melee hit probability

[mushroom patch]

In vanilla, damage computations are either dominated by a constant term, dominated by a sum of several dice, or they're so small that the difference is not that significant (e.g. level 1-10 characters). Vanilla angband does not have hugely varying damage numbers or high miss rates.

Randomized monster behavior is another issue and it's also not good, but it's somewhat made up for in the case you raise by the deterministic nature of the damage dealt. The difference is that if you're complaining about getting breathed on by a dragon or a drolem, it's absolutely your fault, whereas in certain other roguelikes, you may have no realistic alternative to accepting melee engagements in which you will win easily 95% of the time but get hit for crazy damage the other 5%, in spite of no tactical difference between the fights. This is the situation that angband's combat system avoids by using lots of dice, big constant terms in damage calculations, multiple blows per round for the player and monsters, and fairly high hit rates.

I should also say, any system that uses a difference of random numbers, like (small number)d(weapon number) - 1d(AC) with a cutoff at zero will tend to exhibit the same kinds of issues. Damage distributions heavily concentrated at the low end with long tails produce broken combat (e.g. not suitable for competition).

[TJS]

I should also say, any system that uses a difference of random numbers, like (small number)d(weapon number) - 1d(AC) with a cutoff at zero will tend to exhibit the same kinds of issues. Damage distributions heavily concentrated at the low end with long tails produce broken combat (e.g. not suitable for competition).

I don't quite understand how you've come to the conclusion that the Sil system causes more outliers.

Angband system:

Binary chance of hitting/missing causing (x)d(y) damage

Sil system:

Binary chance of hitting/missing causing (x)d(y) - (x2)d(y2) damage
where x2 and y2 are determined by armour (each item has a different set of dice to reduce damage, from 1d1 for gloves to 2d5 for heavier armour)

If anything the Sil version has the binary hit/miss nature softened by the reduction in damage.

Also I don't see how an ancient multi-hued dragon breathing poison can't be treated as an outlier in the same way. They breath or cast a spell 1 time in 5 and there are 5 elements and 3 spells to choose from, so you'd expect one to breath poison around 1 in 40 turns or so. If you can defeat them in 5-6 turns then it would be quite an outlier to be hit by a deadly poison breath before you reduce it's health enough to survive it.

If you're saying that it is the players fault to die to a poison breath because the risks were there however small, then why can't the same logic be applied to melee attacks?

[Derakon]

Angband's approach has a pretty smooth curve specifically because there's so many attacks and each one tends to mostly do damage based on your +to-dam, not your damage dice. The distribution of (2d6 - 1d8) is pretty wide compared to the distribution of, say, (80 + 8d6).

As for surprise breaths, those are indeed demonstrably a problem with Angband.

[mushroom patch]

The difference between poison breath and melee damage is that melee engagements are mundane, unavoidable situations. Nevertheless, the outcome can be made to depend on non-tactical factors (dice rolls). If you've played the game enough, you also know when a poison breath attack might be coming and you know when it could be instant death. The relevant information is available to the player: There's a monster that can breath poison for high damage in line of sight and he knows whether it will kill him or not if it breathes. By contrast, with high variance melee, you're stuck entering into unknowable situations where you could get hit for huge damage or no damage.

As for the Sil system, my impression is that armor typically has one large die and a few smaller ones, usually 1d1. This distribution has a lot of variance. When you subtract that from something like 2d8, you get a distribution with a spike near zero, concentrated at low damage values, with a long tail of much larger damage hits. The tail is the problem.

In the example Derakon raises, a Sil situation with 2d6 damage dice and 1d8 armor dice, you can look at the numbers explicitly:

http://anydice.com/program/5438

The average value is about 3, max is 11, 95 percentile is 9 or so. (You can look at the numbers on the site.) But sil isn't the worst offender. Crawl is what I'm really thinking about re: wacky damage formulas. There you see stuff like 1d30 - 1d27 with a separate to-hit roll that makes the spike at zero huge. Frequently, the standard deviation is higher than the mean (!). Here's that (damage roll only):

http://anydice.com/program/5439

[TJS]

Angband's approach has a pretty smooth curve specifically because there's so many attacks and each one tends to mostly do damage based on your +to-dam, not your damage dice. The distribution of (2d6 - 1d8) is pretty wide compared to the distribution of, say, (80 + 8d6).

The to-dam modifier is just for the player though, so when talking about damage received it shouldn't be relevant.

At the start of the game the player uses an unenchanted weapon and does less blows so the damage distribution is wider at the start than at the end of the game. I wonder if the high to-dam values weren't a design choice but a general number inflation as more powerful monsters and equipment were added.

The slay mechanic seems that it was based on doing damage by dice rolls rather than -to-dam values.

As for surprise breaths, those are indeed demonstrably a problem with Angband.

Yes whether a monster breaths or not does seem to be rather random. The problem is worse with monsters with a wide range of breaths to choose from.

[TJS]

The difference between poison breath and melee damage is that melee engagements are mundane, unavoidable situations.

