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Salanewt
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« on: May 25, 2014, 05:47:41 PM »

Howdy! So uh, yeah. Here's a topic in which we can organize the games' formulas and discuss them a bit. This first post will be separated into two sections; confirmed through code and unconfirmed through code (such formulas may have unknown variables that are as of yet undocumented). Organization will be a little lackluster until we have a decent proportion of the game's formulas in here.



Vanilla

Agility/Turn Order

The following section explains how PC turns are calculated.

Turn Order:
Randomized agility has priority;
PCs have priority over enemies;
Left-most slots have priority;

Agility x 0-FFFF (or ran) = RAN
LSR 14 RAN = #
Agility + #
÷ 2 for additional turns only.

So if Agility = x64 (100 decimal) and ran = xFFFF, then you multiply them;
RAN = 63FF9C
LSR 14 in a programmer's calculator;
# = 6
Add 6 to 100 Agility
= 106
If it's not the first turn (as in second, third, etc. turns);
106 ÷ 2 = 53

It boils down to:

(Agility + Agility*(0~6%))*(Multi-turn penalty)
Multi-turn penalty = 1 if it's a character's first action that turn, and 0.5 otherwise.

Maximum agility values to ensure desired turn order.
PC1: 999
PC2: 940 (941 if right of PC1)
PC3: 884 (885 if right of PC2)
PC4: 832 (833 if right of PC3)


Enemies, on the other hand, are much simpler.

For 4 turns, agility decrements by 1/6th each turn.
For 3 turns, by 1/4th.
For 2 turns, by 1/2.


Turns are normally capped at 4, manually adding more to an enemy's RAM will result in every turn after the first one having only half of its agility value.

0811D0A8 = Check for 4 turns, branch if not equal - Turn 2: 5/6 agility ; Turn 3: 4/6 agility ; Turn 4: 1/2 agility
0811D0D0 = Check for 3 turns, branch if not equal - Turn 2: 3/4 agility ; Turn 3: 1/2 agility
0811D0EE = Check for 2 turns, branch if not equal - Turn 2: 1/2 agility



Ailment Success

(((((((Attacker's elemental level - Defender's elemental level) - Floor(Defender's luck / 2)) * 3) + effect's base chance + (vulnerabity's 25)) * multi_arg) / 100)  >= rnd())

Where "rnd()" is a random number from 0-99 (x00 to x63), and "multi_arg" (previously known as "unk_arg") is for diminishing success rates based on the amount of targets the effect can be used on:
First (Primary Target) = 100%
Second (Next to the target) = 60%
Third = 30%
Fourth = 30%
Fifth = 30%
Sixth = 30%

Notes:
x52 = "82 - May force target out of battle" is always 0% when class is not NPC. (0% for player characters?)

These generate three random numbers... This would make, for example, a chance of 50% (one) to be 87.5% (three), I think.
x43 = "67 - Inflicts Seal"
x50 = "80 - Inflicts Death Curse"
x55 = "85 - May inflict Stun"[/spoiler]

Base success rates (assigned in the function at 080B0514):

Spoiler for Base Rates (with examples):
080B0660 - 70% (12/13 - Def debuffs)
080B0664 - 75% (16/17 - eRes debuffs)
080B0668 - 30% (22 - Charm)
080B066C - 35% (24 - Sleep)
080B0670 - 55% (18/19 - Poison/Venom, 25 - Seal)
080B0674 - 25% (26 - Haunt)
080B0678 - 20% (27 - Instant Death)
080B067C - 65% (20 - Delusion, HP Drain)
080B0680 - 35% (21 - Confuse, 34 - HP to 1)
080B0684 - Flat 60% (56 - Revive to 50%)
080B0688 - Flat 90% (57 - Revive to 80%)
080B068C - Flat 70% (73 - Revive to 60%)
080B0690 - 60% (8/9 - Attack debuffs, 28 - Curse, 32 - PP Drain, 80 - Curse)
080B0694 - 50% (35 - May ignore 50% of Def)
080B0698 - 40% (23 - Stun, 85 - Stun)
080B069C - Flat 100% (Def buffs, eRes buffs, Regen, Reflect, Break... seems to be the default for anything that either shouldn't fail or has its success rate calculated differently)


Ailment Recovery

Note: 5 or fewer turns must remain for this chance to occur.

