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-   -   Damage vs Accuracy (http://angband.oook.cz/forum/showthread.php?t=8863)

Gordon March 27, 2018 21:42

Damage vs Accuracy
 
Dropping down to dlvl 75, I ended up in a small rectangular room. Casting my usual mae, mdf and mcg, I saw no traps, no monsters and only one unknown item in the room. I sauntered over to take a look and saw a Mithril ring. At this point there were only 5 unknown rings, 4 of power and Tulkas. A Mithril ring sure sounded like...yes! Nenya! I can't believe I found it without having to fight my way through a horde of Pit Fiends. Now I can get rid of this shabby looking Hard Leather Cap of Thranduil and finally wear this beautiful Golden Crown of Gondor that I've been hauling around to occasionally protect me from confusion and stunning. I can also lose the Ring of Constitution <+6> that I have been wearing forever, it seems. And my Ring of Speed <+12> is pretty much redundant at this point. Not much difference between speed 34 hasted and speed 46 as far as I can see. This opens up a ring slot and hence my question.

I have two candidate rings, a Ring of Accuracy (+21,0) and a Ring of Damage (0,+15). I see that accuracy is dismissed a lot here, but looking in my monster memory at the Great Wyrm of Chaos, for instance, I see that by wielding the Ring of Accuracy, my chance to hit rises from 35% to 47%. When wielding the Ring of Damage, my sword does 348 damage per round against evil creatures. Multiplying this by 0.35 yields effective damage per round of 121.8. Meanwhile, wielding the Ring of Accuracy gives 292 damage per round. Multiplying by 0.47 yields 137.2 effective damage. The Ring of Accuracy has the additional benefit of fewer wasted shots when I use my bow. So how is it not advantageous to choose the Ring of Accuracy over the Ring of Damage?

Derakon March 27, 2018 22:32

Your chance to hit sounds abysmal. Most characters have a chance to hit in the upper 60th percentile at minimum, and a Ring of Accuracy gives only 1-4% improvement in hit chance, not the 12% you're seeing.

Post a character dump? Something strange is going on.

Gordon March 27, 2018 23:26

Perhaps it is due to the fact that @ is 2'10" and weighs only 13lb ;).


Code:

  [Angband 4.0.5 Character Dump]

 Name  Ringo        Age            24          Self  RB  CB  EB  Best
 Race  Hobbit      Height      2'10"  STR! 18/100  -2  -3 +13 18/180
 Class  Mage        Weight    3st 13lb  INT! 18/100  +2  +3  +6 18/210
 Title  Arch-Mage    Turns used:          WIS! 18/100  +1  +0 +10 18/210
 HP    825/825      Game      2164988  DEX! 18/100  +3  +0  +5 18/180
 SP    394/394      Standard    334507  CON! 18/100  +2  -2 +11 18/210
                    Resting      57125

 Level                50    Armor    [78,+124]    Saving Throw    100%
 Cur Exp          7313706                          Stealth      Superb
 Max Exp          7313706    Melee      4d5,+57    Disarming      100%
 Adv Exp        ********    To-hit      33,+53    Magic Devices    131
                            Blows      4.0/turn    Perception    1 in 1
 Gold            2689831                          Searching        48%
 Burden          174.8 lb    Shoot to-dam    +15    Infravision    40 ft
 Overweight      -5.1 lb    To-hit      38,+44    Speed            24
 Max Depth    3750' (L75)    Shots        1/turn

 You are one of several children of a Hobbit Warrior.  You are a credit
 to the family.  You have hazel eyes, straight auburn hair, and an
 average complexion.


rAcid:......++*.... Nexus:.............
rElec:.+....+...... Nethr:....+........
rFire:.+....++.+... Chaos:........+....
rCold:++.*+.++.+... Disen:......+......
rPois:............. pFear:+.......+....
rLite:+........+... pBlnd:...+.....+...
rDark:....+.+...... pConf:.........+...
Sound:........+.... pStun:.........+...
Shard:............. HLife:...++.......+

Regen:++.++....+... Stea.:.......++..+.
  ESP:...+......... Sear.:..........+..
Invis:+..+.+...+... Infra:............+
FrAct:+..+....+.+.. Tunn.:.............
Feath:...+......++. Speed:+..+...+...+.
S.Dig:+............ Blows:.............
ImpHP:............. Shots:.............
 Fear:............. Might:.+...........
Aggrv:............. Light:+....+...+...


