Best start book of skald

[radinms]

Lv1 replace infusion with freeze
Lv2 replace Shroud of Golubria with Lv3 Spider form

[mps]

Don't mean to bust your... chops... as I appreciate your fresh take on crawl, but the Book of Battle is already the best spellbook in the game.

[radinms]

Skald is too weak in early game. even inferior to transmuter

Early game is one of the most difficult part,
so if you are weak in early game, it is completely meaningless.

[Berder]

Use more shroud of golubria, even recasting it in melee - it's basically +10 hp. Do you have a turn where you'd like +10 hp and shroud isn't up? Cast shroud.

[Sandman25]

Still weaker than Gl or Fi who happily wear first plate/chain they find and don't care about spells. Also more levels for spells means less levels in weapon/fighting/armour.

[Berder]

Yes, it is a weak start compared to gl/fi.

[mps]

Skald isn't a great start, I'll grant you that, but it's not worse than transmuter....

Berder is exactly correct: Skalds should get shroud and cast it constantly. After that, you don't need more spells until later in the game and physical skills/armor provide far more value until you're well into lair. I've definitely seen skalds die to magic fetishism as sandman suggests.

[onget]

As long as you are not a strong species in the early game, that will start in the hybrid background is one of the worst choice.

[bel]

Incidentally, I have seen in other places, this rule that "shroud = +10 hp". Is there some reasoning behind this or is this number drawn from the nether regions?

[Sandman25]

nether regions.

[neil]

Incidentally, I have seen in other places, this rule that "shroud = +10 hp". Is there some reasoning behind this or is this number drawn from the nether regions?

Nether regions of mathematics (namely, calc 1).

When Shroud triggers (1/3 of melee attacks, but this number isn't relevant to the "10 HP"), it either breaks (damage/(10+damage) chance) or completely prevents the damage; "damage" here is post-AC.

Let's say you are taking attacks that would do 10 HP of damage. Then shroud has a 1/2 chance of breaking and a 1/2 chance of preventing the damage with each attack where it triggers. So the expected damage prevention is 10 * (1/2 + 1/4 + 1/8 + ...) = 10: it has a 1/2 chance to last through at least one attack, a 1/4 chance to last through the second attack, etc.

Suppose instead you are taking attacks worth 100 HP of damage each. Then shroud has a 10/11 chance of breaking and a 1/11 chance of preventing the damage. So the expected damage prevention is 100 * (1/11 + 1/121 + 1/1331 + ...) = 100 * 1/10 = 10 HP.

In general, if you are taking attacks worth D HP each, shroud has a D/(10+D) chance of breaking and a 10/(10+D) chance of preventing the damage. The expected damage prevention is then:

• D * (10/(10+D) + 100/(10+D)^2 + 1000/(10+D)^3 + ...)
• = D * 10/(10+D) * ∑_i=0^∞ (10/(10+D))^i (extract one factor so the sum starts at i=0)
• = D * 10/(10+D) * 1/(1 - 10/(10+D)) (sum of a geometric series)
• = D * 10/(10+D) * (10+D)/D (simplify sum)
• = 10 (cancel out common factors)

Edit: If you are taking alternating hits of 10 and 100 HP, with the first hit being for 10, expected prevention is (10/2 + 100/22) + (10/44 + 100/484) + ... = 210/22 + 210/484 + ..., which also works out to 10. Probably you could prove that the expected prevention is 10 for any sequence of hits (ignoring rounding), but I'm too lazy at the moment.

Edit: This is before DD damage shaving, so with DD it is better against big attacks than small ones. In the limit, a bat hitting for 1HP will eventually break the shroud (1/11 chance each time), but all the "prevented" damage would have been shaved anyway.

[mps]

Indeed, your argument generalizes more or less immediately to any bounded sequence of positive damage values.

[Siegurt]

The only problem with that analysis is that while that is the *average* amount of damage prevented, however it's also unbounded from 0 to infinity, so while it may prevent 10 damage on average, it may also prevent anything from 0 to an infinite amount of damage. A lot of times when the shortcut of "It's just 10 more hps" is said, new users interpret that to mean it's *always* 10 hps instead of an *average* of 10 hps.