(((Luck * 3) - (Turns * 5) + base_chance) * 655) >= rand()

Random number is 16-bit (Up to xFFFF)
If chance was 100% and you multiplied by 655, you'd get xFFDC.  Evidently, 656 would make x10040.

Base chances of recovering from an ailment, etc:

Spoiler for Base Chances:
Attack = 30%
Defense = 20%
Resistance = 20%
Delusion = 30%
Confuse = 60%
Charm = 70%
Stun = 20%
Sleep = 50%
Psy-seal = 30%



Healing

This one is pretty simple.

If current HP > 0:
Restored HP = ((Base Value*ePower)/100) + (0~3)
If restored HP > max HP, overwrite with Max HP. Else add restored HP to current.

The 0~3 is basically calculated like so:
(0~3) = 3 AND rand()
Where rand() is a 16-bit value up to xFFFF. Change the 3 to change the amount that can be added to the final result.

I don't think it uses RNG when calculating the amount to restore outside of battle.



Regenerate/Coatlicue

Another easy one that's similar to the Healing formula, minus how the amount to heal is calculated:

If Duration > 0:
((Duration + 1)*Max HP))/10

So basically, having about 5 turns before the effect ends will net you 60% regeneration for that first turn. 3 turns will be 40%, 8 turns would be 90%, and so forth. You will be healed before the duration counter goes down at the end of the round.


Poison/Venom

This one is pretty similar to Regenerate, in that it reads the corresponding ailment value from the unit's RAM before making the calculations.

Located at 0812593C, it skips the calculation if Poison = 0; otherwise:
(Poison * Max HP)/10

A Poison value of 1 (regular poison) will deal about 10% of your Max HP in damage and a Poison value of 2 (venom) will deal about 20%. As an FYI, you can technically go higher than 2 despite there not being a graphic for anything higher than that (or even an effect for it). I should also mention that this does not actually apply in the field; that seems to be coded strictly for Poison values 1 and 2, and those are fixed at 5% for regular poison and 10% for venom as far as I can tell.

However, the field formula works a little differently. It only works if your Poison value is either 1 or 2, and each value uses a slightly different calculation. What I like about them is how they only deal roughly half damage when not in battle... Well anyway, here they are.

Poison: (Max HP + 10) / 20
Venom: (Max HP + 5) / 10








So yeah! I'll work on scouring other topics for fomulas in a bit; please post any that you can think of, I would greatly appreciate it!
« Last Edit: February 08, 2015, 03:06:23 PM by Lord Squirtle » Logged

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« Reply #1 on: May 25, 2014, 06:27:40 PM »

Can you try this in "I don't need a degree in Assembly programming to understand this" version?

For example, that Agility formula confuses the hell out of me.
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« Reply #2 on: May 25, 2014, 06:56:42 PM »

I thought it was pretty clear since he said this afterward:
Quote
It boils down to:

Agility + (Agility x 0~6%) [÷ 2]
Although I'd have notated it as:

(Agility + Agility*(0~6%))*(Multi-turn penalty)
Multi-turn penalty = 1 if it's a character's first action that turn, and 0.5 otherwise.
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Spoiler for quotes:
[9:00:50 PM] Randel Peltier: Ok...what did I do last night?
[9:01:19 PM] Kain: Something boring, repetitive, and lasted for about sixty seconds.
---
[10:45:08 AM] Salanewt: But yeah, the elemental phalluses are being... Stroked up by Saturos and co., and the energy will go towards... Mt. Muffin, where the Golden Climax will arise.
[7:28:42 PM] Salanewt: An added bonus is that Isaac and co. were trying to stop Saturos and co. because their beliefs state that Mt. Muffin should remain a virgin.
---
[9:54:21 PM] Randel Peltier: Guess the number in my head an you get to pick what I say. Number between 1-10
[9:54:28 PM] leaf: 11
[9:54:36 PM] Randel Peltier: @#$%!
---
[8:38:13 PM] Randel Peltier: Shes like this queen up on a pedastal that I have yet to court.
[8:38:29 PM] Kain: You've tried courting her.
[8:38:43 PM] leaf: and failed spectacularly
[8:38:44 PM] Randel Peltier: Ive tried...shes the best dating game ever.
---
[12:24:35 AM] Salanewt: I need to find a picture of a naked person to put on the Christmas tree next year.
---
[2:19:06 PM] Zeadra: wait... Rief's a guy???
---
[1:09:57 PM] Zeadra: well if you want to know if its a new effect or something weird, just check GS1, if side step is there maby it is the nimble dodge thing
[1:10:35 PM] Kioll: For once, you've contributed something useful.  o.O
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« Reply #3 on: May 25, 2014, 07:55:38 PM »

Jamie: No problem! The bolded parts are the formulas done in normal math, and the rest is the more technical stuff (or additional information, etc.).