  [Character Equipment]

a) the Long Sword 'Ringil' (4d5) (+21,+24) <+10, +1>
    Dropped by Hoarmurath of Dir at 3500 feet (level 70)
   
    +10 speed.
    Slays demons (powerfully), trolls, undead, evil creatures.
    Branded with cold.
    Provides resistance to frost, light.
    Provides protection from fear.
    Cannot be harmed by acid.
    Blessed by the gods.  Slows your metabolism.  Speeds regeneration.
      Prevents paralysis.  Grants the ability to see invisible things.
   
    Radius 1 light.
   
    When activated, it creates a frost ball with damage 100.
    Takes 136 turns to recharge at your current speed.
    Your chance of success is 98.6%
   
    Combat info:
    4.0 blows/round.
    Average damage/round: 401.6 vs. creatures not resistant to cold,
    509.2 vs. demons, 348 vs. trolls, 401.6 vs. undead, 348 vs. evil
    creatures, and 294 vs. others.
   
b) the Short Bow of Amrod (x4) (+12,+15) <+2>
    Conjured forth by magic at 2050 feet (level 41)
   
    +2 strength.
    +2 constitution.
    +2 shooting power.
    Provides resistance to lightning, fire, frost.
    Cannot be harmed by acid, fire.
    Speeds regeneration. 
   
c) a Ring of Damage (+0,+15)
    Taken from a chest found at 3500 feet (level 70)
   
d) the Ring of Adamant 'Nenya' (+3,+3) <+2, +5>
    Found lying on the floor at 3750 feet (level 75)
   
    +2 strength.
    +2 intelligence.
    +2 wisdom.
    +2 dexterity.
    +2 constitution.
    +5 speed.
    Provides immunity to frost.
    Provides protection from blindness.
    Cannot be harmed by lightning.
    Sustains intelligence, wisdom, constitution.
    Feather Falling.  Speeds regeneration.  Prevents paralysis.
    Sustains your life force.  Grants telepathy.  Grants the ability
    to see invisible things. 
   
    When activated, it restores your experience to full.
    Takes 686 to 1020 turns to recharge at your current speed.
    Your chance of success is 93.7%
   
e) the Jewel 'Evenstar' <+2>
    Found lying on the floor in a pit at 2050 feet (level 41)
   
    +2 wisdom.
    Provides resistance to frost, dark, nether.
    Sustains wisdom, constitution.
    Speeds regeneration.  Sustains your life force. 
   
    When activated, it restores your experience to full.
    Takes 510 turns to recharge at your current speed.
    Your chance of success is 97.3%
   
f) the Star of Elendil <+3>
    Conjured forth by magic at 2650 feet (level 53)
   
    Cannot be harmed by fire.
    Grants the ability to see invisible things. 
    Radius 3 light.
   
    When activated, it maps the area around you.
    Takes 173 to 340 turns to recharge at your current speed.
    Your chance of success is 98.0%
   
g) the Mithril Plate Mail of Celeborn (-3) [65,+25] <+3>
    Found lying on the floor in a vault at 3500 feet (level 70)
   
    +3 strength.
    Provides resistance to acid, lightning, fire, frost, dark,
    disenchantment.
    Cannot be harmed by acid.
   
    When activated, it removes all non-unique monsters represented by
    a chosen symbol from the level, dealing you damage in the process.
    Takes 1700 turns to recharge at your current speed.
    Your chance of success is 97.3%
   
h) the Elven Cloak of L&Atilde;&ordm;thien [6,+20] <+4, +3, +2>
    Conjured forth by magic at 2050 feet (level 41)
   
    +4 intelligence.
    +4 wisdom.
    +3 stealth.
    +2 speed.
    Provides resistance to acid, fire, frost.
    Cannot be harmed by acid, fire.
   
