Wednesday, July 16, 2014

Back to the Beginning

"Fool, fool, back to the beginning is the rule."
Fezzik, The Princess Bride, by William Goldman

We don't see a characters day-to day health. We don't see how clumsy they are, how often they scrape themselves or stub their toes or fall in the mud. We don't really see height at weight unless we are explicitly told these things. Even if we are, we don't see the breadth of the shoulders, the muscle groups that have developed, whether the person carries the healthy fat of someone who wants not for food, or whether they have simply gorged themselves in a time of feast and will starve again during famine. We don't see which people have trouble seeing, or which ones have trouble hearing. We don't see which people have flat feet, or who have bad luck. We don't see the people who physically and mentally can't take the stress of combat. We don't see the squeamish soldier who vomits every time he smells blood.

We only see hitpoints. This is the only value we have to describe the ability of a person to survive combat. This value represents an assessment of all of the things I mentioned above, and more. It is an assessment that the world reports to us, the players. So, do you play a game where these other factors are worked in to the descriptions of characters are worked in and interact with each other, providing bonuses and penalties in real-time? Or do you play a game with just hitpoints? Because if it is the later, then yes, an orc can see its hitpoints. Rather, it can see all of the things that contribute to hitpoints. They see the runt who can't keep his stomach down in a fight, and we see the orc with 1hp. They see the muscled, well fed, sturdy warrior, and we see the orc with 7 hp. The smart army is going to kick as many of the people that they have assessed as "weak" to the least important positions. They are going to be peeling potatoes, not guarding treasure or ambushing adventurers.
Matt, comment on Save vs. All Wands, July 11

I had intended to move onto other facets of last week's arguments (interrupted by the publishing of my book), but it has been discovered that my math from a week ago Monday did not meet the necessary requirements.  I did not show my work, there were definite failings, and this was pointed out by the fellow I referred to as 'self-deluded.'  That was, in fact, the only personal comment I made about him - all my other insults were directed at the dumbassery of his arguments regarding the 'reality' of hit points.  Let me be clear. He, Oakes Spalding, corrected my math.  The arguments I called a self-deluded dumbassery STILL ARE. As it happens in reality, however, people can be both stupid and correct in unrelated things.  This is a case of that here, with both him and me.

So, I will set about making corrections in that which I got wrong.

Before doing so, however, I am forced by the existence of dumb asses (this being a very personal comment directed at people, and not their ideas) to set out some principles.  I can't believe I have to set out these principles, but the community has gone straight up its own ass and this makes stating the obvious a necessity.

First and foremost:  hit dice are a game mechanic used to give value to a creature's maximum health.  hit points are a finite value used to determine how much damage a creature can withstand in combat.  Hit points are determined traditionally as a set random value assigned as a die or such-and-such number of dice per hit die.  Traditionally, the die used is an 8-sided.  The number assigned by the total rolled dice to determine a creature's hit points is the maximum number of hit points the creature is able to have.

If, due to circumstances of injury, exhaustion, physical difficulty or hampering of combat strength, the number of hit points of a creature are currently less than the total number of its maximum hit points, then it is the DMs responsibility to make clear the total number of hit points of the creature in addition to the creature's present hit points due to circumstances.  The DM would be irresponsible to assume the number of current hit points were merely "something less than the maximum" without also assigning a true number of hit points that the creature would possess if the creature were not suffering from present circumstances.  As the players must keep track of their maximum hit points as well as their current hit points, the DM must keep track of all creatures' maximum and current hit points also.

The DM is also responsible to make evident, in a manner that would be plainly in evidence to a character's eyes, any creature that is currently under plain duress, ie., evidence of exhaustion, injury, pain, suffering, blood on clothes, an inability to walk normally due to a rock in the creature's shoe large enough to lower the creature's hit points and so on, so that parties attacking or being attacked by creatures are able to make a clear and obvious visible assessment of limitations of opponents due to having lost any substantial portion of their hit points prior to being encountered.  A DM failing to do this is guilty of deliberately limiting a player's legitimate knowledge of the circumstances in order to deceive or otherwise fudge the game's present play in the DM's favour.