Leaf: Done and done, thanks for the notation; it's clearer than the one I had before.
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« Reply #4 on: May 25, 2014, 08:02:40 PM »

Yeah, I somehow missed the bolded text.

Is the multi-action penalty really that simple? Personally, I'm under the impression that it stacks. That is, your third action is at *0.5 *0.5, and your fourth action is at *0.5 *0.5 *0.5. The reason I say this is that with one particular boss I made, in my many tests I frequently found that it would take one action before the entire party, and another action before Sheba (who was the party's slowest member due to her class). But it wouldn't take both of its other actions before Sheba got to act. Just one of them.

Spoiler for Off-topic: Sheba is the slowest member?:
If you're wondering why Sheba was the slowest character, classes in this hack were rather heavily modded to emulate standard RPG/Final Fantasy archetypes instead of elemental Psynergy. Sheba's default class, the Magician, focused on damage-dealing spells of all elements. Attack power versus standard foes was good-to-mediocre, but was made up for by her ability to fairly consistently target a foe's weak point for heavy damage. The Magician has incredibly high HP and PP and decent Luck, but low Attack and Agility and abysmal Defense. She could tank base damage spells all day, but a standard physical attack from most foes would flatten her in 3 hits. Contrast Piers the Fencer, who would routinely take 1 damage from most foes' standard physical attacks, but would go down in 3 hits from any half-decent base-damage ability.

Also, weird things happen if you use the "extra turn next round" ability effect on a target multiple times. At 2 uses, the target treats their second action the same as their first, or something like that. For example, if I give an enemy 0 turns by default and another enemy targets it once with a Kite effect, it makes one action at 0.5x Agility. If another enemy targets it twice with a Kite effect, it makes one action at what seems to be either 1x Agility or 0.75x Agility.
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« Reply #5 on: May 25, 2014, 08:39:50 PM »

That's what I was hoping when I initially started looking into it, but I can confirm 100% that it doesn't stack for PCs. In the battle ram section, there's enough room for 20 turns per round from all units. PC turns are input first, and then are rearranged depending on agility values when enemy turns are calculated. Agility is recalculated by reassigning an action for the turn, but consecutive turns are always roughly half of the range of the first turn's agility. You can probably guess that those later turns would scramble around then...

However, looking again against an enemy with 3+ turns, it looks like enemy agility is not randomized with 0-6%. It also divides at a slightly different rate and does stack (I never looked into 3+ turn enemies before, sorry). For them, it looks like the first consecutive turn is multiplied by about 75% (or 0.75), docking off about 25% of the previous value. I'll take another look at the code and see if I can find exactly how it's calculated. Might even make a patch that does this for both PCs and enemies if I can do so without rewriting the entire function.

An enemy with 300 agility will have the following three turns:
300
225 (x.75)
150 (x.50)

Not sure what the values are for 4+ turns, but I'm going to take another look at the code and check for enemy turns this time.


Thanks for pointing that out Jamie!
« Last Edit: May 26, 2014, 12:50:46 AM by Salanewt » Logged

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« Reply #6 on: May 25, 2014, 09:08:45 PM »

I know a player character cannot have more than 1 extra turn, either through equipment mods or the "Extra turn next round" effect. This I was already aware of. At the time, I had assumed that enemies followed the same Agility rules as the player, and so by "your" I was referring to an enemy. When I talked about "stacking" the Agility mod, I was referring to the multi-turn penalty stacking, not to stacking the "Extra turn next round" effect.

But even for player characters, stacking the "Extra turn next round" effect does strange things to your action priority. Targeting a player character twice in one round with that effect seems to cause both of their actions to be made at their full Agility stat. The first action always goes before the second action, however, even if your Agility roll for the second action is higher than for the first. Although, now that I think about it it's entirely possible that rolling higher Agility on the second action than the first pushes the priority of the first action up, to the point where you can act first in the turn even if you are slower than other characters.