I actually personally think it would be a more balanced and better spell if it was actually a set amount of hps every time you cast it, where a random number out of it's pool was subtracted from both the damage done and it's pool, and it broke when it's pool hit 0, and it's pool was determined by spell power (Starting at say, 5 hps and reaching as high as say 15ish hps) But that might just be me.

[Sandman25]

I would prefer the spell removed (if it cannot be changed to work like RMsl). Casting it for every battle is annoying and it is interesting only early game when you should choose between this spell and other spells like Song of Slaying or Infusion due to low MP.

[KoboldLord]

I would prefer the spell removed (if it cannot be changed to work like RMsl). Casting it for every battle is annoying and it is interesting only early game when you should choose between this spell and other spells like Song of Slaying or Infusion due to low MP.

I would like all or most buffs to be changed to work more like RMsl, just because casting them is almost invariably pointless busywork. More specifically, I'd like buffs to work more like demonspawn icemail from their ice facet, which collapses under certain circumstances but slowly restores itself when that circumstance is not currently active. There's no need to require the player to enter an explicit command to apply the bonus the player has already paid for in xp and spell slots. In-battle re-casting would be functionally removed, but that's a corner case that is hardly ever relevant in fights that are actually dangerous anyway.

[Berder]

If you think shroud could be replaced by a passive buff that doesn't recast itself during combat, you don't understand the full potential of the spell. Shroud is one of the spells you actually do frequently want to recast in the middle of combat. It's +10 HP. Any combat turn where you would be helped by drinking a potion of +10 HP -2 MP, you should cast shroud if it's not up. I very frequently recast it in the middle of fights throughout the game.

[Sandman25]

If you think shroud could be replaced by a passive buff that doesn't recast itself during combat, you don't understand the full potential of the spell. Shroud is one of the spells you actually do frequently want to recast in the middle of combat. It's +10 HP. Any combat turn where you would be helped by drinking a potion of +10 HP -2 MP, you should cast shroud if it's not up. I very frequently recast it in the middle of fights throughout the game.

Are you talking about pre-Temple?
I don't think it is a good idea later as the spell is expected to expire immediately when attacked by 21+ damage monsters and such monsters are common even before Lair. I mean when you are expected to get 10.5 damage per turn you should not heal 10 HP (I believe you can ignore misses here as they are irrelevant). It's fine while waiting for teleport of course.

[Berder]

If you think shroud could be replaced by a passive buff that doesn't recast itself during combat, you don't understand the full potential of the spell. Shroud is one of the spells you actually do frequently want to recast in the middle of combat. It's +10 HP. Any combat turn where you would be helped by drinking a potion of +10 HP -2 MP, you should cast shroud if it's not up. I very frequently recast it in the middle of fights throughout the game.

Are you talking about pre-Temple?
I don't think it is a good idea later as the spell is expected to expire immediately when attacked by 21+ damage monsters and such monsters are common even before Lair. I mean when you are expected to get 10.5 damage per turn you should not heal 10 HP (I believe you can ignore misses here as they are irrelevant). It's fine while waiting for teleport of course.

Throughout the game. In vaults:5 even, if I have a corridor.

If you have decent defenses and are fighting a single melee enemy at a time, you're very often taking <10 damage per turn, regardless of what part of the game you're in. It just might not seem that way because when damage happens it's 20 or 30, but in between the damage there are several turns where you take no damage so it averages out.

An easy way to estimate whether damage < 10 is: does the combat last (half your HP) / 10 turns before you are at half hp and need to do something? I think most combats do last that many turns. If you have 100 HP that's just 5 turns. With 200 HP it's 10 turns.

[Sandman25]

Oh, I missed that damage is "post-ac". Then yes, it makes more sense.

[KoboldLord]

If you think shroud could be replaced by a passive buff that doesn't recast itself during combat, you don't understand the full potential of the spell. Shroud is one of the spells you actually do frequently want to recast in the middle of combat. It's +10 HP. Any combat turn where you would be helped by drinking a potion of +10 HP -2 MP, you should cast shroud if it's not up.

If a fight is actually dangerous, I'm likely to be taking more than 10hp/turn and I want to finish that fight as soon as possible. I don't care about spreadsheet-optimizing my battles against river rats, and I do not believe the game mechanics should push me to do so.

