Aqua Flan
Bandersnatch
Bashura
Basilisk
Bat Eye
Belgemine's Aeons
Bite Bug
Black Element
Blue Element
Bomb (both types)
Buer
Bunyip
Cave Iguion
Chimera (both types)
Chimera Brain
Coeurl
Condor
Dark Element
Dark Flan
Defender
Defender X
Defender Z
Demonolith
Dingo
Dinonix
Dual Horn (both types)
Epaaj
Evil Eye (both types)
Exoray
Fallen Monk (both types)
Flame Flan
Floating Death
Floating Eye
Funguar
Gandarewa
Garm
Garuda (all types)
Gemini (both types)
Ghost
Gold Element
Grat
Grenade
Grendel
Guado Guard C
Halma
Ice Flan
Iguion
Imp
Ipiria
Iron Giant
Killer Bee
Klikk
Kusariqqu
Lamashtu
Land Worm
Larvae
Left Fin
Lord Ochu
Machea
Maelspike
Mafdet
Magic Urn
Mandragora
Master Coeurl
Master Tonberry
Maze Larvae
Mech Defender
Mech Guard
Mech Gunner
Mech Hunter
Mech Leader
Mech Scouter
Melusine
Mi'ihen Fang
Mimic (all types)
Murussu
Mushussu
Nebiros
Nidhogg
Ochu
Octopus
Ogre
Phlegyas
Piranha
Puroboros
Ragora
Raldo
Raptor
Red Element
Remora
Right Fin
Sahagin (all types)
Sahagin Chief
Sand Wolf
Sand Worm
Sandragora
Shred
Simurgh
Sin's Core
Sin's Head (a.k.a. "Overdrive Sin")
Sinscale B (S.S. Liki)
Sinscale C (appears with Euchilles)
Sinspawn Ammes
Sinspawn Genais
Skoll
Snow Flan
Snow Wolf
Spirit
Splasher
Swamp Mafdet
Thorn
Thunder Flan
Tonberry
Valaha
Varuna
Vouivre (both types)
Warrior Monk (both types)
Wasp
Water Flan
Wendigo
White Element
Worker
Wraith
Xiphos
YAT-97
YAT-99
Yellow Element
YKT-11
YKT-63
Yowie
Zaurus
Zuu (both types)

ZANMATO LEVEL 2

Barbatos
Behemoth
Behemoth King
Cactuar
Great Malboro
Malboro
Qactuar
Sanctuary Keeper

ZANMATO LEVEL 3

Adamantoise
Anima

ZANMATO LEVEL 4

Biran Ronso
Chocobo Eater
Crawler
Evrae
Evrae Altana
Extractor
Geneaux's Tentacle
Geosgaeno
Grothia
Guado Guard A
Guado Guard B
Gui's Arm
Gui's Head
??? (Kimahri)
Lady Yunalesca
Mortibody
Mortiorchis
Negator
Oblitzerator
Omega Weapon
Pterya
Seymour
Seymour Flux
Seymour Natus
Seymour Omnis
Sin (S.S. Liki)
Sinscale A (Zanarkand)
Sinspawn Euchilles
Sinspawn Geneaux
Sinspawn Gui
Spathi
Spectral Keeper
Spherimorph
Tros
Ultima Weapon
Yenke Ronso

ZANMATO LEVEL 5

All Monster Arena creations (includes Area Conquest, Species Conquest, and
  Original Creations)
Braska's Final Aeon
Yu Pagoda

ZANMATO LEVEL 6

All Dark Aeons

Missing from this list are the following :  

Possessed Aeons/Yu Pagodas/(final boss) - no data on these so far
Penance - at least level 4...different sources give different answers on this



자, 그럼 한번 계산해볼까요? 일단, 요짐보를 구할 때 선택하는 옵션 중에서

3번째 옵션(가장 강한 적을 이기기 위해서)라는 택했다고 가정합니다. 이 옵션3이

참마도 확률이 가장 높습니다. 그리고, 상대는 헤레틱 소환수이니까 참마도 저항

레벨 4이상으로 판단하여 수치가 계산되고, 돈은 1길이고, 임의값은 최대치로

기입하겠으며, 상성도 또한 255로 맥스로 계산하겠습니다. 그리고 노 OD입니다.