    When activated, it restores your experience to full.
    Takes 850 turns to recharge at your current speed.
    Your chance of success is 97.3%
   
i) the Small Metal Shield of Thorin [5,+25] <+3, +4, -1>
    Dropped by Lugdush, the Uruk at 1100 feet (level 22)
   
    +3 strength.
    +4 constitution.
    -1 stealth.
    Provides immunity to acid.
    Provides resistance to sound, chaos.
    Provides protection from fear.
    Cannot be harmed by acid.
    Prevents paralysis. 
   
j) the Golden Crown of Gondor [0,+15] <+3, +2, +1>
    Dropped by a Patriarch at 2950 feet (level 59)
   
    +3 strength.
    +2 wisdom.
    +3 constitution.
    Provides resistance to fire, frost, light.
    Provides protection from blindness, confusion, stunning.
    Cannot be harmed by acid.
    Speeds regeneration.  Grants the ability to see invisible things.
   
    Radius 1 light.
   
    When activated, it heals 500 hit points.
    Takes 850 turns to recharge at your current speed.
    Your chance of success is 97.3%
   
k) a Set of Alchemist's Gloves of Thievery (+6,+1) [0,+15] <+3, +4>
    Found lying on the floor in a vault at 2300 feet (level 46)
   
    +3 dexterity.
    +4 searching skill.
    Cannot be harmed by acid, fire.
    Feather Falling.  Prevents paralysis. 
   
l) a Pair of Leather Boots of Elvenkind [2,+11] <+3, +7>
    Dropped by Eöl, the Dark Elf at 2700 feet (level 54)
   
    +3 stealth.
    +7 speed.
    Cannot be harmed by acid, fire.
    Feather Falling.


jevansau March 28, 2018 00:09

Looks like the worst case for melee - Hobbits have poor melee and mages are the worst.

I think the advice is - for classes that RELY on melee, damage vastly trumps accuracy.

Gordon March 28, 2018 00:22

So perhaps it is conditional then. I'm normally a mhh sort of guy, but when it comes to dragons, I like to get up close and personal. I have observed that when they can use their teeth and claws, they are a lot less likely to breathe all sorts of nasty stuff at you.

Philip March 28, 2018 00:26

The advice to choose Damage over Accuracy is, as jevansau noted, intended for characters capable of melee combat, and who have a lot of blows. As a mage you get 2/3 the advantage a warrior gets from a ring of damage, and your base accuracy is low enough that improving it has actual benefits. That said, watch out. Your character should never fight a Great Wyrm of Chaos or anything that has a similar AC in melee. These calculations would be better made on the type of monster you do end up fighting in melee as an end-game mage, who tend to have much lower AC, meaning your base accuracy is higher, meaning that increasing accuracy is probably less necessary/helpful.
The advice is also kind of a holdover from back when the effect of increased damage was immediately apparent, while the effect of increased accuracy was invisible.

Traditionally I would recommend using a different ring on a mage, except you have absolutely everything including stats, resists, abilities, speed covered quite nicely so you may as well go ahead and use the Accuracy ring. Just don't let it tempt you into actually using melee against anything even remotely threatening, whether it needs to die fast or is scary in melee.

EDIT: Written before I saw your post. Unless something has recently changed, dragons are in fact equally likely to breathe at you at all times. They are, on the other hand, going to do a lot more damage with their breaths in melee range than they would, say, 10 tiles away, since breath attenuation was implemented some time back. Note that other monsters, including Sauron and Morgoth, will also use spells at the same frequency in and out of melee. The only significant difference being in melee causes (outside of effects on breath damage) is that when their AI rolls not to cast a spell, they will hit you if in melee range and move towards you if not.