I very frequently recast it in the middle of fights throughout the game.

And that's terrible.

The game mechanics should not be making you manually press a button to tread water. If a trade of mp for hp is intended, it should be applied directly rather than making you button-mash in a situation that is supposed to be interesting.

[Berder]

If a fight is actually dangerous, I'm likely to be taking more than 10hp/turn and I want to finish that fight as soon as possible. I don't care about spreadsheet-optimizing my battles against river rats, and I do not believe the game mechanics should push me to do so.

How about vault guards though? Or deep troll packs? There are many battles where you are taking <10hp/turn but they are still dangerous because many enemies could wear you down over time.

I don't think you're taking as much damage as you think in most fights, even some dangerous fights. One time in tiles chat we worked out that a hasted executioner vs a deep elf with average extended-game deep elf defenses, was doing <10 dam/turn. This despite the fact that such an executioner might deal 50 damage on a few lucky rolls.

I very frequently recast it in the middle of fights throughout the game.

And that's terrible.

The game mechanics should not be making you manually press a button to tread water. If a trade of mp for hp is intended, it should be applied directly rather than making you button-mash in a situation that is supposed to be interesting.

Yeah, okay, but I'm saying that if you fix this problem just by making shroud get autocast and not re-cast during combat, then that's a substantial nerf to shroud. It should recast itself within like 3 turns of it going down, if you want to maintain the balance.

[CanOfWorms]

Probably you could prove that the expected prevention is 10 for any sequence of hits (ignoring rounding), but I'm too lazy at the moment.

A non-rigourous proof: Let X be the expected amount of damage a shroud blocks. Then X satisfies

X = 10/(10+D)*(D+Y)

where Y is the expected amount of damage a shroud blocks after blocking the first hit (which deals D damage for some D). Of course the first hit doesn't affect the chances of future blocks, so Y is actually X, i.e.

X = 10/(10+D)*(D+X)

If you solve for X you get X = 10. Of course this assumes a shroud doesn't eventually unravel o its own, since if it did then the expected amount of damage a shroud blocks decreases after it blocks a hit.

[Berder]

Quiz: if you're fighting a death yak with 10 AC, 10 EV, how much damage are you taking per turn on average?

Spoiler: show

7-9 damage, depending on GDR. Recast that shroud! This despite the fact that those are awful defenses for fighting death yaks, and death yaks are pretty hard melee hitters.

[bel]

This ignores 3 things:

1. Averages are not the thing which matter in getting you killed, spikes in damage are.
2. Shroud has a higher chance to collapse when you get hit harder, which tends in the same direction.
3. You should test with EV close to 0, because evaded attacks are not relevant for calculating average.

I am actually not sure whether these things will have enough weight to outweigh the advantage.

I tested with AC 10 EV 0 against a death yak, it was about 10.8 avg. With AC 20 EV 0, it was about 7.8 avg. Death Yak accuracy was close to 100%.

The correct way to test is to do a lot of automated fights which recast shroud whenever it falls apart. And then count the number of deaths.

[Berder]

1. Averages are not the thing which matter in getting you killed, spikes in damage are.

Spikes matter, sure, but the average case also matters. If your average case is good then you're less likely to drop into low HP where a damage spike could finish you.

3. You should test with EV close to 0, because evaded attacks are not relevant for calculating average.

No - evaded attacks are relevant. All you need to know is that shroud gives the equivalent of +10 HP, and you're spending a turn to cast it, therefore you don't want to be taking more than 10 HP of damage per turn on average or it's not worth it. Evasion reduces the average amount of damage per turn you're taking, so it counts.

There is one other factor that would tweak the "shroud = +10 hp" idea, namely, that the shroud might fail to trigger before you die, as it only has a 1/3 chance to trigger per attack. So shroud is worth less than 10 HP if you're already at low HP. It's difficult to quantify this exactly since it depends on the damage dealt.

Suppose that you're at 30 HP and the enemy deals 30 damage and you have shroud up. The chance of shroud working is 1/9 (1/3 chance to trigger, 1/3 chance to block the damage if it triggers). So the average amount of HP shroud saves in this case is 30/9 = 3.3, quite low.

