Final Fantasy X Yojimbo Mathematics Guide
(for International/PAL, North American/Original Japanese releases)
Written by jobber2022497 (Ronald W. Davis II, jobber2022497@yahoo.com)
Version 3.0 (25 December 2003)
Made in WordPad (79 characters per line, Courier New Font, Size 10)
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Table of Contents

I. Introduction
 
II. Important Information for ALL releases of FFX

III. International/PAL Section
   
   A.  A Few Words on "Compatibility"
   B.  CALCULATION OF YOJIMBO'S ATTACK
   C.  The Zanmato Level List
   D.  An Example of How The Formula Works
   E.  Notes on the Steps
   F.  Special Math Topic: Guaranteed Zanmato
   G.  Paid Zanmato Probability Charts (new sub-section)

IV. Original Japanese and North American Section
  
   A.  A Few Words on "Compatibility"
   B.  CALCULATION OF YOJIMBO'S ATTACK
   C.  The Zanmato Level List
   D.  An Example of How The Formula Works
   E.  Notes on the Steps
   F.  Paid Zanmato Probability Charts (new sub-section)

V. Administrivia

   A.  Version History
   B.  Credits




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



D.  An Example of How the Formula Works

Suppose that you pick Option 3.  You are fighting against a Zanmato Level 4
enemy, and you Grand Summon Yojimbo. (it's the first time in your entire game.
Also suppose that you lose the "free attack" roll, and Yojimbo prompts you for
payment.  You then pay him 1024 Gil...

Step One:  Looking at the chart, 1024 Gil -> 36 Motivation.  
           Motivation1 = 36.

Step Two:  It's your first time using him, so Compatibility is 128.
           Motivation2 = Motivation1 + [Compatibility/4] = 36 + 32 = 68.

Step Three:  You picked Option 3, not Option 1, so...
             Motivation3 = Motivation2 = 68.

Step Four:  Zanmato Level of the enemy is 4, and you are on Option 3.
            Motivation4 = [Motivation3 * 0.4] = [27.2] = 27.

Step Five:  Thanks to Grand Summon, Yojimbo has Full Overdrive.
            Add 20 points.
            Motivation5 = Motivation4 + 20 = 27 + 20 = 47.

Step Six:  "Random" number is added to Motivation.  The number is between
            0 and 63, so Motivation6 could be any number between 47 and 110.
            The chance of Motivation6 being 80 or more is ((47-16)/64) = 31/64,
            which is just under 50%. 

Step Seven: If you're lucky and Motivation6 is 80 or greater, then the
            then the calculation stops here and Yojimbo will use Zanmato.
            Assume, though, that you're not lucky, and Motivation6 is less
            than 80.  The game goes through a slightly modified calculation
            of steps One through Six (called "Steps 1b-6b" here).

Steps 1b-3b: The first three steps of the recalculation are exactly the same 
             as they were the first time around (and they always will be).
             Motivation1b = 36
             Motivation2b = 36 + [32] = 68
             Motivation3b = Motivation2b = 68 

Step 4b:     During "re-calculation", the Zanmato Level of the enemy is 1, so
             this step changes a bit (multiplier is 0.8 for Zanmato Level 1).
             Motivation4b = [Motivation3b * 0.8] = [68 * 0.8] = [54.4] = 54.

Step 5b:     Same as Step Five (add 20 points due to full Overdrive).
             Motivation5b = Motivation4b + 20 = 54 + 20 = 74.

Step 6b:     A random number ([0..63]) is added to Motivation5b.
             Motivation6b will be between 74 and 137 (inclusive)

Step 7b:     Since Motivation6b can only be greater than 64, the only 
             possible result of re-calculation is "Wakizashi on all 
             enemies."

So, in this situation (after payment), Yojimbo has a 31/64 (48.4375%) 
chance of using Zanmato, and a 33/64 (51.5625%) chance of using 
Wakizashi on all enemies.  He will not use any of his other attacks this turn.
   


E.  Notes on the Steps

Step 1:  Motivation1 = ([ln(P)/ln(2)] - 1) * 4,  for P = payment > 1 Gil.  
         Unless you picked Option 1, you should only pay Yojimbo in powers
         of 2 (the minimum amount at which Motivation1 changes).  Under
         Option 2 and Option 3, paying him 1000 wastes 478 Gil (it affects 
         him the same as paying 512 would do).  Pay either 512 or 1024 
         instead. 

Step 3:  Option 1 makes Motivation partially dependent on the ratio of your 
         payment to the total amount of Gil that you had before payment. 
         It yields greater Motivation than Option 2 if you pay more
         than half your total Gil (up to 25% greater before Step 5 if you 
         pay all your Gil).  If you pay less than half of your total Gil, 
         you will get less Motivation (as low as 75% of what you would     
         get from Option 2 before Step 5).

Step 4:  Against enemies with Zanmato Level 1, Option 1 is potentially the best
         (due to the possible 25% boost from Step 3), followed by Option 2 
         (which has no decrease like Option 3 or ratio dependence like 
         Option 1).  Option 3 is superior against all other enemies, 
         though. Its multiplier (0.8 for Level 2-3, 0.4 for Level 4+) is
         higher than what you can get from either of the other two options
         against Levels 2 through 6 (even with the "high ratio" bonus from 
         Step 3 with Option 1). 

Step 5:  How important is the "Full Overdrive" bonus?  The 20 points cannot be
         reduced in any way, so even with zero Motivation from the previous 
         steps, you will have a 1 in 16 chance of getting Zanmato (regardless 
         of the enemy's Zanmato Level).  Full Overdrive can add up to 31.25 
         to your percentage chance of getting Zanmato.

Step 6:  You need 80 Motivation points after this step in order to get Zanmato.
         Since the "random" amount will be between 0 and 63, you need at 
         least 17 points at "Motivation5" to get any chance for Zanmato
         (17 + 63 = 80).  The chance of getting a paid Zanmato (based on 
         this "random" factor) is ((Motivation5 - 16)/64), assuming that
         Motivation5 is between 16 and 80 (inclusive).  If Motivation5 is
         16 or less, there is no chance to get Zanmato.  If Motivation5 is
         80 or more, Yojimbo will definitely use Zanmato, regardless of the
         "random" number (more on that in the next section).         



F.  Special Math Topic: Guaranteed Zanmato

(Note:  This sub-section may be more easily read using Notepad due to the
        appearance of "curly brackets" ({}).  Here, they are used to
        represent the "ceiling" function ({x} gives the smallest 
        integer >= x (examples: {4.0} = 4, {4.1} = 5, {4.9} = 5, {-0.9} = 0).
        
        The symbol >= is read as "greater than or equal to".) 

"How much do I pay to get Zanmato?"  This question has been asked at the 
GameFAQs.com message boards many times, but it is not answered easily.  
As shown in the "Calculation" sub-section, payment is not the only (or even 
the most important) factor in Yojimbo's attack choice.  Fortunately, most of
the other factors can be controlled by the player.   In fact, if you keep track
of the Motivation formula through step 5, you can find the chance of Zanmato:
      
  zanmato_prob = (M-16)/64, where M = "Motivation5" (Motivation after Step 5)

If Motivation5 is greater than or equal to 80, then the chance of Zanmato 
is 100%, and it is "guaranteed" that Yojimbo will use Zanmato.  The big
question here is, "how can you get Motivation that high with just the 
factors that you can control (such as payment)?"  It is possible to get more 
than 80 Motivation points through payment only, but in most cases, that 
Motivation will be reduced below 80 in the Zanmato Level steps of the attack 
formula (Steps 3 and 4).  