Enemies are locked to a maximum of four turns. Even an "Extra turn next round" effect cannot override that limit, and an enemy can only gain 1 extra turn per round through that effect regardless of how many times they are targeted by it. But just as I said for player characters, the "Extra turn next round" effect does strange things to action priority when applied multiple times to a single target.
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« Reply #7 on: May 25, 2014, 09:46:00 PM »

Yeah, it's weird. My best guess is that it has something to do with ability and item effects not working 100% properly when it comes to granting extra turns (the ability effect being a buff that doesn't have stack). You can simply overwrite a PC's turn value in RAM and it'll work the way I've described, which I assume is how it is supposed to work. You can also do this in an enemy's RAM, so it isn't 100% locked to four turns; the downside is that the agility division stuff doesn't seem to work properly for 5+ turns (does the same thing as the PC agility formula without the randomization). You have to keep in mind, however, that you still only get a maximum of 20 turns total. PCs also get buggy if you give them too many turns...


So after testing with a Druj enemy, it seems that the agility ratings for consecutive turns are actually based on how many turns an enemy has; the x.75 multiplier doesn't apply with four turns. Likewise, the /2 thing also works for enemies if they only have two turns (which just reminded me that I knew the 0~6% thing didn't apply to enemies and forgot). This also happens to every turn after #2 if an enemy has more than four turns for some reason. So uh, I'll check the code to see if I can find the exact enemy turn formula.

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« Reply #8 on: May 25, 2014, 10:05:00 PM »

I suspect the enforced cap on turn counts is probably deliberate. Either that, or it was a bug that they never bothered to fix because it never, under any circumstances possible in-game, would actually need fixing.

It actually almost makes sense for having extra turns above the cap to behave the way it does, honestly. I would like to know what the exact mechanics are that result in the strange mess of action priority I've just described, though.

Maximum 20 turns total, huh? Okay. In that case, I'll remember not to give 4 turns each to enemies that come in groups of 5...
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« Reply #9 on: May 25, 2014, 10:24:51 PM »

Well, as it turns out, the function that reads and does the calculations for enemy turn order is entirely different from the one that calculates PC turns (and that is a part of the same function that deals with attack/psynergy/defend/etc. action commands in battle).

I've noticed so far that this function grabs both the agility and turn values. It kind of looks like this is one of the functions that Teawater took a brief glimpse at, but there isn't much documented here. It also looks like it calculates an enemy's turns differently depending on how many turns an enemy has, not using the amount they have. There's a branch for "if /= 4 turns," which goes to a "if /= 3" and so forth. I'll work on documenting this and figuring out exactly how it works.


Yep! I can't say if the RAM right after the battle stuff is used for anything or not either, so 20 is the effective cap right now. PCs also tend to bug out if you go much higher than 4-5 turns, but it's not like you can really do that anyway.

Edit: Looks like Teawater is taking a look. All I'll say for now is that, before calculating the new values, it does a series of checks that somewhat resemble the following:

If Total Turns /= 4, branch;
If Current Turn = 0 (first one), branch;
If Current Turn /= 1 (second), branch;
...
If Total Turns /=3, branch;

And so forth. Unless he wants me to explain what he's finding, then I will let him finish studying them and post the info himself.
« Last Edit: May 25, 2014, 10:53:19 PM by Salanewt » Logged

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« Reply #10 on: May 25, 2014, 11:02:02 PM »

A Master Formula List? Sounds like a plan!

Do you plan on putting the addresses of code locations in the list for future reference? (Then again, the only people who are likely to use it is you and me... but still, someone else might one day join us in our studies. Unlikely, but you never know?)


Quote
and post the info himself.
For 4 turns, agility decrements by 1/6th each turn.
For 3 turns, by 1/4th.
For 2 turns, by 1/2th...