Alternatively, suppose that you're at 30 HP and the enemy is poking you for 1 HP every turn. A quick Python simulation shows this saves you 7.35 HP on average before 30 damage is dealt.

So, shroud is worth closer to 10 if you have higher HP and the enemy isn't hitting you as hard.

[bel]

1. Averages are not the thing which matter in getting you killed, spikes in damage are.

Spikes matter, sure, but the average case also matters. If your average case is good then you're less likely to drop into low HP where a damage spike could finish you.

Fine, so we agree that spikes matter. Your average case analysis then doesn't take this into account.

3. You should test with EV close to 0, because evaded attacks are not relevant for calculating average.

No - evaded attacks are relevant. All you need to know is that shroud gives the equivalent of +10 HP, and you're spending a turn to cast it, therefore you don't want to be taking more than 10 HP of damage per turn on average or it's not worth it. Evasion reduces the average amount of damage per turn you're taking, so it counts.

The point is that evading attack reduces the average damage, but in this case it is irrelevant whether you have a shroud or not, because evaded attacks are not blocked by a shroud. To see this, consider the case where you have some monster doing 1000 damage, but it only has accuracy 1%. The average damage is 10, but shroud is useless here.

[Berder]

The point is that evading attack reduces the average damage, but in this case it is irrelevant whether you have a shroud or not, because evaded attacks are not blocked by a shroud. To see this, consider the case where you have some monster doing 1000 damage, but it only has accuracy 1%. The average damage is 10, but shroud is useless here.

No, this is mixing up the ideas. It doesn't matter that evaded attacks are not blocked by a shroud. In your example shroud is still worth 10 HP (approximately - I edited my post above with some refinement of that idea).

Suppose you have a potion of +10 HP that you can drink this turn or else it vanishes. Do you drink it? That depends on whether you're getting damaged faster than 10 HP per turn or not, taking evasion into account. Shroud is just like this.

[bel]

I am arguing that average is fundamentally the wrong way to think about this. To see this, suppose you are adjacent to the monster I described above (1000 damage, 1% accuracy). Suppose you can 2-shot the monster. Do you cast shroud, or do you try to kill it immediately?

If you cast the shroud, and then try to kill it, you allow it 2 shots at you, so your death chance is roughly 2%.
If you simply try to kill it, you allow it only 1 shot at you, so your death chance is 1%.

By casting shroud, you have doubled your death chance.

[Berder]

I am arguing that average is fundamentally the wrong way to think about this. To see this, suppose you are adjacent to the monster I described above (1000 damage, 1% accuracy). Suppose you can 2-shot the monster. Do you cast shroud, or do you try to kill it immediately?

If you cast the shroud, and then try to kill it, you allow it 2 shots at you, so your death chance is roughly 2%.
If you simply try to kill it, you allow it only 1 shot at you, so your death chance is 1%.

By casting shroud, you have doubled your death chance.

The shroud = 10 hp notion only works if the enemy deals sufficiently low damage relative to your current HP, on the hits that it deals nonzero damage. There need to be enough hits for the shroud to do its work. Your example with 1000 damage is not realistic. You shouldn't use shroud when you're one hit from death.
..
If the enemy was dealing 1000 damage (with 1% accuracy) and you have 100,000 HP, then shroud would be worth 10 HP almost exactly.

[bel]

Indeed it is not realistic, it was a thought experiment.

I agree that shroud is valuable when the enemy damage is low compared to your current HP. But these are the situations of the least value, because you are in little danger of dying.

[Berder]

I ran a simulation to determine effectiveness of shroud. The columns are a given starting HP total, and the rows are a given amount of damage. The entries show how many HP shroud saves on average. e.g. the entry for 90 HP, 3 damage, shows what happens if you're being repeatedly hit for exactly 3 damage, and have 90 HP initially. Shroud would save 9.6 HP on average in that case, before the shroud breaks or you run out of HP.