Below, I will show a way to determine the exact payment needed to "guarantee"
Zanmato (given a certain set of conditions for the other determining factors).

Suppose that you picked Option 3 and you want to guarantee Zanmato against
a Level 1 monster (it could also be a Level 2 or 3 monster, because paid 
attacks are calculated the exact same way against Level 1, 2, and 3 monsters 
under Option 3).  For a better chance of getting Zanmato, you fill Yojimbo's 
Overdrive meter.

Under Option 3 with full overdrive, Motivation5 is as follows:

M = [[([log_2(G)] - 1) * 4 + C/4] * 0.8] + 20


M -- Motivation5
log_2(G) -- base 2 logarithm function (same as (ln(G)/ln(2)))
            (examples: log_2(2) = 1, log_2(4) = 2,  log_2(8) = 3,
            log_2(32) = 5)    
G -- Gil paid (assuming payment is greater than 1 Gil)
C -- Compatibility

"Guaranteed" Zanmato requires that Motivation5 be greater than or 
equal to 80, so:

[[([log_2(G)] - 1) * 4 + C/4] * 0.8] + 20 >= 80

From this we can find the minimum amount of payment needed to guarantee 
Zanmato at varying levels of Compatibility. 

This part requires a bit of algebra:

[[([log_2(G)] - 1) * 4 + C/4] * 0.8] + 20 >= 80
[[([log_2(G)] - 1) * 4 + C/4] * 0.8] >= 60
[([log_2(G)] - 1) * 4 + C/4] * 0.8 >= {60}
[([log_2(G)] - 1) * 4 + C/4] * 0.8 >= 60
[([log_2(G)] - 1) * 4 + C/4] >= 75
([log_2(G)] - 1) * 4 + C/4 >= {75}
([log_2(G)] - 1) * 4 + C/4 >= 75
([log_2(G)] - 1) * 4  >= 75 - C/4
([log_2(G)] - 1)  >=  18.75 - C/16
[log_2(G)]  >=  19.75 - C/16
[log_2(G)]  >=  20 - C/16 - 4/16
[log_2(G)]  >=  20 - (C + 4)/16
log_2(G)  >=  {20 - (C + 4)/16}
log_2(G)  >=  20 - [(C + 4)/16]
G  >=  2 ^ (20 - [(C + 4)/16])

So, with the conditions outlined above (Option 3, enemy Zanmato Level 1-3,
Full Overdrive), the minimum payment needed to assure that Yojimbo will
use Zanmato is 2^(20-[{C+4)/16]), with C = Compatibility.  That means when
Compatibility is zero, you will need to pay 2^20 = 1,048,576 Gil in order 
to guarantee Zanmato.  At 255 (maximum) Compatibility, the amount required
is only 2^(20-[(255+4)/16]) = 2^(20-[259/16]) = 2^(20-16) = 2^4 = 16 Gil!

If you picked Option 3 and either fight a Level 4-6 enemy or fail to fill
Yojimbo's Overdrive meter, then the payment needed in order to guarantee 
Zanmato increases.  Using a similar procedure to the one shown above, we 
can derive the formulae for the amount needed to guarantee Zanmato against 
high-level enemies and/or without full Overdrive.  In order to save space, 
I will show only the final results for each case.

Against Level 1-3 with full Overdrive:
G = 2 ^ (20 - [(C+4)/16])   (shown for comparison)

Against Level 1-3 without full Overdrive:
G = 2 ^ (26 - [C/16])

Against Level 4-6 with full Overdrive*:
G = 2 ^ (39 - [(C+8)/16])

Against Level 4-6 without full Overdrive**:
G = 2 ^ (51 - [C/16]) 

Remember that the maximum effective amount of Gil that you can pay is 2^29.
The guarantee amounts are a bit different under Options 1 and 2.  
They are not shown here, but they may be covered in a future update of 
this guide. 

*-In this case, it is impossible to guarantee Zanmato for 
  Compatibility < 152 (because of the game's Gil limit). 

**-In this case, it is impossible to guarantee Zanmato for any 
   Compatibility value (because of the game's Gil limit).  
   This is a theoretical amount that is impossible for the player to have.

Of course, you can secure a very good chance of Zanmato with payments that
are significantly lower than these (see below).



G.  Paid Zanmato Probability Charts

The following charts show the percentage chances that Yojimbo will use Zanmato
on a paid attack in FFX International and FFX PAL at various levels of payment
and Compatibility (percentages are rounded to the nearest whole number).

Due to time and space considerations, the charts below apply only to those
who picked Option 3 in the cave ("To defeat the strongest enemies").
There are four charts: one for each combination of Overdrive status (FULL
or not full) and enemy Zanmato Level (1-3 or 4-6).

The rows represent payment levels, which are exactly the same as in Step One
of the attack formula.  The columns are Compatibility levels.  Keep in mind
that the default Compatibility level is 128.  Remember that this information
pertains to paid attacks only; free attacks are an entirely separate issue.


International/PAL version
Option 3
no Overdrive
vs. Zanmato Level 1-3
 _____________________________________________________________________
|                       ||                 Compatibility              |
|                       ||  0 | 32 | 64 | 96 |128 |160 |192 |224 |252 |
|-----------------------||--------------------------------------------|
|         1 - 3         ||  0 |  0 |  0 |  5 | 14 | 25 | 34 | 44 | 53 |
|         4 - 7         ||  0 |  0 |  0 |  9 | 19 | 30 | 39 | 50 | 58 |
|         8 - 15        ||  0 |  0 |  5 | 14 | 25 | 34 | 44 | 55 | 63 |
|        16 - 31        ||  0 |  0 |  9 | 19 | 30 | 39 | 50 | 59 | 69 |
|        32 - 63        ||  0 |  5 | 14 | 25 | 34 | 44 | 55 | 64 | 73 |
|        64 - 127       ||  0 |  9 | 19 | 30 | 39 | 50 | 59 | 69 | 78 |
|       128 - 255       ||  5 | 14 | 25 | 34 | 44 | 55 | 64 | 75 | 83 |
|       256 - 511       ||  9 | 19 | 30 | 39 | 50 | 59 | 69 | 80 | 88 |
|P      512 - 1023      || 14 | 25 | 34 | 44 | 55 | 64 | 75 | 84 | 94 |
|a     1024 - 2047      || 19 | 30 | 39 | 50 | 59 | 69 | 80 | 89 | 98 |
|y     2048 - 4095      || 25 | 34 | 44 | 55 | 64 | 75 | 84 | 94 |100 |
|m     4096 - 8191      || 30 | 39 | 50 | 59 | 69 | 80 | 89 |100 |100 |
|e     8192 - 16383     || 34 | 44 | 55 | 64 | 75 | 84 | 94 |100 |100 |
|n    16384 - 32767     || 39 | 50 | 59 | 69 | 80 | 89 |100 |100 |100 |
|t    32768 - 65535     || 44 | 55 | 64 | 75 | 84 | 94 |100 |100 |100 |
|     65536 - 131071    || 50 | 59 | 69 | 80 | 89 |100 |100 |100 |100 |
|    131072 - 262143    || 55 | 64 | 75 | 84 | 94 |100 |100 |100 |100 |
|    262144 - 524287    || 59 | 69 | 80 | 89 |100 |100 |100 |100 |100 |
|    524288 - 1049575   || 64 | 75 | 84 | 94 |100 |100 |100 |100 |100 |
|   1048576 - 2097151   || 69 | 80 | 89 |100 |100 |100 |100 |100 |100 |
|   2097152 - 4194303   || 75 | 84 | 94 |100 |100 |100 |100 |100 |100 |
|   4194304 - 8388607   || 80 | 89 |100 |100 |100 |100 |100 |100 |100 |
|   8388608 - 16777215  || 84 | 94 |100 |100 |100 |100 |100 |100 |100 |
|  16777216 - 33554431  || 89 |100 |100 |100 |100 |100 |100 |100 |100 |
|  33554432 - 67108863  || 94 |100 |100 |100 |100 |100 |100 |100 |100 |
|  67108864 - 134217727 ||100 |100 |100 |100 |100 |100 |100 |100 |100 |
| 134217728 - 268435455 ||100 |100 |100 |100 |100 |100 |100 |100 |100 |
| 268435456 - 536870911 ||100 |100 |100 |100 |100 |100 |100 |100 |100 |
| 536870912 - 999999999 ||100 |100 |100 |100 |100 |100 |100 |100 |100 |
 ---------------------------------------------------------------------



