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If anyone knows how these stats are calculated or can tell me where the hex code is located, I would appreciate it.

(Using v1.06 from Anthology - DOSBox v0.74-3-3)

A Mages starting Health is 25+d6, according to the manual. If you re-roll the stats for the Mage you will quickly see a low of 24 and a high of 31. This matches what is expected. 25 + 6-sided dice role (0-5).


However, if you try this with the Thief, things don’t add up. A Thieves starting Health is 25+d10, according to the manual. So, we should expect values in the range of 25-34. However, when re-rolling stats for the Thief, you quickly see values larger than 35. In my testing, I’ve found the range to be 25-39 making the starting Health 25+d15. The other thing I discovered was that rolling a 25 or 39 was VERY difficult.


I experimented using the Warrior which has a starting Health of 25+d20 (EDIT- needs more testing as this is not uniform with 0 being an option. It was also written before I was taking the Endurances Health modifier into consideration.), both according to the manual and also my testing. The range of rolls you get are between 26-45, however, rolling a 26 or 45 felt nearly impossible. So, I did a comparison between two online d20 dice rollers and Arena using 50 rolls each. For each set, the average time a number was rolled was 2.5. That matches the expected; 50 rolls divided by 20 options = 2.5 times each number can be expected to appear. The mode (the most common number of times a number appeared) for the online rollers was 3, while for Arena was 2. That’s still about right. It’s a small sample size (only 50 rolls). Most of the time, out of 50 rolls, you will see most numbers come up 2 or 3 times.

In a very basic statistical view, Arena appears to be calculating the same as an average d20 dice roll. However, this is not true in reality. With a dice roll you have an equal chance of rolling any of the 20 numbers. In Arena, the middle is weighted heavily and the extremes are weighted very light. You are VERY likely to roll a +8-13, but the higher or lower from that range, the less likely you are to see it. Online, the numbers that didn’t roll at all, rolled the most, or rolled an average amount of times are scattered throughout the numbers of 1-20. In Arena, however, 8-13 are rolled ~5 times, while 14-20 were rolled 1 or 2 times, and on the low end 1-4 were rolled 0 times and 5-7 were rolled an average of 3 times.

This was only one test of 50 rolls for Arena, but I had previously rolled hundreds of times and noticed this pattern, which is why I decided to do a formal test. Also, although 1-4 were rolled 0 times during my test, I did record rolling a 1 during other testing. It can be assumed that all the values are possible, but some are unlikely.

Wow, thanks for that explanation, @ArgonianAccount! I'm not sure I follow all of it, but that's because the logic they used for n>8 seems needlessly complicated.

Thanks @ArgonianAccount. It's going to take me a bit to process that, but it is EXTREMELY helpful to me.

Could you also direct me to the OpenTESArena wiki?

I located a post that had some info and then mentions that they were putting the rest on the wiki, but every time I try to look I seem to only find general updates and completion/needs work notices for OpenTESArena and not anything from the original game.

I think you've pretty much got it, but I now see I could have worded some parts better.

When I said, "The range is from 0 to n-1 inclusive for values of n <= 8", what I meant was, "When n <= 8, the range is from 0 to n-1 inclusive." Does that make more sense?

@SeaGtGruff - The main reason I called it "pseudo" code was because of all the various "random" functions that were doing the same thing. It's possible that different authors re-created their own versions, but it seemed....messy. Their downloadable source code looks very organized, though I don't think these functions are a part of that code as of yet. They just feel, to me, more like work-boards rather than copies or finished code.

@Argonian Account - With your code on the "multiple_test"; that's pretty clear. Though I can see how I could accidentally overlook that it drops out before actually running d4's. I realized last night that I can actually prove whether or not it uses d4's. Four d4's or three d6's have finite possibilities as well as specific and distinct probability maps. So I could just run some sets and compare the probability map Arena produces.


It's pretty clear Arena isn't using d4's here. Though the d6 map comparison isn't as clear as I would like it to be. The differences at "1" and "2" could possibly be explained by that funky "+1 if 0" thing, but it's still a little off. But "16" !?! It doesn't match at all. I would really like to know what that "throwXdY" function is doing and why it is different from rolling for d6 and d8.

I've just been using DOSBox debug builds to step through the game, but it can be a little fiddly. Whenever I want to find some value in memory, I have to create a dump file containing the whole memory and search through that, then locate that address in the debugger. And then there are segment registers to deal with as well.

I think the '0x1655B' in your last post might have been the result of a copy-paste typo. In version 1.06 (decompressed), the '1' byte appears to be at 0x17196 for health, and there's another one at 0x171C0 which I assume is for stats.

There's also an extra '0x19' value for Health Bonus at 0x16560. The first value seems to be added to your maximum health, and the second gets added to current health.

EDIT: Information on this post is invalid - The odd results were cause by a bug in the way I was creating my character. The next post corrects the information.

I've been testing the Health gain when you gain a lvl of experience. So far it seems similar to the roll for stats. However, testing this takes much longer and I've not yet come across any odd sided dice. (For stats rolls using greater than d8 you get one additional side. ex: d10 gives 11 possible results.) So far a d6 results in 1-6 and a d10 results in 1-10. If your Health is 25 and you are a mage with a d6 and a +1 Health bonus from Endurance; at lvl 2 your Health will be Health(25) + END bonus (+1) + d6 (1-6) resulting in {27..32}.

The reason I bring this up is because those two bytes that affect the initial Health (If H = 0 then H=1), also affect what's added to health during a level up - but not in the same way. Truthfully - I'm not really sure what they are doing. During initial health roll, "0x17196" appears to be the "+1" and "0x17191" appears to be the "if<1" But changing these and testing the LVL health gain, I get weird results

Health = 26; Dx = d3; END bonus = +0
NO CHANGE to the two bytes - after lvl-up result is 27, 28 or 29
Change only (+1 byte) to 0, 2 or 8 and the result is the same; 27, 28, or 29
Change the (<1 byte) to 0 or 2 and the result is the same; however change it to 8 and the result is 27, 29-35. (values that occurred during limited testing)
Changing both bytes to 8 and I get; 27-29; and 37 (also limited testing but was heavy on the low end and not spread out like the test before.)

I really have no clue what's going on here for the lvl up with these bytes. It's possible that while it seems consistent and obvious what they do for the initial stat roll, that it's just a coincidence, and rather than values, I'm messing with the math functions. These are not values that are changed from 0x01 regardless of class, race, or gender. It would be helpful to point to them as a means of certainty in describing what is happening, but either way it doesn't change what actually occurs.