Max hitpoint variance

[Conker]

Do any stats exist on things like the max, min, and average hitpoints of particular class-race combinations at certain levels? I ask because after receiving my third consecutive increase of just 1, I'm often left wondering whether my totals by, say, level 10, are average to slightly unlucky, abysmal, or whether I'm just having my perspective clouded by memories of the last couple of incarnations that were quite lucky with the hp rolls (I tend to only take notice when they seem to be very high or very low) and the fact that I'm currently playing gnome mages.

Also, is the amount of hit points gained per level up governed by a 'life rating' determined at birth, similar to ToME? If so, what do people think of that? As regards hit point rolls in general, I'm in two minds - the randomness adds variety and surprise, but something niggles at me about the fact that a substantial degree of my character's survivability right through the game seems to rest on something uncontrollable and invisible. I know that the effect is lessened in the late game, as a greater proportion of hitpoints are garnered from CON bonuses, but I'd have thought that for race-class combinations with a large number of hit dice (typically warrior characters), the overall difference could be quite significant. Of course, as I don't know the actual numbers involved, that's just conjecture.

Does anyone have more information?
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[henryngo]

If you want to look at spoilers for this, they are found here
http://www.juti.nl/hugo/Angband/Spoiler/ability.spo

Basically, use that to look up the Base Hit Dice for your class/race combo. For example, I play a gnome mage usually so that means my base HD is 8. You start the game with the number of HP equal to your base HD, plus any constitution bonuses. Each them you level up, you gain 1d(base HD) plus CON bonuses. So, for me, I gain 1d8 HP plus bonuses.

I never thought about the "average" HP you should have, but I guess the best way to figure this is to compare your HP to how much HP you would have if you rolled the middle number every time. So, for me, I am currently level 38, with a CON of 18/140. So, the calculations would be as follows:

I start with 8 HP.
Let's say I roll 4.5 for every level up (middle of 1d8)*. 37*4.5 = 166.5.
Now, my CON of 18/140 gives a bonus of 7HP/level, so 38*7 = 266.
Thus, in total my HP should be 8 + 166.5+ 266 = 440.5.

My current HP is 458, so I guess I'm doing a little better than "average"

*I got 4.5 from average the numbers 1 to 8. A quick way to do the average of XdY is (X+Y)/2
----Corrected by Big Al: The average of XdY is X*(1+Y)/2. (X+Y)/2 only works if X=1.

**Note: If I forget about any other sources of HP, just add them in here and then the numbers will be right again.

[Big Al]

A quick way to do the average of XdY is (X+Y)/2

If I know anything about math, this is totally wrong.

The average of XdY is (1 + Y)/2 * X, which happens to be the same as (X+Y)/2 if only X = 1.

Average(2d4) = average(1d4) + average(1d4) = 2.5 + 2.5 = 5 != 8 = 2 * 4

[Daven_26d1]

If I know anything about math, this is totally wrong.

The average of XdY is (1 + Y)/2 * X, which happens to be the same as (X+Y)/2 if only X = 1.

Average(2d4) = average(1d4) + average(1d4) = 2.5 + 2.5 = 5 != 8 = 2 * 4

Yep, and actually he did his calculation correctly (1 + 8)/2 = 4.5, but gave the wrong working.

EDIT- duh! because X = 1. Which you just mentioned.

[henryngo]

If I know anything about math, this is totally wrong.

The average of XdY is (1 + Y)/2 * X, which happens to be the same as (X+Y)/2 if only X = 1.

Average(2d4) = average(1d4) + average(1d4) = 2.5 + 2.5 = 5 != 8 = 2 * 4

Indeed, my mistake. I was thinking in terms of HP gain, where it's always 1dY. I found the average then figured out a formula without thinking of the cases where X is not 1.

Thanks for the correction.

[Conker]

If you want to look at spoilers for this, they are found here
http://www.juti.nl/hugo/Angband/Spoiler/ability.spo

Gah! I specifically looked at the spoilers to avoid this happening. But I checked 'stats' instead of 'abilities'. D'oh. Now I'm embarassed.

Thanks for the maths though. It helped me out.

As for my other point, I had a quick look at the table and did a bit of investigation, working with the maximum hit dice available, 21, as a half-troll warrior. Now my previous worries were based on thoughts that bar CON bonuses, I could theoretically gain anywhere from

1 * 49 to 21 * 49 = 49 to 1029 HP

Quite an advantage/disadvantage. But then I saw the 50+(150*(base HD-1))/8 and 50+(250*(base HD-1))/8 line, and a few sums put my fears to rest.

50 + (150 * (20))/8 to 50 + (250 * (20)) /8

50 + (3000 / 8) to 50 + (5200 / 8)

425 to 700

Creating a total difference of less than 300 even in the most extreme example - not a lot, considering the total.

For kicks, I worked it out the other way, with a gnome mage (a hobbit mage would have been slightly lower (1 hit-dice), but they're nowhere near as common).

50 + (150 * (7))/8 to 50 + (250 * (7)) /8

50 + (1050 / 8) to 50 + (1750 / 8)

181.25 to 268.75

Less than 100 HP - handy, but not crippling if the roll goes awry.

Algebra probably shows that better, but I like actual numbers just for the quick reference-ability. Though they're probably wrong :P

Thanks again for the re-direction
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