International/PAL version
Option 3
FULL Overdrive
vs. Zanmato Level 1-3
 _____________________________________________________________________
|                       ||                 Compatibility              |
|                       ||  0 | 32 | 64 | 96 |128 |160 |192 |224 |252 |
|-----------------------||--------------------------------------------|
|         1 - 3         ||  6 | 16 | 25 | 36 | 45 | 56 | 66 | 75 | 84 |
|         4 - 7         || 11 | 20 | 31 | 41 | 50 | 61 | 70 | 81 | 89 |
|         8 - 15        || 16 | 25 | 36 | 45 | 56 | 66 | 75 | 86 | 94 |
|        16 - 31        || 20 | 31 | 41 | 50 | 61 | 70 | 81 | 91 |100 |
|        32 - 63        || 25 | 36 | 45 | 56 | 66 | 75 | 86 | 95 |100 |
|        64 - 127       || 31 | 41 | 50 | 61 | 70 | 81 | 91 |100 |100 |
|       128 - 255       || 36 | 45 | 56 | 66 | 75 | 86 | 95 |100 |100 |
|       256 - 511       || 41 | 50 | 61 | 70 | 81 | 91 |100 |100 |100 |
|P      512 - 1023      || 45 | 56 | 66 | 75 | 86 | 95 |100 |100 |100 |
|a     1024 - 2047      || 50 | 61 | 70 | 81 | 91 |100 |100 |100 |100 |
|y     2048 - 4095      || 56 | 66 | 75 | 86 | 95 |100 |100 |100 |100 |
|m     4096 - 8191      || 61 | 70 | 81 | 91 |100 |100 |100 |100 |100 |
|e     8192 - 16383     || 66 | 75 | 86 | 95 |100 |100 |100 |100 |100 |
|n    16384 - 32767     || 70 | 81 | 91 |100 |100 |100 |100 |100 |100 |
|t    32768 - 65535     || 75 | 86 | 95 |100 |100 |100 |100 |100 |100 |
|     65536 - 131071    || 81 | 91 |100 |100 |100 |100 |100 |100 |100 |
|    131072 - 262143    || 86 | 95 |100 |100 |100 |100 |100 |100 |100 |
|    262144 - 524287    || 91 |100 |100 |100 |100 |100 |100 |100 |100 |
|    524288 - 1049575   || 95 |100 |100 |100 |100 |100 |100 |100 |100 |
|   1048576 - 2097151   ||100 |100 |100 |100 |100 |100 |100 |100 |100 |
|   2097152 - 4194303   ||100 |100 |100 |100 |100 |100 |100 |100 |100 |
|   4194304 - 8388607   ||100 |100 |100 |100 |100 |100 |100 |100 |100 |
|   8388608 - 16777215  ||100 |100 |100 |100 |100 |100 |100 |100 |100 |
|  16777216 - 33554431  ||100 |100 |100 |100 |100 |100 |100 |100 |100 |
|  33554432 - 67108863  ||100 |100 |100 |100 |100 |100 |100 |100 |100 |
|  67108864 - 134217727 ||100 |100 |100 |100 |100 |100 |100 |100 |100 |
| 134217728 - 268435455 ||100 |100 |100 |100 |100 |100 |100 |100 |100 |
| 268435456 - 536870911 ||100 |100 |100 |100 |100 |100 |100 |100 |100 |
| 536870912 - 999999999 ||100 |100 |100 |100 |100 |100 |100 |100 |100 |
 ---------------------------------------------------------------------



International/PAL version
Option 3
no Overdrive
vs. Zanmato Level 4-6
 _____________________________________________________________________
|                       ||                Compatibility               |
|                       ||  0 | 32 | 64 | 96 |128 |160 |192 |224 |252 |
|-----------------------||--------------------------------------------|
|         1 - 3         ||  0 |  0 |  0 |  0 |  0 |  0 |  5 |  9 | 14 |
|         4 - 7         ||  0 |  0 |  0 |  0 |  0 |  2 |  6 | 13 | 16 |
|         8 - 15        ||  0 |  0 |  0 |  0 |  0 |  5 |  9 | 14 | 19 |
|        16 - 31        ||  0 |  0 |  0 |  0 |  2 |  6 | 13 | 17 | 22 |
|        32 - 63        ||  0 |  0 |  0 |  0 |  5 |  9 | 14 | 19 | 23 |
|        64 - 127       ||  0 |  0 |  0 |  2 |  6 | 13 | 17 | 22 | 27 |
|       128 - 255       ||  0 |  0 |  0 |  5 |  9 | 14 | 19 | 25 | 28 |
|       256 - 511       ||  0 |  0 |  2 |  6 | 13 | 17 | 22 | 27 | 31 |
|P      512 - 1023      ||  0 |  0 |  5 |  9 | 14 | 19 | 25 | 30 | 34 |
|a     1024 - 2047      ||  0 |  2 |  6 | 13 | 17 | 22 | 27 | 31 | 36 |
|y     2048 - 4095      ||  0 |  5 |  9 | 14 | 19 | 25 | 30 | 34 | 39 |
|m     4096 - 8191      ||  2 |  6 | 13 | 17 | 22 | 27 | 31 | 38 | 41 |
|e     8192 - 16383     ||  5 |  9 | 14 | 19 | 25 | 30 | 34 | 39 | 44 |
|n    16384 - 32767     ||  6 | 13 | 17 | 22 | 27 | 31 | 38 | 42 | 47 |
|t    32768 - 65535     ||  9 | 14 | 19 | 25 | 30 | 34 | 39 | 44 | 48 |
|     65536 - 131071    || 13 | 17 | 22 | 27 | 31 | 38 | 42 | 47 | 52 |
|    131072 - 262143    || 14 | 19 | 25 | 30 | 34 | 39 | 44 | 50 | 53 |
|    262144 - 524287    || 17 | 22 | 27 | 31 | 38 | 42 | 47 | 52 | 56 |
|    524288 - 1048575   || 19 | 25 | 30 | 34 | 39 | 44 | 50 | 55 | 59 |
|   1048576 - 2097151   || 22 | 27 | 31 | 38 | 42 | 47 | 52 | 56 | 61 |
|   2097152 - 4194303   || 25 | 30 | 34 | 39 | 44 | 50 | 55 | 59 | 64 |
|   4194304 - 8388607   || 27 | 31 | 38 | 42 | 47 | 52 | 56 | 63 | 66 |
|   8388608 - 16777215  || 30 | 34 | 39 | 44 | 50 | 55 | 59 | 64 | 69 |
|  16777216 - 33554431  || 31 | 38 | 42 | 47 | 52 | 56 | 63 | 67 | 72 |
|  33554432 - 67108863  || 34 | 39 | 44 | 50 | 55 | 59 | 64 | 69 | 73 |
|  67108864 - 134217727 || 38 | 42 | 47 | 52 | 56 | 63 | 67 | 72 | 77 |
| 134217728 - 268435455 || 39 | 44 | 50 | 55 | 59 | 64 | 69 | 75 | 78 |
| 268435456 - 536870911 || 42 | 47 | 52 | 56 | 63 | 67 | 72 | 77 | 81 |
| 536870912 - 999999999 || 44 | 50 | 55 | 59 | 64 | 69 | 75 | 80 | 84 |
 ---------------------------------------------------------------------