Gordon March 28, 2018 00:51

Hmm, this is not what I have observed. When fighting dragons from a distance, they almost always breathe. When fighting at melee range they rarely breathe. It takes a long time to whittle them down with so little damage per round, but @ can take melee damage with 252 AC after mee, since they tend to miss often. So far @ has defeated 15 Great Wyrms with this strategy. Of course, I am using melee mainly to preserve mana here, so I do tend to throw in a few Mana Storms to help with the whittling.

Gordon March 28, 2018 01:16

Another advantage of melee is that it tends to keep neighboring creatures asleep. As a Hobbit @ has enough stealth to be safe from anything that is not permanently awake, such as Zephyr Hounds and Quylthulgs. In fact, @ needs to walk up and bop a Great Wrym on the nose to get its' attention.

Philip March 28, 2018 02:05

It is possible having a lot of AC helps make the melee damage of a Great Wyrm less scary (they are not particularly powerful), but it still stands that they are just as likely to breathe (I am quite certain), and their breaths do full damage, rather than the damage being reduced (of which I am entirely certain). Additionally, by taking dragons down slower, you give them a lot more time (which they can use to breathe) and because you are doing damage slowly, they remain capable of doing a lot of damage with their breaths for longer.

There are a lot of cognitive biases that come into play when playing angband, which has a lot of unintuitive probabilities and emotional baggage (you notice the third consecutive failed teleport a lot more when it makes you die etc.).

I don't know much about how monster awakeness works, and it's possible something changed with the tweaks to pathfinding and such, but last I recall, the only activities that really affected how monsters wake up or not was whether you had damaged them or shone a light in their direction. I doubt that melee is significantly quieter (especially when you factor in the extra time killing the monster takes) than spellcasting, in any case.

As for conserving mana, yeah, that's always nice to do. I recommend relying a bit more on devices to supplement mana, mages get a lot of bonus damage with those in current V. A wand of annihilation with a mage can consistently do around 300 damage a round, at range, with the only mana cost being recharging. Even rods would be likely to outdamage your melee, I think.

Gordon March 28, 2018 02:41

I gave up on wands a long time ago. I had a Wand of Drain Life that I tried on a monster that had 840 HP and it only took it down 1 star per hit which I assume is 84 HP. This in spite of the fact that it claimed to do 150 HP damage and my device skill would raise that by some large percentage. I do have a Wand of Annihilation in my home that claims to do 250 HP damage and my device skill will currently raise that by 71 percent for presumably 427.5 HP damage. I'll give it a try to see if that is correct or not.

Gordon March 28, 2018 02:52

I am rather curious has to how I can easily go 10 rounds of melee against a dragon without a breath attack if what you say is true. As to awakeness, I can also easily melee them to death without waking anything nearby, even in a crowded vault. One ball spell however, wakes everything within range, of course.

Derakon March 28, 2018 04:32

Quote:

Originally Posted by Gordon (Post 128753)
Hmm, this is not what I have observed.

Humans are very good at seeing patterns that aren't there. :) I encourage you to collect statistics on what monsters do with their turns when you're in melee range vs. not in melee range. I would be very much surprised to find that their behavior differed substantially based on where you stand.

Ingwe Ingweron March 28, 2018 06:31

Quote:

Originally Posted by Gordon (Post 128748)
Perhaps it is due to the fact that @ is 2'10" and weighs only 13lb ;).

Just a note: @ weighs 3 stone and 13 pounds, not just 13 pounds. Historically ranging from 5 to 40 pounds, the modern English imperial unit of mass "stone" equals 14 pounds. Thus, your hobbit @ likely weighs 55 pounds. Still pretty light for melee, but a damned sight better than 13 pounds! :D

Werbaer March 28, 2018 13:07

Quote:

Originally Posted by Philip (Post 128752)
They are, on the other hand, going to do a lot more damage with their breaths in melee range than they would, say, 10 tiles away, since breath attenuation was implemented some time back.

That was introduced in 4.1.0. The character in question plays 4.0.5. So full breathe damage at range.

