Final Fantasy X - Penance is a cheap superboss

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Final Fantasy X
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Duration: 2:11
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ファイナルファンタジーX - 苦行は安いスーパーボスです

Hiring Yojimbo:
"To train as a summoner."
"To gain the power to destroy fiends."
"To defeat the most powerful of enemies." (This option is the best to maximize the odds of Zanmato)

Formula Variables:
1) Compatibility
2) Motivation
3) RNG (Random Number Generator)

1) Compatibility
Can be 0-255, will be always 128 when you first get Yojimbo.

Zanmato +4
Wakizashi +1 to +3
Kozuka 0
Daigoro -1
Dismiss Inmediately -3
KOed -10
Pay 0 Gil -20

✴ The Free Move
‣ Chance of happening:
Compatibility / 1024

‣ When you first get him:
128/1024 = 1/8

‣ At 255 Compatibility:
255/1024 = 1/4 (approx)

Which move will it use?
(Compatibility / 4) + RNG (0...63)

If the result is:
80 + ➼ Zanmato
64-79 ➼ Wakizashi (all)
48-63 ➼ Wakizashi
32-47 ➼ Kozuka
0-31 ➼ Daigoro
Note: You will NOT see a free Zanmato vs Monster Arena Creations, Dark Aeons or Penance.

2) Motivation
In this section we have 4 variables: Gil Motivation, Choice Motivation, Zanmato Level Motivation & Overdrive Motivation

✶ Gil Motivation

Payment | Motivation
----------------------------|---------------------------------------
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

✶ Compatibility Motivation = Gil Motivation (0 to 112) + Compatibility (0 to 255) / 10
✶ Choice Motivation = Compatibility Motivation (If we picked Option 3 when hiring Yojimbo)

✶ Zanmato Level Motivation
Zanmato Level Motivation (if ZL 1-3) = Choice Motivation * 0.8
https://i.imgur.com/A9EkqrE.png

Zanmato Level Motivation (if ZL 4-6) = Choice Motivation * 0.4
https://i.imgur.com/SmljUz0.png

✶ Overdrive Motivation = Zanmato Level Motivation + 20 (If Overdrive is full, if not OL = ZLM)

⌭⌭⌭ Full explanation of what is happening in my video ⌭⌭⌭
- We are fighting Penance (ZL 6)
- Chose Option 3 when hiring
- Yojimbo's Overdrive is full
- Compatibility is 0 (yes, i did it on purpose)

What if we pay him 1 Gil?
1.- Gil Motivation = 0
2.- Compatibility Motivation = 0 + (0/10) = 0
3.- Choice Motivation = Compatibility Motivation = 0
4.- Zanmato Level Motivation = Choice Motivation * 0.4 = 0
5.- Overdrive Motivation = 0 + 20 = 20
6.- RNG Motivation = 20 + (0...63) = A range from 20 to 83

7.- We need 80 or more, so the RNG must be at least 60. There are 4 values it could be (60, 61, 62, 63). Therefore we have a 4/64 chance of getting a Zanmato = 6.25%







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