International/PAL version
Option 3
FULL Overdrive
vs. Zanmato Level 4-6
 _____________________________________________________________________
|                       ||                 Compatibility              |
|                       ||  0 | 32 | 64 | 96 |128 |160 |192 |224 |252 |
|-----------------------||--------------------------------------------|
|         1 - 3         ||  6 | 11 | 16 | 20 | 25 | 31 | 36 | 41 | 45 |
|         4 - 7         ||  8 | 13 | 19 | 23 | 28 | 33 | 38 | 44 | 47 |
|         8 - 15        || 11 | 16 | 20 | 25 | 31 | 36 | 41 | 45 | 50 |
|        16 - 31        || 13 | 19 | 23 | 28 | 33 | 38 | 44 | 48 | 53 |
|        32 - 63        || 16 | 20 | 25 | 31 | 36 | 41 | 45 | 50 | 55 |
|        64 - 127       || 19 | 23 | 28 | 33 | 38 | 44 | 48 | 53 | 58 |
|       128 - 255       || 20 | 25 | 31 | 36 | 41 | 45 | 50 | 56 | 59 |
|       256 - 511       || 23 | 28 | 33 | 38 | 44 | 48 | 53 | 58 | 63 |
|P      512 - 1023      || 25 | 31 | 36 | 41 | 45 | 50 | 56 | 61 | 66 |
|a     1024 - 2047      || 28 | 33 | 38 | 44 | 48 | 53 | 58 | 63 | 67 |
|y     2048 - 4095      || 31 | 36 | 41 | 45 | 50 | 56 | 61 | 66 | 70 |
|m     4096 - 8191      || 33 | 38 | 44 | 48 | 53 | 58 | 63 | 69 | 72 |
|e     8192 - 16383     || 36 | 41 | 45 | 50 | 56 | 61 | 66 | 70 | 75 |
|n    16384 - 32767     || 38 | 44 | 48 | 53 | 58 | 63 | 69 | 73 | 78 |
|t    32768 - 65535     || 41 | 45 | 50 | 56 | 61 | 66 | 70 | 75 | 80 |
|     65536 - 131071    || 44 | 48 | 53 | 58 | 63 | 69 | 73 | 78 | 83 |
|    131072 - 262143    || 45 | 50 | 56 | 61 | 66 | 70 | 75 | 81 | 84 |
|    262144 - 524287    || 48 | 53 | 58 | 63 | 69 | 73 | 78 | 83 | 88 |
|    524288 - 1049575   || 50 | 56 | 61 | 66 | 70 | 75 | 81 | 86 | 91 |
|   1048576 - 2097151   || 53 | 58 | 63 | 69 | 73 | 78 | 83 | 88 | 92 |
|   2097152 - 4194303   || 56 | 61 | 66 | 70 | 75 | 81 | 86 | 91 | 95 |
|   4194304 - 8388607   || 58 | 63 | 69 | 73 | 78 | 83 | 88 | 94 | 97 |
|   8388608 - 16777215  || 61 | 66 | 70 | 75 | 81 | 86 | 91 | 95 |100 |
|  16777216 - 33554431  || 63 | 69 | 73 | 78 | 83 | 88 | 94 | 98 |100 |
|  33554432 - 67108863  || 66 | 70 | 75 | 81 | 86 | 91 | 95 |100 |100 |
|  67108864 - 134217727 || 69 | 73 | 78 | 83 | 88 | 94 | 98 |100 |100 |
| 134217728 - 268435455 || 70 | 75 | 81 | 86 | 91 | 95 |100 |100 |100 |
| 268435456 - 536870911 || 73 | 78 | 83 | 88 | 94 | 98 |100 |100 |100 |
| 536870912 - 999999999 || 75 | 81 | 86 | 91 | 95 |100 |100 |100 |100 |
 ---------------------------------------------------------------------



Chart Notes:

- The probabilities here are listed in percentages, but the actual
random factor is taken from 64 possible values, not 100.  Thus, most of the
percentages in the tables are rounded.  There are a few percentages that are
exact, though.  Those are 0, 25, 50, 75, and 100.

- The maximum Compatibility level is 255, but the maximum effect on
Motivation is obtained at 252 Compatibility (or greater).  Therefore, the
the "252" column in the tables applies for any Compatibility level greater
than or equal to 252.

- Since the column values increase by 32, and the actual change in
Motivation occurs at four-point Compatibility intervals, intermediate values
of Compatibility (such as 144 or 200) will most likely have a percentage
chance somewhere between those listed for the two nearest Compatibility
values (in the case of 144, it would be somewhere between the chances at
128 Compatibility and 160 Compatibility).


END INT/PAL 
R.W.D.




IV.   Original Japanese and North American 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 50.  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 original Japanese Yojimbo attack formula (also for the North American 
version) originally appeared in the FFX Battle Ultimania Guide 
(Digicube/Studio Bentstuff).  It was then posted at the GameFAQs Secrets 
and Side Quests board by Shinryu.  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 less than a 1 in 20 chance of 
attacking for free, but 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 forthcoming) 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 is 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                  |           2
   8-15 Gil                 |           4
   16-31 Gil                |           6
   32-63 Gil                |           8 
   64-127 Gil               |          10
   128-255 Gil              |          12
   256-511 Gil              |          14
   512-1023 Gil             |          16
   1024-2047 Gil            |          18
   2048-4095 Gil            |          20
   4096-8191 Gil            |          22
   8192-16383 Gil           |          24
   16384-32767 Gil          |          26
   32768-65535 Gil          |          28
   65536-131071 Gil         |          30
   131072-262143 Gil        |          32
   262144-524287 Gil        |          34
   524288-1048575 Gil       |          36
   1048576-2097151 Gil      |          38
   2097152-4194303 Gil      |          40
   4194304-8388607 Gil      |          42
   8388608-16777215 Gil     |          44
   16777216-33554431 Gil    |          46
   33554432-67108863 Gil    |          48
   67108864-134217727 Gil   |          50
   134217728-268435455 Gil  |          52
   268435456-536870911 Gil  |          54
   536870912-999999999 Gil  |          56
 

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/30]


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 Resistance Level of the enemy 
(Zanmato Levels range from 1 to 5) 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]


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 + 2.
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 + 2. 
 (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 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
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
Malboro (Japanese version)
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 (North American version)
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

Missing from this list are the following :  

Possessed Aeons/Yu Pagoda/(final boss) - no data on these so far
Belgemine's Aeons - still no clue on this one at this time



D.  An Example of How the Formula Works

Suppose that you pick Option 3.  You are fighting against a Zanmato Level 4
enemy, and you Grand Summon Yojimbo. (it's the first time in your entire game.
Also suppose that you lose the "free attack" roll, and Yojimbo prompts 
you for payment.  You then pay him 1024 Gil...