Not sure what you mean here as melee is by far the easiest engagements to avoid in the game. When you have phase door, teleportation or teleport other then you can remove/avoid the danger when they are still safely the other side of the room. Breathers just need to be in your line of sight to hit you randomly for a massive breath.

Nevertheless, the outcome can be made to depend on non-tactical factors (dice rolls). If you've played the game enough, you also know when a poison breath attack might be coming and you know when it could be instant death. The relevant information is available to the player: There's a monster that can breath poison for high damage in line of sight and he knows whether it will kill him or not if it breathes. By contrast, with high variance melee, you're stuck entering into unknowable situations where you could get hit for huge damage or no damage.

Learning which monsters can hit for large damage seems similar to learning which monsters can breath for high damage to me (you need to do that currently for grand master mystics who will knock you out in melee for example). I can't quite understand the distinction you are making between the two. Although I don't believe my proposal would cause more variance in melee anyway.

As for the Sil system, my impression is that armor typically has one large die and a few smaller ones, usually 1d1.

Not really, the highest one dice roll is 1d4 I believe for leather armour with 1d1, 1d2, 1d3 normally for smaller items (gloves, boots etc.) and more dice for higher level armour (eg. 2d5).

You typically have armour that can absorb between 4-7 damage early on in the game.

This distribution has a lot of variance. When you subtract that from something like 2d8, you get a distribution with a spike near zero, concentrated at low damage values, with a long tail of much larger damage hits. The tail is the problem.

You only get a longer tail if you assume that weapon damage dice will have to rise to go with armour absorption. But because absorption replaces part of the current AC (which causes hits to miss completely) you will hit more often and have some of that absorbed by armour. Overall you will do similar damage but the curve is smoothed out somewhat.

In the example Derakon raises, a Sil situation with 2d6 damage dice and 1d8 armor dice, you can look at the numbers explicitly:

http://anydice.com/program/5438

The average value is about 3, max is 11, 95 percentile is 9 or so. (You can look at the numbers on the site.)

You need to model the same attack dice roll but factor in that it is less likely to hit so does 0 damage a lot of the time. The max goes up to 12 with no absorption and the average value is still around 3 because of attacks missing completely meaning there is actually even more variance with the current system.

I don't think 1d8 would be good dice for armour anyway, more smaller dice would give better results I think.

But sil isn't the worst offender. Crawl is what I'm really thinking about re: wacky damage formulas. There you see stuff like 1d30 - 1d27 with a separate to-hit roll that makes the spike at zero huge. Frequently, the standard deviation is higher than the mean (!). Here's that (damage roll only):

http://anydice.com/program/5439

I don't much like the sound of the Crawl system to be honest.

[Derakon]

At the start of the game the player uses an unenchanted weapon and does less blows so the damage distribution is wider at the start than at the end of the game. I wonder if the high to-dam values weren't a design choice but a general number inflation as more powerful monsters and equipment were added.

I wouldn't be remotely surprised if there wasn't any real guiding principle behind a lot of the design "decisions" in Angband. However, the system does, for the most part, work well as it is implemented. It's opaque and mechanically kind of silly (hulking warriors using the tiniest daggers they can find with the biggest possible enchantments, for example), but it's pretty well-balanced and has a fairly smooth curve.

[mushroom patch]

The difference is that in almost all cases, you can find out whether something is safe to melee in vanilla angband, from a purely damage standpoint, by trying it and bailing if you have to. Whether something is safe to melee is a constant across different games and scenarios within a game in angband, whereas if you had a different system, like crawl's, whether something is safe to melee is not constant across different instances of the same match up. Even if a typical engagement is non-threatening, there may still be unlikely scenarios in which you die or come dangerously close purely as a matter of chance.

If you think Derakon's Sil dice scenario is unlikely, you should address your comments about it to him. I suspect you can see similar phenomena if you try a more Sil-typical dice combination on the site I showed you, but I agree that if you have a large number of dice with a small number of sides, you get better distributions (this was one of my original points and it is the reason incoming damage in vanilla angband works out smoothly, at least at higher levels). On the other hand, whenever your average reduction exceeds the average damage roll, the situation again begins to degenerate. I really don't care about Sil, specifically. I don't play it and until there are online facilities with spectating and scores available for it, I won't play it.

You're right that my simulation does not take misses into account and you're correct to say that's an important omission. Factoring misses into the distribution tends to make the situation I describe with outliers even worse. The difficulty is that I don't know how hit rolls work precisely in Sil or Crawl, so I can't give you a good simulation. If you know how they work, in either case, I'd be interested to see a more realistic simulation on anydice.

To summarize: Combat systems should be such that a small number of rounds accurately reflect typical combat against a given opponent, from the standpoint of average damage per round, almost surely. This is a question about variance of damage per round. Using damage formulas with large dice, differences of dice with similar averages or where the subtracted part has average greater than the damage part, or having high miss rates are all at odds with this principle. Using formulas with large constant terms or large numbers of small dice help, as do multiple blows per round. (Crawl has the unhappy combination of single, big dice, differences of such dice, high miss rates, and usually one blow per round.)