I consider that an act of railroading and robbing the players of the fair ability to play in an unrigged game.

Very well.  Let's start again.  And this time I'll show all my work, a LOT more clearly that Oakes shows his, and we'll see where we are.

Let us take 800 one-hit-die creatures, because it actually doesn't matter if the attacked creature can use a weapon where this argument is concerned.  Let us assume that by perfect, possible chance we roll their hit points (using 1d8), getting exactly 100 rolls of each possible hit point value:  100 with 1 hit point, 100 with 2 hit points, 100 with 3 hit points and so on.  Really, this is the sort of thing I assumed people could understand when I wrote my original post, but people - it turns out - are really, really fucking stupid.  So it has to be said very slowly and in great detail so they will understand.

(Incidentally, my published book, How to Run, doesn't do this.  It is an Advanced Guide, so for some of you, it is really going to be too difficult.  It has English words and stuff).

Let's start with 100 creatures of 1HD that each have 1 hit point.

Now, in my original post I never said what was attacking the humanoids (or creatures, as we are now calling them).  I said that whatever it was had a 35% chance of hitting, because I was rating the creature as AC 6.  I was, in fact, assuming a 1st level fighter, that hits AC 6 on a 14.  For the very, very slow, that means a 1st level fighter would hit on a 14, 15, 16, 17, 18, 19 and 20.  That's 7 possible facings out of 20, or 35%.  I know this is really hard for some of you, but there you are.  Try to keep up.

Because some of you seem to think everything makes a big difference how many creatures attack the 1HD/1hp creature per round, I won't use rounds. I'll just refer to attacks.  Someone attempts to attack the 1 hit die creature at some point.  It doesn't matter if the creature attacks first, or succeeds, or if it kills 50 creatures before it is actually attacked, because for this argument, that doesn't matter.  We know from experience that it probably won't kill 50 first, but that isn't important right now.  Sooner or later, if it keeps getting into combats, it is going to get attacked.

Since we are starting with 100 creatures (to make our math easier), we assume that they're all going to get attacked a first time.  There's no need to assume that this is all going to happen at the same time, or in the same round, because within the function of this argument, that still doesn't matter.  For those who think it does matter for some reason, you're too young to read this blog.  Go ask your mommy or daddy.

Let us assume that in this universe, the chances of hitting exactly equal the actual hits that are done, so that in the first round, 100 creatures are attacked with a 35% chance of hitting them, and 35 creatures are hit. Miraculous!  And all done through the power of supposition.

Bif, bang, boom, 35 1HD/1hp creatures die.  That leaves 65.  Now we have a second attack.  We assume, again, that if they're still around, eventually they will be attacked a second time.  Being attacked is extraordinarily common in combat, so we can presume they'll probably have to take that risk again.

2nd Round:  35% x 65 creatures = 22.75 creatures are going to be hit.  To keep our numbers nice and round, let's say that fractions in this universe are dispersed by the gods, so that we only hit 22 creatures.  All 22 of those creatures are now dead.

3rd Round:  The 43 creatures that remain are attacked again.  This time, 35% x 43 = 15.05.  We drop the fraction and 15 die.

And here is where Oakes is correct when he tells me there wouldn't be 4 left.  I honestly don't understand right now how I wound up with 4 originally.  Some goofy thinking there.  Wow, I sure fucked up.  I must be really, really stupid.  Oh well.

Still, I count 28 left.  What happens if they're attacked another round.  We must assume, mustn't we, that these creatures, if still alive, are going to be attacked again, right?  Well, to save time, assuming they are attacked for a whole bunch of rounds, nine rounds in all, I find the remaining 1HD/1hp creatures diminish thusly (each number is a round, for those who are having trouble) - please try to remember I'm dropping fractions:  19, 13, 9, 6, 4 and 3.

I sure conflated that with the last post.  My math really sucks.