Step One:  Looking at the chart, 1024 Gil -> 18 Motivation.  
           Motivation1 = 18.

Step Two:  It's your first time using him, so Compatibility is 50.
           Motivation2 = Motivation1 + [Compatibility/4] = 18 + [50/30] 
           = 18 + 1 = 19.

Step Three:  You picked Option 3, not Option 1, so...
             Motivation3 = Motivation2 = 19.

Step Four:  Zanmato Level of the enemy is 4, and you are on Option 3.
            Motivation4 = [Motivation3 * 0.4] = [19 * 0.4] = [7.6] = 7.

Step Five:  Thanks to Grand Summon, Yojimbo has Full Overdrive. 
            Add two (2) points.
            Motivation5 = Motivation4 + 2 = 7 + 2 = 9.

Step Six:  "Random" number is added to Motivation.  The number is between
            0 and 63, so Motivation6 could be any number between 9 and 72.
            The chance of Motivation6 being 80 or more is zero. 

Step Seven: Motivation6 is less than 80.  The game will go through a slightly
            modified "re-calculation" of steps One through Six (called 
            "Steps 1b-6b" here).

Steps 1b-3b: The first three steps of the recalculation are exactly the same
             as they were the first time around (and they always will be).
             Motivation1b = 18
             Motivation2b = 18 + [50/30] = 19
             Motivation3b = Motivation9 = 19 

Step 4b: During "re-calculation", the Zanmato Level of the enemy is 1, so
         this step changes a bit (multiplier is 0.8 for Zanmato Level 1).
             Motivation4b = [Motivation3b * 0.8] = [19 * 0.8] = [15.2] = 15.

Step 5b:  Same as Step Five (add 2 points due to full Overdrive).
             Motivation5b = Motivation4b + 2 = 15 + 2 = 17.

Step 6b:  A random number ([0..63]) is added to Motivation12.
             Motivation6b will be between 17 and 80 (inclusive).

Step 7b:  Motivation6b will be between 17 and 80 (as stated above).  
             If it is between 17 and 31, Yojimbo will use Daigoro.
             If it is between 32 and 47, Yojimbo will use Kozuka.
             If it is between 48 and 63, Yojimbo will use Wakizashi (one).
             If it is between 64 and 80, Yojimbo will use Wakizashi (all).

The overall chances for each attack on this turn (assuming no "free attack") 
are as follows:

Zanmato:  0
Wakizashi (all):  17/64 = 26.5625%
Wakizashi (one):  16/64 = 1/4 =  25%
Kozuka:  16/64 = 1/4 = 25%
Daigoro:  15/64 = 23.4365%



E.  Notes on the steps

Step 1:  Motivation1 = ([ln(P)/ln2] - 1) * 2  for P = payment > 1 Gil.  
         Unless you picked Option 1, you should only pay Yojimbo in powers
         of 2 (the minimum amount at which Motivation1 changes).  Under
         Option 2 and Option 3, paying him 1000 wastes 478 Gil (it affects 
         him the same as paying 512 Gil).  In that case, pay either 
         512 or 1024 instead. 

Step 2:  Surprisingly, Compatibility does not have much influence on Yojimbo's
         paid attacks (especially compared to the newer International/PAL 
         formula).  At the start, it only adds [50/30] = 1 point of 
         Motivation (which can be reduced by Step 3 or 4).  Even when it is
         "maxed out" at 255, Compatibility only adds 8 reducible points of 
         Motivation (compare to the Int/PAL version, which adds 32 at the 
         beginning, and "maxes out" at 63).  It's still worth it to raise 
         Compatibility, because when Compatibility is high, you will get
         free attacks often (including free Zanmato against Level 1 enemies).

Step 3:  Option 1 makes Motivation partially dependent on the ratio of your 
         payment to the total amount of Gil that you had before payment. 
         It yields greater Motivation than Option 2 if you pay more
         than half your total Gil (up to 25% greater through step 4 if you 
         pay all your Gil).  If you pay less than half of your total Gil, 
         you will get less Motivation (as low as 75% of what you would
         get from Option 2 through Step 4).

Step 4:  Against enemies with Zanmato Level 1, Option 1 is potentially the best
         (due to the possible 25% boost from Step 3), followed by Option 2 
         (which has no decrease like Option 3 or ratio dependence like 
         Option 1).  Option 3 is superior against all other enemies, 
         though. Its multiplier (0.8 for Level 2-3, 0.4 for Level 4+) is
         higher than what you can get from either of the other two options
         (even with the "full payment" bonus from Option 1) for 
         Levels 2 through 5.

Step 5:  How important is the "Full Overdrive" bonus?  It really doesn't
         do much at all.  It adds two points to Motivation after the Zanmato
         Level part, so it might help you out a bit (but don't expect 
         too much). 

Step 6:  You need 80 Motivation points after this step in order to get Zanmato.
         Since the "random" amount will be between 0 and 63, you need at 
         least 17 points at "Motivation5" to get any chance for Zanmato
         (17 + 63 = 80).  The chance of getting a paid Zanmato (based on 
         this "random" factor) is ((Motivation5 - 16)/64), assuming that
         Motivation5 is between 16 and 80 (inclusive).  If Motivation5 is
         16 or less, there's no chance to get Zanmato.  If Motivation5 is
         80 or more, Yojimbo will definitely use Zanmato, regardless of the
         "random" number (that will not happen except under the most extreme
         circumstances, though).         



F.  Paid Zanmato Probability Charts

The following charts show the percentage chances that Yojimbo will use Zanmato
on a paid attack at all levels of payment and Compatibility in the 
North American and original Japanese versions of FFX (percentages are 
rounded to the nearest whole number).

Due to time and space considerations, the charts below apply only to those
who picked Option 3 in the cave ("To defeat the strongest enemies").
There are four charts: one for each combination of Overdrive status
(FULL or not full) and enemy Zanmato Level (1-3 or 4-5).

The rows represent payment levels, which are exactly the same as in Step One
of the attack formula.  The columns are Compatibility levels.  Keep in mind
that the default Compatibility level is 50 (for which you would look at the
"30" column -- see the third Note below the tables).  Remember that this
information pertains to paid attacks only; free attacks are an entirely
separate issue.