Quote from: from documentation - edits from me and Salanewt
Executes at the start of a round.
0811CFD0 = Start
 0811D0A2 = Write Enemy’s Slot ID to battle RAM
 0811D0A4 = Write Enemy Agility to battle RAM
 0811D0A6 = Write Enemy’s current turn (0-3)
 0811D0A8 = Check for 4 turns, branch if not equal - Turn 2: 5/6 agility ; Turn 3: 4/6 agility ; Turn 4: 1/2 agility
 0811D0D0 = Check for 3 turns, branch if not equal - Turn 2: 3/4 agility ; Turn 3: 1/2 agility
 0811D0EE = Check for 2 turns, branch if not equal - Turn 2: 1/2 agility
0811D126 = Call Enemy AI
0811D15E = End

Edit: @5+ turns... it seems like the first turn is 100%  agility, and remaining turns are 50% agility? (non-stackable) ; That is assuming that I looked at the code right, ofcourse? The way it was coded makes me think that 5+ turns wasn't supposed to be a feature in GS. (The same 1/2 agility code is used where necessary.)


EDIT: /= looks like division, you could try != or <>, though.
« Last Edit: May 25, 2014, 11:37:47 PM by Teawater » Logged

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« Reply #11 on: May 25, 2014, 11:27:36 PM »

Terrific, thanks for the info Teawater; I have added what is necessary to the first post. I also plan on including more technical info later, since it would be nice to have an area where those experienced with assembly hacking can just find all of the game's formulas.

On that note, can you think of any more formulas that I can add to this topic? I remember researching the HP Healing one back when I made the HP% formula, so I'll try finding the .png/.gif I stored it on. It's pretty much the same as what has been documented by countless others fortunately.
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« Reply #12 on: May 26, 2014, 02:29:02 AM »

You found Ailment success?!  MOTHER FREAKING +1!  NICE JOB!
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« Reply #13 on: May 26, 2014, 02:37:58 AM »

Haha! Um, thanks for the compliment I guess. You know that Teawater is the one who found the formula a while back, right?
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« Reply #14 on: May 27, 2014, 11:03:00 PM »

No, I didn't.  I'd been looking for that sucker for quite some time now, and the times I had visited in the past must have been before then.
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Luna_blade: back from vacation
August 17, 2017, 02:29:26 AM
Fox: That moment when you realize that there is a lot of chatting going on on Discord, that there is no point in trying to keep up. :P  Hm....
August 16, 2017, 04:50:22 AM
Fox: (Then again, just because posting is disabled, doesn't necessarily mean the buttons would be removed as well.)
August 16, 2017, 04:48:55 AM
Fox: (I mean, buttons I would expect to be similar to that.... rather than those specifically since I recall posting there to be disabled.)
August 16, 2017, 04:33:02 AM
Fox: Yeah... I like to think of it as a page loaded with ads. And it's not just the forum home page either... check the sub-forums/topics themselves. == New Topic/Reply/etc. buttons were affected.
August 15, 2017, 07:04:30 PM
Salanewt: Lol, nice. :P
August 15, 2017, 06:33:02 PM
Foxhttp://z9.invisionfree.com/Golden_Sun_Hacking/index.php? == Hahaha! GSHC Classic looks funny now that Photobucket killed the images. :P Anyway, how is everyone doing today?
August 14, 2017, 07:12:02 PM
Salanewt: So yeah, I'm typing up a non-academic essay on why GS2 was rushed; expect that sometime soon!
August 07, 2017, 05:53:11 AM
Fox: But anyway, such a hack mod is simply an idea, and I do not have any current plans to work on it at this time, so.....
August 07, 2017, 05:51:46 AM
Fox: Okay, cool. I think my idea works best without an ability to swap PCs (OR to just simply make that use it the PC's turn.) Hmmm... And with that, I question if a turn list is even needed with my approach. (Outside of maybe 1 entry, if that shortens the modifications.)
August 07, 2017, 05:13:26 AM
Salanewt: To be honest I've been thinking of expanding the battle turn section and also adding code for PCs to have more than two turns in the AI overhaul, but I probably won't allow anyone to have more than four.
August 06, 2017, 12:22:17 AM
Fox: Oh, and if that approach was taken = Would like to also have it so you select the spell to use when it is actually your turn rather than at round start.
August 06, 2017, 12:12:37 AM
Fox: Would take a lot of balancing, but I can see an adept being very slow, and yet very powerful.
August 06, 2017, 12:06:11 AM
Fox: And bosses can have an Agility that is above half of the maximum possible Agility. Mwahaha.

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