Okay, let's take one-hit-die creatures with 8 hit points.  We have 100 of those too, remember?  We could work our way up through each number of hit points up to 8, but this post is getting long enough, so let's just jump to the top.  After all, we know that since my original argument that there would be far more 1HD/8hp creatures left was totally bogus since my math sucks so much, we might as well prove that there isn't going to be a difference. There isn't going to be a difference, right?

Well, this is going to be more complicated (and here's why my math was screwed up, because I was trying to manage the 8hp creature and I overcomplicated the 1hp creature; oh well, live and learn).

Again, everyone is attacked and of 100 8hp creatures, 35 are hit.  These all die, and . . .

Wait a minute.  Wait just a minute.  None of them die, do they?  Seems to me that I came to that conclusion before, but my math really sucks, so let me look at it again.

All 35 that get hit take 1-6 damage from the spear I had originally applied in my first post.  That would mean that 5.83 suffer 1 damage, 5.83 suffer 2 damage, 5.83 suffer 3 damage, 5.83 suffer 4 damage, 5.83 suffer 5 damage and 5.83 suffer 6 damage.  I felt I should list them all off, since I don't want any of my readers thinking I've pulled a fast one.

Well, we still want to keep round numbers, but just for shits and giggles, let's say that the gods really hate 1HD/8hp creatures and that they insist on all fractions being kept.  Makes it harder for me, but . . . well, they're gods.

Let me put this into a table, because that will be easier for everyone:


Now, maybe it's just me, but the fact that I have to make a table for these, that I didn't have to make for the 1HD/1hp creatures, ought to say something of itself, but there we are.  Let's look at the second attack.

Of the ones that were hit above, each of those has a 35% chance of being hit.  This works out to 2.0405 of each of those that gets hit a second time, and 3.7895 not being hit by the second attack.  Taking one of those groups as an example, if we just take those with 2 hit points remaining, 84.33333% are killed, while 16.66667% take 1 damage.  See?  This is really simple math, isn't it?

So to see who gets hit and who doesn't, and how many take how much damage, let's have a look at this table:


We can then compare the above numbers with those that are killed:


And from that we can get a lay out of how many are left with each amount of hit points:


Total: 86.61741667

Hm.  Maybe it's just me, but it seems like even if a troop of 1 hit die humanoids had been attacked prior to meeting the party, most of those with 8 hit points to start would still have 8 hit points.  Isn't that strange?  I must be reading the numbers wrong.

Well, I've shown my work, and the means of getting there, so let's just jump to the end.  Let's see how the 1HD/8hp creatures would fare to the end of 9 rounds (*sorry, for easier reading, I'm going to limit it to 3 decimal places - the reader will have to trust I'm not lying about decimal numbers I'm not showing):



There!  Proof positive that the reader is absolutely right.  There is no difference  whatsoever between creatures having 8 hit points and surviving combats and creatures having 1 hit point.

Damn.  Glad that's settled.







12 comments:

Oddbit said...

Hrm, does this mean that we should get rid of hit points and just track hits?

Guillaume JAY said...

You should put a warning "High Level of Sarcasm : Toxic for kids and pets" :)

I'm impressed : arguments based on mathematical facts are always beautiful.
To tell the truth, I was a believer since your first post on the subject (but... since the only D&D ruleset I DMed in the last 25 years was 4E, the idea of (nearly)-fixed HP was not sacrilegious for me )

(warning : English is not my first language)

Issara Booncharoen said...

Huh, I made a pretty piss poor assumption about your math back there, apologies. Lesson learned, actually check the maths before making any statements.

I'm still not sure why it matters, no one was claiming the chance of a 1 hitpoint monster surviving a number of attacks was equal or greater than the chance of a 8 hit point character surviving the same. And that's the only argument that would, mathmatically refute yours.

Ozzie Pippenger said...