North American/Original Japanese version
Option 3
no Overdrive
vs. Zanmato Level 1-3
 _____________________________________________________________________
|                       ||                Compatibility               |
|                       ||  0 | 30 | 60 | 90 |120 |150 |180 |210 |240 |
|-----------------------||--------------------------------------------|
|         1 - 3         ||  0 |  0 |  0 |  0 |  0 |  0 |  0 |  0 |  0 |
|         4 - 7         ||  0 |  0 |  0 |  0 |  0 |  0 |  0 |  0 |  0 |
|         8 - 15        ||  0 |  0 |  0 |  0 |  0 |  0 |  0 |  0 |  0 |
|        16 - 31        ||  0 |  0 |  0 |  0 |  0 |  0 |  0 |  0 |  0 |
|        32 - 63        ||  0 |  0 |  0 |  0 |  0 |  0 |  0 |  0 |  0 |
|        64 - 127       ||  0 |  0 |  0 |  0 |  0 |  0 |  0 |  0 |  0 |
|       128 - 255       ||  0 |  0 |  0 |  0 |  0 |  0 |  0 |  0 |  0 |
|       256 - 511       ||  0 |  0 |  0 |  0 |  0 |  0 |  0 |  0 |  2 |
|P      512 - 1023      ||  0 |  0 |  0 |  0 |  0 |  0 |  2 |  3 |  5 |
|a     1024 - 2047      ||  0 |  0 |  0 |  0 |  2 |  3 |  5 |  6 |  6 |
|y     2048 - 4095      ||  0 |  0 |  2 |  3 |  5 |  6 |  6 |  8 |  9 |
|m     4096 - 8191      ||  2 |  3 |  5 |  6 |  6 |  8 |  9 | 11 | 13 |
|e     8192 - 16383     ||  5 |  6 |  6 |  8 |  9 | 11 | 13 | 13 | 14 |
|n    16384 - 32767     ||  6 |  8 |  9 | 11 | 13 | 13 | 14 | 16 | 17 |
|t    32768 - 65535     ||  9 | 11 | 13 | 13 | 14 | 16 | 17 | 19 | 19 |
|     65536 - 131071    || 13 | 13 | 14 | 16 | 17 | 19 | 19 | 20 | 22 |
|    131072 - 262143    || 14 | 16 | 17 | 19 | 19 | 20 | 22 | 23 | 25 |
|    262144 - 524287    || 17 | 19 | 19 | 20 | 22 | 23 | 25 | 25 | 27 |
|    524288 - 1048575   || 19 | 20 | 22 | 23 | 25 | 25 | 27 | 28 | 30 |
|   1048576 - 2097151   || 22 | 23 | 25 | 25 | 27 | 28 | 30 | 31 | 31 |
|   2097152 - 4194303   || 25 | 25 | 27 | 28 | 30 | 31 | 31 | 33 | 34 |
|   4194304 - 8388607   || 27 | 28 | 30 | 31 | 31 | 33 | 34 | 36 | 38 |
|   8388608 - 16777215  || 30 | 31 | 31 | 33 | 34 | 36 | 38 | 38 | 39 |
|  16777216 - 33554431  || 31 | 33 | 34 | 36 | 38 | 38 | 39 | 41 | 42 |
|  33554432 - 67108863  || 34 | 36 | 38 | 38 | 39 | 41 | 42 | 44 | 44 |
|  67108864 - 134217727 || 38 | 38 | 39 | 41 | 42 | 44 | 44 | 45 | 47 |
| 134217728 - 268435455 || 39 | 41 | 42 | 44 | 44 | 45 | 47 | 48 | 50 |
| 268435456 - 536870911 || 42 | 44 | 44 | 45 | 47 | 48 | 50 | 50 | 52 |
| 536870912 - 999999999 || 44 | 45 | 47 | 48 | 50 | 50 | 52 | 53 | 55 |
 ---------------------------------------------------------------------



North American/Original Japanese version
Option 3
Full Overdrive
vs. Zanmato Level 1-3
 _____________________________________________________________________
|                       ||                Compatibility               |
|                       ||  0 | 30 | 60 | 90 |120 |150 |180 |210 |240 |
|-----------------------||--------------------------------------------|
|         1 - 3         ||  0 |  0 |  0 |  0 |  0 |  0 |  0 |  0 |  0 |
|         4 - 7         ||  0 |  0 |  0 |  0 |  0 |  0 |  0 |  0 |  0 |
|         8 - 15        ||  0 |  0 |  0 |  0 |  0 |  0 |  0 |  0 |  0 |
|        16 - 31        ||  0 |  0 |  0 |  0 |  0 |  0 |  0 |  0 |  0 |
|        32 - 63        ||  0 |  0 |  0 |  0 |  0 |  0 |  0 |  0 |  0 |
|        64 - 127       ||  0 |  0 |  0 |  0 |  0 |  0 |  0 |  0 |  0 |
|       128 - 255       ||  0 |  0 |  0 |  0 |  0 |  0 |  0 |  2 |  3 |
|       256 - 511       ||  0 |  0 |  0 |  0 |  0 |  2 |  3 |  3 |  5 |
|P      512 - 1023      ||  0 |  0 |  0 |  2 |  3 |  3 |  5 |  6 |  8 |
|a     1024 - 2047      ||  0 |  2 |  3 |  3 |  5 |  6 |  8 |  9 |  9 |
|y     2048 - 4095      ||  3 |  3 |  5 |  6 |  8 |  9 |  9 | 11 | 13 |
|m     4096 - 8191      ||  5 |  6 |  8 |  9 |  9 | 11 | 13 | 14 | 16 |
|e     8192 - 16383     ||  8 |  9 |  9 | 11 | 13 | 14 | 16 | 16 | 17 |
|n    16384 - 32767     ||  9 | 11 | 13 | 14 | 16 | 16 | 17 | 19 | 20 |
|t    32768 - 65535     || 13 | 14 | 16 | 16 | 17 | 19 | 20 | 22 | 22 |
|     65536 - 131071    || 16 | 16 | 17 | 19 | 20 | 22 | 22 | 23 | 25 |
|    131072 - 262143    || 17 | 19 | 20 | 22 | 22 | 23 | 25 | 27 | 28 |
|    262144 - 524287    || 20 | 22 | 22 | 23 | 25 | 27 | 28 | 28 | 30 |
|    524288 - 1048575   || 22 | 23 | 25 | 27 | 28 | 28 | 30 | 31 | 33 |
|   1048576 - 2097151   || 25 | 27 | 28 | 28 | 30 | 31 | 33 | 34 | 34 |
|   2097152 - 4194303   || 28 | 28 | 30 | 31 | 33 | 34 | 34 | 36 | 38 |
|   4194304 - 8388607   || 30 | 31 | 33 | 34 | 34 | 36 | 38 | 39 | 41 |
|   8388608 - 16777215  || 33 | 34 | 34 | 36 | 38 | 39 | 41 | 41 | 42 |
|  16777216 - 33554431  || 34 | 36 | 38 | 39 | 41 | 41 | 42 | 44 | 45 |
|  33554432 - 67108863  || 38 | 39 | 41 | 41 | 42 | 44 | 45 | 47 | 47 |
|  67108864 - 134217727 || 41 | 41 | 42 | 44 | 45 | 47 | 47 | 48 | 50 |
| 134217728 - 268435455 || 42 | 44 | 45 | 47 | 47 | 48 | 50 | 52 | 53 |
| 268435456 - 536870911 || 45 | 47 | 47 | 48 | 50 | 52 | 53 | 53 | 55 |
| 536870912 - 999999999 || 47 | 48 | 50 | 52 | 53 | 53 | 55 | 56 | 58 |
 ---------------------------------------------------------------------