  Code:

Dam \ HP      10    20    30    40    50    60    70    80    90   100
1            3.6   5.8   7.5   8.3   9.0   9.3   9.6   9.8   9.9  10.1
2            3.3   5.4   7.0   7.9   8.8   9.0   9.3   9.6   9.7   9.7
3            3.0   5.2   6.5   7.6   8.4   8.8   9.3   9.5   9.7   9.6
4            2.8   4.9   6.3   7.4   8.2   8.9   9.0   9.3   9.7   9.8
5            2.6   4.6   6.1   6.9   7.9   8.6   8.9   9.1   9.4   9.5
6            2.4   4.3   5.8   6.9   7.6   8.1   8.5   9.1   9.4   9.5
7            2.3   4.1   5.6   6.4   7.5   8.0   8.7   8.8   9.0   9.3
8            2.2   3.9   5.2   6.3   7.1   7.9   8.3   8.5   8.9   9.3
9            2.1   3.7   5.0   6.1   6.9   7.6   8.2   8.4   8.7   9.0
10           2.0   3.6   4.9   5.8   6.9   7.4   8.0   8.4   8.6   8.9
11           1.8   3.4   4.7   5.5   6.3   7.2   7.7   8.3   8.4   8.8
12           1.7   3.3   4.4   5.6   6.2   7.0   7.8   8.3   8.2   8.5
13           1.7   3.2   4.3   5.4   6.1   6.9   7.3   7.7   8.3   8.5
14           1.5   3.1   4.3   5.1   6.1   6.5   7.2   7.9   8.2   8.6
15           1.6   2.9   4.1   5.2   5.6   6.4   7.0   7.4   8.0   8.3
16           1.5   2.9   3.8   4.9   5.6   6.4   7.0   7.1   7.6   8.2
17           1.4   2.8   3.7   4.7   5.7   6.0   6.6   7.3   7.6   7.9
18           1.3   2.6   3.7   4.6   5.4   6.0   6.5   7.3   7.5   7.9
19           1.3   2.5   3.6   4.3   5.1   5.9   6.5   7.0   7.5   7.9
20           1.2   2.4   3.2   4.5   5.1   5.8   6.2   6.8   7.4   7.7
21           1.2   2.6   3.5   4.3   5.0   5.6   6.2   6.7   7.0   7.4
22           1.2   2.3   3.2   3.9   4.9   5.5   6.0   6.6   7.2   7.5
23           1.0   2.2   3.3   3.9   4.9   5.2   6.0   6.4   6.5   7.1
24           1.1   2.2   2.9   3.8   4.6   5.5   5.9   6.3   6.7   7.2
25           1.0   2.0   3.0   3.9   4.6   5.1   5.5   6.4   6.5   6.9
26           1.0   2.0   3.0   3.7   4.4   5.2   5.5   5.9   6.5   6.8
27           1.0   2.0   2.8   3.4   4.3   4.9   5.6   6.1   6.6   6.9
28           0.9   1.8   2.9   3.4   4.3   4.9   5.2   5.9   6.5   6.6
29           1.0   1.8   2.8   3.5   4.1   4.8   5.2   5.7   6.2   6.5
30           0.9   1.8   2.7   3.3   4.1   4.6   5.2   5.8   6.4   6.5
31           0.9   1.7   2.6   3.3   4.0   4.7   5.1   5.6   6.1   6.1
32           0.9   1.8   2.5   3.2   3.9   4.5   5.1   5.5   5.9   6.2
33           0.8   1.7   2.5   3.3   3.9   4.3   5.1   5.4   6.0   6.0
34           0.8   1.7   2.4   3.0   3.8   4.3   4.8   5.3   5.8   6.3
35           0.8   1.6   2.5   3.1   3.6   4.4   4.5   5.4   5.4   5.9
36           0.7   1.6   2.4   3.0   3.7   3.9   4.7   5.2   5.2   6.1
37           0.8   1.6   2.1   2.9   3.5   4.1   4.7   4.9   5.3   5.9
38           0.8   1.5   2.4   3.0   3.5   4.0   4.4   4.8   5.4   5.9
39           0.7   1.5   2.2   2.9   3.4   3.8   4.4   4.7   5.5   5.5


Perhaps the most significant finding of this table is that if you have 10 HP - like a level 1 character - shroud is worth about 3 HP, not 10. If you have 20 HP it's worth 5 HP, not 10.

[neil]

I ran a simulation to determine effectiveness of shroud.