Werbaer March 28, 2018 13:14

Quote:

Originally Posted by Gordon (Post 128757)
I gave up on wands a long time ago. I had a Wand of Drain Life that I tried on a monster that had 840 HP and it only took it down 1 star per hit which I assume is 84 HP. This in spite of the fact that it claimed to do 150 HP damage and my device skill would raise that by some large percentage. I do have a Wand of Annihilation in my home that claims to do 250 HP damage and my device skill will currently raise that by 71 percent for presumably 427.5 HP damage. I'll give it a try to see if that is correct or not.

At least in 4.0.4., there was a bug that denied you the bonus damage from magic device skill. I don't know whether it was fixed in 4.0.5; judging from your number, it looks like it wasn't. Your wand of drain life did 150 damage; but 2 stars are 168 HP, so the monster at full health lost only 1 star at the first attack.

Wands of Annihilation are still usefull even at 250 damage, if you're low on mana.

Werbaer March 28, 2018 13:24

Quote:

Originally Posted by Gordon (Post 128758)
I am rather curious has to how I can easily go 10 rounds of melee against a dragon without a breath attack if what you say is true.

A Great Wyrm of Chaos has a chance of 1 in 3 to use a spell or breath attack; with 5 spells and 2 breaths to chose from, that's a 2 in 21 chance of a breath attack each turn. Now you have speed +34 when hasted; the dragon has +10. So in your 10 rounds of melee, he gets 5 actions. Chance of no breath attack within your 10 turns is 60%, no matter where you are.

Pete Mack March 28, 2018 16:53

Do not neglect archery. If you find a high end crossbow or Belthronding, you'll be doing more damage with (branded) arrows than any other offense. And you get all the benefits of the Ring of Accuracy with none of the downside.

Gordon March 28, 2018 20:49

Well, I guess I've been disabused of a fantasy that I thoroughly enjoyed, pooh!

That rather nasty bug has not been fixed in 4.0.5. I tested on an Istar with average 1800 HP and it took 8 charges from the Wand of Annihilation to bring it down. Seven times 250 plus 50 from the eighth charge. Any thoughts on a backport for the fix? 4.1 seems to be a whole different game.

Thanks for the info on @'s weight. I didn't know what an Angband stone was, so I just assumed that 13lb was the equivalent of 3 stone. It did seem rather ridiculously low.

Regarding archery, @ did recently find a Sling of Buckland (x4) (+18, +17) <+5, +2> that I've been thinking about giving a try. Trouble is, I've been passing up high grade sling ammo all game, so I'd need to start accumulating it from scratch. Also, up until now, I've needed the stats from the bow @ is currently wielding. That is no longer the case though.

One other thing. When I was looking for a monster to try the Wand of Annihilation on, I ran into Ariel, Queen of Air. Seeing as I knew that the wand wouldn't work on her, I cast Mana Storm instead. It failed five times in a row. With @'s current 14% chance of failure for this spell, the probability of that happening by chance is 1 in 18593. Has anyone checked the RNG used for spell failure for correlation?

Derakon March 28, 2018 21:44

Quote:

Originally Posted by Gordon (Post 128772)
One other thing. When I was looking for a monster to try the Wand of Annihilation on, I ran into Ariel, Queen of Air. Seeing as I knew that the wand wouldn't work on her, I cast Mana Storm instead. It failed five times in a row. With @'s current 14% chance of failure for this spell, the probability of that happening by chance is 1 in 18593. Has anyone checked the RNG used for spell failure for correlation?

Yes, many times. It is on average quite random. Humans are bad at recognizing randomness. :)

Pete Mack March 28, 2018 23:27

You don't need fancy ammo with that sling, which is essentially the best shooter in the game. Just buy some shots from the store and brand them. (You'll get Poison, Cold, and Fire brands on ~+5,+5 shot. You'll find better shot soon enough.)