[debo]

I don't play it and until there are online facilities with spectating and scores available for it, I won't play it.

I'm curious, since you seem to not like crawl either -- which roguelike has online play+spectating, and isn't crawl? (Quite a few people do stream their Sil games on termcast.org.)

There are a lot of people who dislike games with the combat 'feel' you described, and I think for good reason. I don't mind it (although I prefer the more ridiculous variants to vanilla), but I do think it's rather more odd than e.g. the Sil style. I don't often get into a fight with someone, and after being punched in the face three times think 'wow if this guy punches me in the face 14 more times, I'm going to be in serious trouble.'

[Timo Pietilä]

As for surprise breaths, those are indeed demonstrably a problem with Angband.

Problem with angband or problem with newbies not learning the danger fast enough?

I don't see a problem with deadliness of breath weapons. If you take out the randomness, you turn game into boring repetition with always the same outcome.

[quarague]

I don't often get into a fight with someone, and after being punched in the face three times think 'wow if this guy punches me in the face 14 more times, I'm going to be in serious trouble.'

First, serious lol. But to the discussion in point: real life combat is never a good model for fun to play computer game combat. Real life combat almost always is highly unpredictable, has massive variance and tends to be a series of extremely biased events. If you send 12 tanks against 10 tanks in a computer game, the 12 will usually win but suffer heavy casualties, in real life once side will wipe out the other with minimal losses, but the winner depends on a number of minor random effects and is rather unpredictable.
For Angband, combat that has a random component but is fairly predictable due to small variance makes good gameplay because it is predictable. You can make strategic decision because you have a pretty good feel beforehand what the outcome would be. People make combat decisions in real life (on a small or large scale) because they believe they can predict the outcome but they can't. If both sides would predict correctly they would come to the same result and one side would back out of the fight beforehand.

[Derakon]

I'm curious, since you seem to not like crawl either -- which roguelike has online play+spectating, and isn't crawl? (Quite a few people do stream their Sil games on termcast.org.)

I know NetHack has online servers with spectating, and I think DoomRL does now too, though they're relatively recent.

Problem with angband or problem with newbies not learning the danger fast enough?

The latter, or more generally, players not being aware of how much danger they're in. Should I be punished for forgetting that, say, the Phoenix can breathe light? Say I have all my other resists covered, but I forget that one because to be fair it's kind of unintuitive -- do I deserve that instadeath?

I mean, obviously Angband's current gameplay balance relies heavily on monsters that can do massive amounts of damage in a single turn, which then means that plenty of characters who can't take massive amounts of damage are in danger of instadeath. But should that danger be transparent, or opaque? Since it is by nature an instadeath, "use Rods of Probing" doesn't really sit well with me -- that takes a turn, which might well be one turn too many.

[mushroom patch]

I'm curious, since you seem to not like crawl either -- which roguelike has online play+spectating, and isn't crawl? (Quite a few people do stream their Sil games on termcast.org.)

I actually do like crawl, I just don't like its combat system. It does a lot of things right, but not melee unfortunately. As for online play, nethack also has a well-developed scene, though I don't play nethack.

That's interesting about Sil on termcast, didn't know. Sil would still benefit from having a real public telnet scene.

late edit: Also, re:

There are a lot of people who dislike games with the combat 'feel' you described, and I think for good reason. I don't mind it (although I prefer the more ridiculous variants to vanilla), but I do think it's rather more odd than e.g. the Sil style. I don't often get into a fight with someone, and after being punched in the face three times think 'wow if this guy punches me in the face 14 more times, I'm going to be in serious trouble.'

Realism is a poor guide to game design. If roguelike combat were as involved as actual sword (or fist) fighting, then I could agree with this assessment. And in games where you have more action oriented combat, e.g. fps's, where there is a lot more feedback about what's happening when your opponent misses or causes you little damage, it's a totally reasonable position. But I don't think people really think high variance, high miss rate combat in roguelikes is a good idea. They, like me, just like certain games in spite of it. When you ask someone what they think about something they like, they tend to say they like it. Some even get defensive if you start to get at aspects they realize they don't like.

[Timo Pietilä]

The latter, or more generally, players not being aware of how much danger they're in. Should I be punished for forgetting that, say, the Phoenix can breathe light? Say I have all my other resists covered, but I forget that one because to be fair it's kind of unintuitive -- do I deserve that instadeath?

I mean, obviously Angband's current gameplay balance relies heavily on monsters that can do massive amounts of damage in a single turn, which then means that plenty of characters who can't take massive amounts of damage are in danger of instadeath. But should that danger be transparent, or opaque? Since it is by nature an instadeath, "use Rods of Probing" doesn't really sit well with me -- that takes a turn, which might well be one turn too many.

Generally speaking, I agree, I just don't know what to do about that. Probing is slow and monster descriptions are not that describing.

Maybe monsters should have "rune-based ID" as well, so that you could tell what they can or might be able to do before actually encountering that something they do.

[Nick]

Maybe monsters should have "rune-based ID" as well, so that you could tell what they can or might be able to do before actually encountering that something they do.

That's an interesting idea.