Decided to do a little agility testing.

1st test:
Jindrich, level 115 Dragonewt Fighter (16 agility)
0, level 1 Fairy Thief (24 agility)

Had both characters use potions for 8 rounds. 0 went first 7 times, Jindrich only 1 time.

Conclusion: Level does not affect initiative.

2nd test:
6, Dragonewt Fighter (6 agility)
15, Fairy Thief (15 agility)
Both level 1

Over 9 rounds, 6 went first 2 times, 15 7 times.

Conclusion: Unlike many other things determined by stats, there is a difference between 6 and 15.

My assumption is that Agi works in such way for determining order of turns:
1. If you have same agi as enemy you have 50% chance to go first.
2. Each point of difference changes this chance by 2.5 % or by 5% (with 2.5% or 5% chance being minimum).
So 9 points of difference in Agi should give 95% chance to go first.
9 rounds is definitely not much to make conclusion on %. But 8 points of difference is sweet point to check (90% vs 70% chance of going first).

After that need to check what Dice of Fate shows when trying to run from enemies (preferably if enemy encounter consist of 1 type of enemies, so no AGI variation on their side).

It's worth looking at how some other games handle turn order.

SaGa 2 (Final Fantasy Legend 2):
Initiative is determined by taking the character's agility (with a 25% bonus for party members) and multiplying it by a random number between 1 and 2. Note that (except in the DS version) it is possible for this calculation to overflow.

SaGa Frontier:
Initiative is Agility times a random number between 1/2 and 1. (Note that that game's mechanics are incredibly complicated.)

Dragon Quest 3 (FC version):
Initiative is Agility time a random number between 1/4 and 1.

Wizardry:
Initiative is 1d10 with modifiers for low or high agility. (No difference between 8 and 14) Interestingly, it looks like lower is better, and initiative can't go below 1 or above 10. Enemy initiative is 1d8 + 2.
(Note that Agility also affects the chance of surviving when teleporting into the moat.)

Bard's Tale series:
Don't have exact mechanics, but it's something like half the character's level plus a bonus from agility or luck (don't know which). This is the reason I did the first test.

My guess is that initiative in Elminage Gothic works something like in the SaGa games, but with the random multiplier going as low as 0. (Think I've heard of at least one game doing that.)

SaGa and Dragon Quest games are entirely different games from Wizardry in terms of mechanics, and even some mechanics in Wizardry differ from Elminage (stat capped at 18, different damage contribution from Strength, etc.).

I had a very intensive testing for Vovalketer (testing those different AC values), which have also shown that he has around 10% chance to do Lightning Attack (Swift Attack perk), has around 10% chance to start combat hidden, and I had around 5%-10% chance to act before he attacks (17 and 18 Agi versus 26). Hmmm, looks more like my assumption with 5% being minimum chance to act first, and 5% (de-)increase per point of difference. Just need to do more targeted testing on this.

Random notes:
- It also looks like minimum 5% chance of failure on traps (identifying and triggering them by Thief and failing to avoid triggered traps). I opened way too many chests (and amassed a lot of gold - is it even useful for anything in this game?).
- There is no minimum % of success/failure when identifying high level items by Bishop. if you are too low level, you will always touch things of too high quality (e.g., Item Encyclopedia: after a LOT of save-scumming, I had to pay 17500 Gold to identify it). If you are too high level, you will identify item from 1st attempt. Item Level seems to be dependent from Item Price as no other column in database makes sense for it.

Off-Topic: do you know how faithful were SNES ports of first 5 Wizardries? Were they just graphical improvements or some mechanics were changed? I get a huge urge to mess around with them again, but PC versions aren't as readily accessible to me. I don't like to play rebalanced versions, so if SNES has even slightly rebalanced versions, I'd rather.skip them.

Gold has two late-game uses. First, you can use it to train new characters (limited to just under 10 million). Second, there's a spot where you can buy Aura Punch for 1 million, and another spot where you can use up the Aura Punch to get a random high-level ore.

A monte carlo simulation of the "initiative between 0 and Agility" mechanic would predict you acting about a third of the time, which does not appear to be what you observed.

Describing the version differences between Wizardry games would be worthy of its own topic, but for your question:
1 has the Wizardry 2 version of (Ma)haman (allowing you to choose an effect from a random list of three), and floors 5 through 8 were completely changed (but who visits those floors anyway?), but is otherwise more faithful than 2 or 3.
2 (Knight of Diamonds) was completely redesigned to account for the fact that you start with level 1 characters. It was also given a different number due to the order in which the Famicom versions were released. (Danger: Teleport traps are dangerous on the cave level.)
3 (Legacy of Llylgamyn) I haven't played, but I believe the main change here was the removal of riddles.
4 did not get released for SFC/SNES. If you see a SNES Wizardry 4, it's really Wizardry Gaiden 4.
5 is actually pretty faithful. Stat caps were changed to be base +10 (instead of 18) and conversation was simplified because of the lack of a keyboard, but those seem to be the only real differences.
(These games did add an automap feature, but that can be disabled in the settings.

Of course, the PC versions aren't entirely faithful. Non-Apple versions of Wizardry 1 were indeed rebalanced (Fewer enemy groups on the first floor, spells disabled during ambushes) when compared to the Apple II version. Furthermore, the Wizardry Archives versions of Wizardry 1-3 have a serious bug that causes stats to drop much more often than they should. Therefore, if you want to play a non-rebalanced version, your only option is the Apple II version.