Ighalli March 29, 2018 05:23

Quote:

Originally Posted by Derakon (Post 128773)
Yes, many times. It is on average quite random. Humans are bad at recognizing randomness. :)

What seems stranger than the allegedly streaky RNG is how frequently the fairness of it is questioned. :D

Pondlife March 29, 2018 19:33

Quote:

Originally Posted by Ighalli (Post 128777)
What seems stranger than the allegedly streaky RNG is how frequently the fairness of it is questioned. :D

I think the mathematical definition of random differs from the "common sense" definition of random. See for example "The Black Swan: The Impact of the Highly Improbable" by Nassim Nicholas Taleb; or Apple's decision to change the shuffle algorithm from true random because that didn't "feel" random to users.

I beleive the Angband RNG is random in the mathematical and statistical sense; but often it seems "unfair" or "streaky" to humans.

Pete Mack March 29, 2018 21:20

Um. No pseudorandom RNG is "random in the mathematical sense." And there are a whole lot of statistical ways to analyze a sequence for randomness. I suspect the angband RNG is good under some of the basic ones, which is usually good enough.

Gordon March 29, 2018 22:19

Well, 1 in 18593 is slightly less probable than flipping a coin and having it come up heads 14 times in a row. I think any intelligent being would look upon that coin with suspicion. That said, I was glad to hear that this RNG had been tested for correlation. Serial correlation analysis is just as important as uniformity analysis when evaluating a RNG and is often neglected.

Pete Mack March 29, 2018 23:33

When evaluating likelihood of an event like repeated fails on a 5% throw, it's better to ignore the first failure, as you are looking at a case where there is at least one failure. So the first failure should be considered a prior. 1 in 18000 isn't all that unlikely when integrated over all games and players.

t4nk March 30, 2018 01:16

Quote:

Originally Posted by Gordon (Post 128772)
One other thing. When I was looking for a monster to try the Wand of Annihilation on, I ran into Ariel, Queen of Air. Seeing as I knew that the wand wouldn't work on her, I cast Mana Storm instead. It failed five times in a row. With @'s current 14% chance of failure for this spell, the probability of that happening by chance is 1 in 18593. Has anyone checked the RNG used for spell failure for correlation?

This is a fun question. I searched the internet for answers and this article seems pretty good: http://www.askamathematician.com/201...swer-is-known/
I skipped the formulas, of course (maybe Nick can verify them :)). But there are also some human language examplanations and even some code. So I played a bit with it on my machine. If you cast mana storm 100 times, you'll get a streak of 5 or more failures in a row with about 1% probability. 18000 casts give you more than 50% chance of getting a bad run.
I guess there is a useful lesson here - always be prepared for the worst :)

Gordon March 30, 2018 17:07

Here is a prettied up version of a python script for calculating this that I found on a link on that site.

Code:

import argparse

argparser = argparse.ArgumentParser(description='Calculate the probability of run of n events in m trials where p is the probabilty of an event')
argparser.add_argument('-n', type=int, required=True, help='run length')
argparser.add_argument('-m', type=int, required=True, help='number of trials')
argparser.add_argument('-p', type=float, required=True, help='probability of an event')
args = argparser.parse_args()

N = args.n
M = args.m
p = args.p
q = 1-p #probability of failure

#setting up P_i (P[i] will be the probability that we see a run of length n in i flips)

P = [None for i in range(0,M+1)] #initialize list to all Nones

for i in range(0,N): #set boundary conditions, (not including P_N (r)
    P[i] = 0

P[N] =p**N #P_N (r) is now equal to p^N


#now for main recursion (using a loop here instead)
for i in range(N,M):
    P[i +1] = P[i] + (1-P[i-N]) * q * P[N]

print 'A run of',N, 'events of probability',p, 'has a chance of 1 in',1.0 / P[M], 'of occuring in',M, 'trials'


Chud April 12, 2018 22:51

The other thing people often lose track of (or don't think about in the first place) is just how many trials are really being run in a typical game. I'll bet it's a *lot* more than most people realize, so when you do the math and come up with a 1 in 18,000 chance of something, you think "come on, that'll never happen" when in fact there are so many trials that it's to be expected a lot more than you think.


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