My one issue with this idea (and maybe you addressed this and I missed it) is that it doesn't seem to account for any kind of bell curve in terms of health. In player characters there is some kind of bell curve in terms of constitution bonuses (if you do stats by rolling 3d6) and in differing amounts of HP gained from each level.

If you really want health to be realistic, it seems to me that monsters need a bell curve of health as well. I'm sure every orc would have 8 HP if they got to decide. But it seems more likely that there are lots of orcs with 4, 5, and 6 HP who wish they were one of the great warriors but just had bad luck. Naturally these would die off at a higher rate than the 8 HP orcs, but wouldn't there be more of them in the first place? I haven't done the specific math, but I think that generally, both extremely low and high HP orcs should be rare, and that low HP orcs should die at the highest rate, making them extra rare.

I think a way to account for this is to use multiple dice instead of just one. If you roll two four sided dice, you get a range from 2-8, with 5 being the most common. This seems reasonable to me, since and orc with 5 HP can usually survive a single hit. The combination of being near the center of the bell curve and just strong enough to usually survive fights would make them the most common.

I agree that if you roll a D8 and apply basic logic to your world, then 8 HP orcs would be the most common. But if you're going for realism, why use a D8 in the first place?

Maxwell Joslyn said...

Oddbit: it does change the numbers, since one "hit" is destroyed by one successful attack (unlike HP where several HP are destroyed by one successful attack.) But ultimately the concept is the same: more hits is more survivability, whether they deplete 1-to-1 with attacks or not. Having hits instead of HP just makes the divisions less fine-grained.

Alexis Smolensk said...

Ozzie,

I don't want health to be realistic. I want there to be a verisimilitude to the game I'm playing. Hit points being what they are, this is how they manifest when attacks land.

Wanting a bell curve to be there doesn't mean there's a bell curve. Lots of mathematics, particularly algorithmic mathematics, does not incorporate the bell curve. Review your precepts.

Alexis Smolensk said...

Issara,

The point of the original post was that, given the likelihood of 1HD/1hp creatures dying in combat, there ought to be way less of them within the construct of the game's world. Rolling a strictly random 1HD = 1d8 hit point total does not make sense if we consider the creatures the party is fighting have had a fight any time before in their lives.

Oddbit said...

Maxwell: Apologies, I should have noted the post was sarcastic and based on the conclusion that 8 HP would survive as long as 1 HP.

Issara Booncharoen said...

I hope I managed to demostrate in all previous comments that I understood the particular point you just mentioned. It's this post that bothers me, everyone who pointed out your maths was incorrect failed to demonstrate that your maths being incorrect made your argument invalid. So I guess this was your way of explaining slowly and carefully that this was the case.

It's how you deal with the group of people who are essentially saying either
a) these changes make me uncomfortable because it changes the way I've been playing the game.
b) these changes aren't worth the time to think about and apply (even though they would take up no more time than rolling a bunch of d8s would).
And the two most puzzling to me c) these changes contradict the rules as written and therefore can never be elevated to anything about a mere preference.
d) Hit points are a gaming construct and have no application in setting.
Or e) some combination of the above.

As far as I can see no one has refuted your argument on its own terms (though I think some have added to it) which leaves the main objections coming from people who do not want to think about the game, or think about game in a completely different way. It seems that if you're going to convince them correcting your math wont cut it, and if you're not interested in convincing them you then you probably have more interesting depths to explore.

Alexis Smolensk said...

You're absolutely right, Issara.

Only, my original plan was to do more math, on more subjects, so I felt that - for me - it was uncomfortable going on without first correcting my work.

My being accurate is important for ME. That is enough reason for me to redo the work properly.

Barrow said...

The Hooded Counsel Leader : I am glad that you have corrected your math and realigned yourself with the conventional majority. Your statements about 1HP Orcs were...troubling, to say the least. As you well know, 1HP Orcs are and always will be part of the convention. After your ritual self-flagellation, you may re-hood yourself before stepping out of our pentagram. And, Alexis, if you try to change the convention again, we will be displeases.

Issara Booncharoen said...

Understood and respected Alexis.