Did you take into account that shroud triggers on only 1/3 of damaging hits? That would shift the total down even further when the dam/HP ratio is high.

[Berder]

I ran a simulation to determine effectiveness of shroud.

Did you take into account that shroud triggers on only 1/3 of damaging hits? That would shift the total down even further when the dam/HP ratio is high.

Yes, I accounted for that.

  Code:

# calculate whether shroud of golubria triggers for a given dam
# 0 = doesn't trigger
# 1 = blocks damage
# -1 = fails
def shroud(dam):
     if random.randint(1,3) != 1:
          return 0
     if random.randint(1, dam+10) <= 10:
          return 1
     return -1

# simulate being dealt dam damage repeatedly, from starting hp of hp
# return the amount of damage prevented by shroud before the shroud fails or you die
def shroudsim(hp,dam):
     shroudpower = 0
     tdam = 0
     while tdam < hp:
             s = shroud(dam)
             if s == -1:
                     return shroudpower
             if s == 1:
                     shroudpower += min(dam, hp - tdam)
             else:
                     tdam += dam
     return shroudpower

def shroudtable():
     print "Dam \ HP".ljust(10),
     for hp in xrange(10,110,10):
          print str(hp).rjust(5),
     print
     for dam in xrange(1,40,1):
          print str(dam).ljust(10),
          for hp in xrange(10,110,10):
               sim = sum([shroudsim(hp,dam) for x in xrange(10000)]) / 10000.
               print ("%.1f" % sim).rjust(5),
          print


[Sandman25]

So shroud is less effective vs high damage attacks, am I reading it right?

[Berder]

Yes, and more effective if you have high HP.

An anecdote on the late game usefulness of Shroud: with a couple different characters I have been in long corridor fights in vaults:5 where I cast and recast shroud many times over the course of the combat - maybe 5 or 6 times in one combat. I was also recasting regen. My HP stayed in a safe area, but not quite full. In this particular case, because each cast of shroud actually did its job long enough to fail, each cast of shroud was actually worth about the full 10 HP, and casting it 5 or 6 times means at the end of the fight I had 50 or 60 HP more than if I hadn't used shroud. If I hadn't used shroud then I would have been 50 or 60 HP lower, and would have been in a dangerous position, being overwhelmed by the horde.

[ThreeInvisibleDucks]

What about Infusion vs Shroud in the early game? When you have a tiny amount of MP do you prefer to cast Infusion or Shroud of Golubria? Both would be "optimal" if you never failed to cast a spell or ran out of MP to help your infusion attacks, but MP is a scarce resource early in the game.

I used to prefer Shroud, but it seems that I'm almost always casting Infusion nowadays. It seems to work better, but I can't put my finger on exactly why it seems to be the case.

[Siegurt]

Yes, and more effective if you have high HP.

An anecdote on the late game usefulness of Shroud: with a couple different characters I have been in long corridor fights in vaults:5 where I cast and recast shroud many times over the course of the combat - maybe 5 or 6 times in one combat. I was also recasting regen. My HP stayed in a safe area, but not quite full. In this particular case, because each cast of shroud actually did its job long enough to fail, each cast of shroud was actually worth about the full 10 HP, and casting it 5 or 6 times means at the end of the fight I had 50 or 60 HP more than if I hadn't used shroud. If I hadn't used shroud then I would have been 50 or 60 HP lower, and would have been in a dangerous position, being overwhelmed by the horde.

This fails to account for the less damage you would've taken by doing damage with those 50 or 60 aut instead, which would depress the numbers slightly (by how much depends on how much damage you do and how much the creature does to you as well as how many hps it has). Also it's rarely *actually* as high as 10 hps per cast, because you can die, and the duration can expire.

The more damage that the creature does, the more likely it is to expire or for you to die before triggering for it's full average of 10 hps, because it takes longer and longer for that random chance to block a shot, against a hard-hitting creature, you may burn through it's entire duration or die before it blocks even 1 attack.

Note that duration is something that you also didn't happen to simulate, but certainly makes a significant difference, if it only has a 1 in 10 chance of working, it's very very likely that it's duration (Which maxes at 50 aut) will expire before it has a chance to block 10 damage worth of attacks.