1 million is nothing, but Aura Punch doesn't look much useful as it seems to only hit Devils. You say spot, so you mean you can farm ore later in the game? Initiative is definitely based on Agility difference between you and monster. I'd compare it to roll where if you roll less than (Level difference * X) + 50 wirh 1d100, you go first (unless you roll 96+ or 5-). X seems to be no less than 5. What is special about floors 5 to 8 so noone visits them? Yeah, and it was never localized on English sadly. I'd probably skip Wizardry 4 entirely because according to reviews it was a bit upside-down game :) So it seems my only valid option from Wiz1-5 is SNES Wizardry 5. Well, better for me then, as I am already being torn apart between Elminage Gothic, Original and replay of Final fantasy XII. And there are still many games on GoG which I bought and never even installed >.<

Actually, Aura Punch is ineffective against everything, including Devils. It can be useful when you don't want to damage the enemy (hunter's persuit sweep and trying to get a brawler to lower an enemy's summon resistance) or you can use equipment, Harias or alchemy to make it effective. There is an elevator on the 4th floor that, once unlocked, lets you skip straight to the 9th floor. Furthermore, there really is nothing of note on the 5th through 8th floors, aside from the fact they can sometimes be treacherous. (Apparently, in at least one version, you can be trapped in a room with (i think) spinners after climbing down because there's no stairs up.) I have actually played Wizardry 4, and I actually enjoyed it. It is very different from the rest of the series. One of the puzzles does expect you to have played Wizardry 1, so you do need to play it first. If you want more games of this genre, check out the classic Bard's Tale games. (The Bard's Tale game on GoG is very different from the classics, but it does include the classics as an extra.)

It is. Guess what did I use against Locusts in that one hole to make Strength table?:) Yeah I have them lying around. Something was stopping me from playing them, I am not sure what. Perhaps with kickstarter company for Bard's Tale IV, I should give them a go. I still have Wizardry VI unfinished, Wizardry Tale of the Forsaken Lands and Class of Heroes II (good anime Wizardry-like). And I wanted to see how do random dungeons look in Elminage 3, and I am even ok with learning some gaming basics of Moonfolk speech for that :)

I really hope we get all other Elminages here, they got some interesting ideas in them. Elminage Original allows you to marry monsters and have children from them, it also deals with actual Elminage location (series-namer, but I wasn't there yet) and it has interesting take on NewGame+. Also background music is fantastic. Elminage 3 has randomized dungeon with boss in it. I don't know what made Elminage 2 special. Elminage Ibun has something to do with monster-infested school and school-children and it had very disturbing graphical approach... it happened to be last game in series (I think no need to guess why).

I tried testing a 14 Agility character (attacking with Aura Punch) against Avi. I wasn't careful with data, but it seemed that each was equally likely to go first (assuming Avi decided to actually attack).

One other observation: +20 to hit would usually hit AC 3 (occasionally hitting only 9 times and once only 8) and would always hit AC 7 (after casting Hallobuti).

Character was a level 1 Dragonewt Fighter with 12 strength.
The monster was Avi. Avi was not in the back row, but my fighter was,
Also, it is quite possible that Avi was defending in the rounds it wasn't attacking, giving it AC 0 (4 after Hallobuti). Maybe one should pay attention to see if the <10 hits occurs only when Avi does not attack.

Even against 0 AC you should be hit capped with +20 weapon and 12 Str..

I just made my own testing. Also Dragonewt Fighter, 1 Lv, 12 Str, and I've put him in front row (I geared him from shop so he could survive). He was indeed hit capped, but when Avi was defending, suddenly Fighter started to miss some hits (8-9 hits per attack were connecting). It means that monsters' "Defend" lowers AC by more than 3 (as I mentioned before, in Elminage Original "Defend" was lowering AC by 10, looks like monsters still know how to "Defend" properly, though 10 looks like too big difference, I think it is more like 5 or 6).

Too bad that Locusts and Gremlins defend almost all the time, they greatly skew all Hit Chance statistics. I need to find couple floor masters with AC difference of only 1 to derive Level formula for Hit Chance, and then we can calculate monsters' AC gain from "Defend".

Testing againat Akabey (Grotto floormaster) (AC -2):
Setup is similar: Level 1 fighter with 12 defense. One major difference: I petrified the enemy first. Petrify, unlike Sleep or Paralysis, does not raise the target's AC. Hence, I prevent the enemy from defending while still allowing the enemy's AC to work.

At AC -2, the character hit 7-10 times, with 8 being particularly common.

After one Hallobuti (enemy AC 2), hit 10 times consistently.

Another thing that might help: Apparently, failing to draw the Chariot tarot will set enemy AC to -10. (I suggest using a Bard that doesn't yet have her High Mastery skills here.)

Edit: One more random fact: Enemy Teleport miracle on a floor master counts as killing it. It does not make the monster move to a different spot on the map.

So that means that base Hit Chance from being a Level 1 isn't higher than 1. Need to find enemy with -1 AC to be sure on base Hit Chance for Lv1 fighter. Bely (Floor Master of Dezaporlia) should work, Manmo (Floor Master of Ice Cave) also has -1 AC.
For lower AC and higher level testing there is Knight of the Realm right in the city with -6 AC, and I am sure some Floor Masters or other convenient monsters also have AC in that vicinity. Due to how Hit Chance works here (drastic difference per 1 point), need to have several consecutive AC values for testing.