참마도 발동 = 동기값5 + 임의값

동기값 5 = No OD시, 동기값4와 동일

동기값4 =  동기값3 * 0.4(참마도저항레벨4이상일 경우)

동기값3 = 동기값2 (옵션 1을 제외한 경우. 옵션1의 경우는 수치가 곱해진다.)

동기값2 =  동기값 1 + [255/4]

각 동기값은 무조건 정수로 봅니다. 반올림도 반내림도 아니고, 그냥 소수점 이하는

무조건 버립니다. 자 위의 공식에 하나씩 대입해보겠습니다.

동기값1 =  위의 표를 참고해보면 0 입니다.
동기값2 = 0 +[63.75] = 0 + 63 = 63
동기값3 = 동기값2 =  63
동기값4 =  63 * 0.4 = [25.2] =25
동기값5 = 25

최종 참마도 발동률 = 25+63 = 88  ............... 참마도가 나가기는 하겠군요.

음 전에 계산을 잘못했나... 그러면 발동 확률을 봅시다. 참마도가 나가려면

최종값이 80이상이어야 합니다. 즉 80-25 = 55 임의값 55부터 가능하다는 소리군요.

그럼 확률을 계산하면, [(63-55)/63]*100 = 12.6984.... 계산하기 편하게 12%로 치면,

3/25 즉, 25번에 3번 정도 나간다는 소리군요. 정확히는 63번에 8번꼴로 나갑니다.

제가 지적한 부분.. 참마도 1길로는 헤레틱 못잡다는 말 일단 취소하겠습니다.

이 지적은 잘못되었군요. 변명하자면, 전의 계산에서는 1길로는 도저히 나오지

않았기 때문에.. 그러나, 무료 참마도와, 참마도 공격이 빈번하다는 건 증명되지

않습니다. 무료 참마도는 상성도/4 한 값에 임의값을 더하는 것인데, 아무리 수치가

80이상이 되어도, 저항레벨 1에게만 참마도가 나가도록 설정되어있습니다.

그리고, 25번에 3번 꼴로 나간다면, 빈번하다고 볼수는 없네요. 그렇지만, 일단

나간다는 사실은 공식상 증명이 되었고, 또 빈번하다 잘 안나간다는 느낌은

주관적 느낌이기 때문에 일단 나가는 것이 확실하면, 빈번하다고 느낄수는 있다고

생각합니다.

결론

헤레틱에게 1길로도 참마도가 가능하다.(예전에 했던 계산들 중에 1길에 관한 것은 실수
                                                       했군요.)
무료참마도는 나갈수 없다.

25번 시도에 3번꼴로 헤레틱 상대로 1길 참마도 발동이 가능하다.


첨가: 저는 직접적인 실험에서 임의값은 순서대로, 즉 0,1,2,3,...63 순서대로
차례로 돌아가는 것이 아니며, 25번 전투를 해서 3번꼴로 반드시 발동하지 않는
다는 것을 알게 되었습니다. 예전에 했던 것인데, 3000길 투자하면 헤레틱 상대로
약 10번에 4-5번꼴로 참마도가 나가야 하는데, 실제 실험에서는 10번에 1-2번이었습니다.
최고로 많은 것이 10번에 3번 나간 것이었습니다. 이것은 임의값이 반복 된다는 것을
의미합니다. 즉, 저번 전투에서 임의값 0 으로 계산되었다면, 다음 번에는 0 아닌 다른
수치가 계산될 수도 있고, 또다시 0으로 계산될 수 있다는 것입니다. 임의값이 어떤
룰에 지배받는 것이 아니라, 그냥 '운'인 것이지요. 그래서 전에 제가 오리지날
몬스터급 이상에게는 운이라고 봐야 된다고 했던 것입니다. 헤레틱 상대로 1길
참마도를 쓰려면 임의값이 55이상이어야 하는데 100번 싸워도 임의값이 55가
안넘어 갈수도 있다는 얘기입니다. 물론 이 얘기는 죄다 상성치 255 맥스 기준이구요.

읽느라 고생하셨습니다. 그리고 아래 태클 글은 지우지 않겠습니다. 일부분에 대해서

지적이 잘못되었지만, 쉽게 지워버리면 잘못된 지적에 대한 사과가 아니라고

생각합니다.  그럼.