North American/Original Japanese version
Option 3
no Overdrive
vs. Zanmato Level 4-5
 _____________________________________________________________________
|                       ||                Compatibility               |
|                       ||  0 | 30 | 60 | 90 |120 |150 |180 |210 |240 |
|-----------------------||--------------------------------------------|
|         1 - 3         ||  0 |  0 |  0 |  0 |  0 |  0 |  0 |  0 |  0 |
|         4 - 7         ||  0 |  0 |  0 |  0 |  0 |  0 |  0 |  0 |  0 |
|         8 - 15        ||  0 |  0 |  0 |  0 |  0 |  0 |  0 |  0 |  0 |
|        16 - 31        ||  0 |  0 |  0 |  0 |  0 |  0 |  0 |  0 |  0 |
|        32 - 63        ||  0 |  0 |  0 |  0 |  0 |  0 |  0 |  0 |  0 |
|        64 - 127       ||  0 |  0 |  0 |  0 |  0 |  0 |  0 |  0 |  0 |
|       128 - 255       ||  0 |  0 |  0 |  0 |  0 |  0 |  0 |  0 |  0 |
|       256 - 511       ||  0 |  0 |  0 |  0 |  0 |  0 |  0 |  0 |  0 |
|P      512 - 1023      ||  0 |  0 |  0 |  0 |  0 |  0 |  0 |  0 |  0 |
|a     1024 - 2047      ||  0 |  0 |  0 |  0 |  0 |  0 |  0 |  0 |  0 |
|y     2048 - 4095      ||  0 |  0 |  0 |  0 |  0 |  0 |  0 |  0 |  0 |
|m     4096 - 8191      ||  0 |  0 |  0 |  0 |  0 |  0 |  0 |  0 |  0 |
|e     8192 - 16383     ||  0 |  0 |  0 |  0 |  0 |  0 |  0 |  0 |  0 |
|n    16384 - 32767     ||  0 |  0 |  0 |  0 |  0 |  0 |  0 |  0 |  0 |
|t    32768 - 65535     ||  0 |  0 |  0 |  0 |  0 |  0 |  0 |  0 |  0 |
|     65536 - 131071    ||  0 |  0 |  0 |  0 |  0 |  0 |  0 |  0 |  0 |
|    131072 - 262143    ||  0 |  0 |  0 |  0 |  0 |  0 |  0 |  0 |  0 |
|    262144 - 524287    ||  0 |  0 |  0 |  0 |  0 |  0 |  0 |  0 |  0 |
|    524288 - 1048575   ||  0 |  0 |  0 |  0 |  0 |  0 |  0 |  2 |  2 |
|   1048576 - 2097151   ||  0 |  0 |  0 |  0 |  0 |  2 |  2 |  3 |  3 |
|   2097152 - 4194303   ||  0 |  0 |  0 |  2 |  2 |  3 |  3 |  3 |  5 |
|   4194304 - 8388607   ||  0 |  2 |  2 |  3 |  3 |  3 |  5 |  5 |  6 |
|   8388608 - 16777215  ||  2 |  3 |  3 |  3 |  5 |  5 |  6 |  6 |  6 |
|  16777216 - 33554431  ||  3 |  3 |  5 |  5 |  6 |  6 |  6 |  8 |  8 |
|  33554432 - 67108863  ||  5 |  5 |  6 |  6 |  6 |  8 |  8 |  9 |  9 |
|  67108864 - 134217727 ||  6 |  6 |  6 |  8 |  8 |  9 |  9 |  9 | 11 |
| 134217728 - 268435455 ||  6 |  8 |  8 |  9 |  9 |  9 | 11 | 11 | 13 |
| 268435456 - 536870911 ||  8 |  9 |  9 |  9 | 11 | 11 | 13 | 13 | 13 |
| 536870912 - 999999999 ||  9 |  9 | 11 | 11 | 13 | 13 | 13 | 14 | 14 |
 ---------------------------------------------------------------------



North American/Original Japanese version
Option 3
Full Overdrive
vs. Zanmato Level 4-5
 _____________________________________________________________________
|                       ||                Compatibility               |
|                       ||  0 | 30 | 60 | 90 |120 |150 |180 |210 |240 |
|-----------------------||--------------------------------------------|
|         1 - 3         ||  0 |  0 |  0 |  0 |  0 |  0 |  0 |  0 |  0 |
|         4 - 7         ||  0 |  0 |  0 |  0 |  0 |  0 |  0 |  0 |  0 |
|         8 - 15        ||  0 |  0 |  0 |  0 |  0 |  0 |  0 |  0 |  0 |
|        16 - 31        ||  0 |  0 |  0 |  0 |  0 |  0 |  0 |  0 |  0 |
|        32 - 63        ||  0 |  0 |  0 |  0 |  0 |  0 |  0 |  0 |  0 |
|        64 - 127       ||  0 |  0 |  0 |  0 |  0 |  0 |  0 |  0 |  0 |
|       128 - 255       ||  0 |  0 |  0 |  0 |  0 |  0 |  0 |  0 |  0 |
|       256 - 511       ||  0 |  0 |  0 |  0 |  0 |  0 |  0 |  0 |  0 |
|P      512 - 1023      ||  0 |  0 |  0 |  0 |  0 |  0 |  0 |  0 |  0 |
|a     1024 - 2047      ||  0 |  0 |  0 |  0 |  0 |  0 |  0 |  0 |  0 |
|y     2048 - 4095      ||  0 |  0 |  0 |  0 |  0 |  0 |  0 |  0 |  0 |
|m     4096 - 8191      ||  0 |  0 |  0 |  0 |  0 |  0 |  0 |  0 |  0 |
|e     8192 - 16383     ||  0 |  0 |  0 |  0 |  0 |  0 |  0 |  0 |  0 |
|n    16384 - 32767     ||  0 |  0 |  0 |  0 |  0 |  0 |  0 |  0 |  0 |
|t    32768 - 65535     ||  0 |  0 |  0 |  0 |  0 |  0 |  0 |  0 |  0 |
|     65536 - 131071    ||  0 |  0 |  0 |  0 |  0 |  0 |  0 |  0 |  2 |
|    131072 - 262143    ||  0 |  0 |  0 |  0 |  0 |  0 |  2 |  2 |  3 |
|    262144 - 524287    ||  0 |  0 |  0 |  0 |  2 |  2 |  3 |  3 |  3 |
|    524288 - 1048575   ||  0 |  0 |  2 |  2 |  3 |  3 |  3 |  5 |  5 |
|   1048576 - 2097151   ||  2 |  2 |  3 |  3 |  3 |  5 |  5 |  6 |  6 |
|   2097152 - 4194303   ||  3 |  3 |  3 |  5 |  5 |  6 |  6 |  6 |  8 |
|   4194304 - 8388607   ||  3 |  5 |  5 |  6 |  6 |  6 |  8 |  8 |  9 |
|   8388608 - 16777215  ||  5 |  6 |  6 |  6 |  8 |  8 |  9 |  9 |  9 |
|  16777216 - 33554431  ||  6 |  6 |  8 |  8 |  9 |  9 |  9 | 11 | 11 |
|  33554432 - 67108863  ||  8 |  8 |  9 |  9 |  9 | 11 | 11 | 13 | 13 |
|  67108864 - 134217727 ||  9 |  9 |  9 | 11 | 11 | 13 | 13 | 13 | 14 |
| 134217728 - 268435455 ||  9 | 11 | 11 | 13 | 13 | 13 | 14 | 14 | 16 |
| 268435456 - 536870911 || 11 | 13 | 13 | 13 | 14 | 14 | 16 | 16 | 16 |
| 536870912 - 999999999 || 13 | 13 | 14 | 14 | 16 | 16 | 16 | 17 | 17 |
 ---------------------------------------------------------------------



Chart Notes:

- The probabilities here are listed in percentages, but the actual 
random factor is taken from 64 possible values, not 100.  Thus, many of the 
percentages in the tables are rounded.  There are a few percentages that 
are exact, though.  Those are 0, 25, and 50.

- The maximum Compatibility level is 255, but the maximum effect on
Motivation is obtained at 240 Compatibility (or greater).  Therefore, the
"240" Compatibility column in the tables applies for any Compatibility level
greater than or equal to 240.

- The Compatibility intervals between the columns of the tables (which is 30)
matches the actual interval of effectiveness for Compatibility in the
NA/original JP version.  In other words, Compatibility matters in multiples
of 30 only.  An intermediate value is treated the same as the largest multiple
of 30 less than it.  For example, 50 Compatibility produces the same chances as
30 Compatibility, and 115 Compatibility is effectively the same as
90 Compatibility.  If the Compatibility is between two numbers on the table,
use the column on the left.


END JP/NA (ORIGINAL)

 

V. Administrivia

A.  Version History

3.0 (25 December 2003, 76.7 KB):  I told you that I might not get back to the
            guide for a while. ^_^  Anyway, I've been slowly but steadily
            working on this update through the semester, and this is the
            end result.  Sections III and IV now conclude with Zanmato
            probability charts for paid attacks.  If you picked Option 3
            and tracked your Compatibility, you can use the charts to find
            the approximate chance of Zanmato at any payment level.
            This will most likely be the last major addition to the guide;
            there's not much more to cover and it's time for me to move on
            to other projects.  Minor new stuff for this update includes
            alphabetical labeling for sub-sections and a slightly different
            section layout (Version History has moved from Section I to here).

2.1 (31 August 2003, 51.7 KB):  Minor update.  The Zanmato Level of Malboro
           was fixed, and some silly typographical errors were corrected.  
           It's back to school for me, so the next major update may not be 
           out for some time.  This is the first version that will be 
           submitted to Neoseeker (all previous versions were submitted to 
           GameFAQs exclusively).  

2.0 (16 August 2003, 50.8 KB):  The addition of a new sub-section 
          ("Special Math Topic: Guaranteed Zanmato" in Section III) 
          is the biggest change for this version (big enough to warrant 
          a jump to "2.0" IMO).  Some Zanmato Level data was added and/or 
          corrected, and those changes are noted in the new "Additions and 
          Corrections Recognition" part of the Credits.  Also, a few words 
          in the existing parts of the guide were changed (the differences
          are quite minor).  "Stuff to add in the future" is unchanged,
          but there are no exact plans on which things to add first.

1.1 (28 July 2003, 44.6 KB):  Some slight changes were made in this version.  
         The Example and Notes subsections were switched.  Replaced  
         "truncation" in the math section with "floor".  Thanks to 
         Christine Bomke, this version has some new monster data 
         (the Zanmato Levels of two enemies near the end of the game).
         The "stuff to add in the future" is the same as it was for v1.0,
         but the math information has the highest priority.

1.0 (12 July 2003, 43.1 KB): First version of guide released to the public.  
         Contains Yojimbo formula, Zanmato Level lists, brief notes on each 
         step of the Yojimbo formula, and one example turn for both the Int/PAL
         and NA/original JP Yojimbo formulae.  Stuff to add in the future: 
         section on acquiring Yojimbo, an actual FAQ section, more examples,
         and more math stuff.  Also add something to make navigation easier.


B.  Credits 

jobber2022497 - Compiled all the information for the guide and wrote 
                everything here that is not credited to somebody else.

This guide could not have been possible without the contributions of many 
talented individuals.  First, I'd like to thank GameFAQs board users 
Dual Zero, Shinryu, and Olivier Hague for creating and posting in the 
original "Mathematics of Yojimbo" topic on the Final Fantasy X 
Secrets/Side Quests Board during the Spring and Summer of 2002.  
The formulae in this guide came directly from those posts (I made a few 
modifications to the format of it, though, and the text explanations of 
each step were written by me).  The source of the posts in that topic was in 
the Final Fantasy X Ultimania guides (published by DigiCube/Studio Bentstuff),
so thanks to the makers of those guides, too. 

Also, a special thanks goes out to CJayC for creating GameFAQs and for 
posting this guide on GameFAQs.com (C-NETTED!)

Other thanks for vital information that helped me launch this guide go out 
to the following GameFAQs board users:

nFNTy - For making "Someone Repost the 'Yojimbo Mathematics' Topic" on the 
        S/SQ board in January 2003.

ramses - For replying to that same topic by posting the original JP/NA formula,
         and for bumping the topic in my absence.  As of this writing, it has
         been on the board for about 15 months and it's still there.

Olivier Hague (yes, again) - for re-posting the International formula 
        at my request.

Ceebs - For all her excellent FFX guides, especially the Monster Encyclopedia 
        (that's where I got the data for the Zanmato Level lists), Monster 
        Arena FAQ, Bribe FAQ, Equipment Remodeling Guide, and Ultimate 
        Weapons Guide.  

Theoden - For answering my question on the Power values of Yojimbo's attacks,
          and also for being the most dedicated user of the Final Fantasy X 
          board during my 15+ months there. 

Terence - For his battle and AP mechanics information (please finish the 
          damage formula stuff and get it posted in a guide soon!).  His work
          helped me to make (and later confirm) my guesses on the attack 
          powers of Yojimbo's moves.

Some short messages to other users who inspired me to make this FAQ:

Masamune3 - I've known you since you first came to the FFX boards.  When you
            started making FAQs like the Armour Guide and all those character
            guides for that DBZ game, I started thinking "damn, I should get
            off my ass and start writing something...I know just as much about
            FFX as this little [expletive deleted]."  (Just kidding.) 

hey im on the net - 
        In a topic called "Yojimbo, has this ever happened to u?", I offered 
        to demonstrate the difference in the two versions of the Yojimbo 
        formula.  You simply replied with this:
        
       "If you could Jobber...ta".  
         
        For whatever reason, this possessed me to make about 15 in-depth posts
        on the Yojimbo formula, including examples and a long post about 
        "Guaranteed Zanmato" (which has been modified into a sub-section of
        the Int/PAL part of this guide (Section III)).  Some of the posts took
        a long time to make, and part of the reason why I wanted to make
        the FAQ was so that I wouldn't have to waste time posting the same 
        stuff all over again someday.


Additions and Corrections Recognition:

Ceebs - Added Zanmato Levels of Braska's Final Aeon and Yu Pagoda
Baowoulf - Corrected Zanmato Level of Malboro 
           (North American version, source: Bradygames FFX Guide)
penance44 - Added Zanmato Levels of Belgemine's aeons,
            corrected Zanmato Level of Malboro
            (PAL version, source: Piggyback FFX Guide)

And finally, thanks to NastyNate82, for no particular reason.

Contact Info

I can be reached at the email address given at the beginning of the guide
(jobber2022497@yahoo.com).  Please email me if you have any questions,
comments, complaints, or corrections.  Also, you must email me if you want
permission to use this guide on your website.  I can also be reached on MSN
("jobber2022497") and AIM ("Jobber123RD"), but I will not grant permission 
to use my guide over Instant Messaging.  

Finally, you can ask me questions about the guide on the GameFAQs 
Final Fantasy X Message Board:

http://cgi.gamefaqs.com/boards/gentopic.asp?board=2000004

I check that board more often than I check my email, so you might get
a quicker response from me that way.  My user name on the GameFAQs message
boards is "jobber2022497".



Thanks for reading the Final Fantasy X Yojimbo Mathematics Guide.

This guide is Copyright 2003 Ronald W. Davis II.

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