Monte Carlo Level Simulation

[ewert]

That's a second order effect. I doubt it is noticeable. The way to think of it is to assume you pick the base, and then ask for the probability that after you create one artifact, if you tried again the very next try would produce the other one. Even if there are 20 more such pairs in randarts vs standarts, unless the chances to produce the randarts are over 1/20 on a single try [which seems excessive] that still comes to less than 1 a game on average.

You guys complaining about too many randarts before the last change may have forgotten how many standarts are typically produced.

Okay talking probabilities and statistics in a foreign language gets hard, but I think we are talking slightly different here.

If we have 20 base types, of which all have 1 artifact, and game creates x number of each base type (approximately), then compare to 20 base types of which 10 have two artifacts ... I think need to check up on the artifact creation code, if it is like I recall: "item good, check for artifact chance, pass, check to see if available artifact, check to pass artifact creation roll", then there would definitely be a noticeable difference in the 10x2 case versus 20x1. Since the x2 creates no extra chance for artifact creation until an artifact of that base type has been created, but the "blank" base types halve artifact creation chance from the get-go ...

Depends on code, that is what I am saying. If the code is like I recall, then a quickie thought process about the probabilities gives me a result of "yes it could make a noticeable difference".

[PowerDiver]

What I wrote was pretty accurate. Another thing you are missing is the number of standart daggers and gauntlets. The most important term is the number of pairs of artifacts with the same base item, which is quadratic in artifacts per base item. It would not be shocking to me if the effect is in the direction opposite to what you are expecting.

[Estie]

...
You guys complaining about too many randarts before the last change may have forgotten how many standarts are typically produced.

That is very likely, given that my last standart game was back in...well, some version before 1.3.x

My "complaint" was based purely on what I felt while playing to be too much. Too many items turning out to be artifacts diminishes the special feeling (hah!), too few and the game becomes a grindy drag. I am aware that this is highly subjective.

If equivalence of standart and randart game is wanted, then, assuming the property algorithm is balanced, fizzix´s numbers must be brought to match. Any conjectures about item types affecting generation chance are moot: the guy who finds 60 artifacts is worse off than the one who finds 70. Noticably so.

[fizzix]

If equivalence of standart and randart game is wanted.

This is a big if. Consider the following possibilities.

1. randarts are considered a challenge option at birth. You have an unknown set of artifacts, and you are slightly less likely to find them.

2. to equalize difficulties, randarts need to be slightly more common than standarts. Because randarts are unbalanced, you may need more of them to come up with a suitable endgame kit.

3. to equalize difficulties, randarts need to be less common. This is because you are more likely to find a very powerful randart in the early-middle game than in a standart game. (again due to the lack of balance.)

I have no opinions anymore on which of the three is accurate, true, or should be aimed for.

[Derakon]

I think it's reasonable to want to get a similar number of randarts as standarts in a given game. However, it's also reasonable to want a challenge game where artifacts as a whole are less common, though not eliminated outright. Basically, a slider that ranges from 0 (no artifacts) to 5 (standard distribution) to 10 (artifacts are very common).

[ewert]

What I wrote was pretty accurate. Another thing you are missing is the number of standart daggers and gauntlets. The most important term is the number of pairs of artifacts with the same base item, which is quadratic in artifacts per base item. It would not be shocking to me if the effect is in the direction opposite to what you are expecting.

God I can talk medical English, but math English is ... gah. =P

I'll grant you the daggers, but still isn't there like atleast one artifact of almost each base type in standarts? I guess the first issue would be to define the spread of artifacts in standart vs. the probabilities of # of "blanks" in random sets. The artifact number is low enough that it won't get balanced well enough compared to the manually assigned standart set, as far as I would hazard a guess. Meaning I'd haphazard a guess that randart sets have much more blank "base" spots on average.

Anyways, a more even spread of artifacts per base items would result in an average higher total amount of artifacts found in a collection of enough samples of "gamesims", I can't really see how on earth one could get to the opposite resolution in any math based view of the issue ... Granted, haven't done high math in a dozen years or so really. :P But still.

PS. Is the sim removing a found artifact from further "finds"? I think I read earlier in the thread something about that not being done yet in the sim at that point.

[PowerDiver]

I think you are missing something basic. Suppose you have two artifacts and two base types. Say each base type is 50% and each artifact has rarity 10%. Then if both artifacts are in the same slot, you have a 50% chance to choose that slot, then whatever chance to decide to try for an artifact [depending on DROP_GOOD etc], then a 19% chance to generate an artifact [.1 + .1 - .1*.1 since each possible matching artifact type is checked until one matches]. If one artifact of each base type, whatever chance for artifact, then a 10% chance. So you are comparing proportionally 9.5% to 10.0% until one is created. After one is created, the time to generate the second artifact would be the same in either scenario.

[fizzix]

PS. Is the sim removing a found artifact from further "finds"? I think I read earlier in the thread something about that not being done yet in the sim at that point.

Yes, it does this now. There are currently two supported modes, that I've termed Diving and Clearing. Diving mode starts each level assuming no artifacts are found and no uniques are killed. This was the first sim I made, and is what you are referring to. Clearing mode assumes the player clears every level, killing all uniques and picking up all items. (yet no monsters are spawned or summoned) Killed uniques stay dead, and found artifacts are removed from the set. The player clears all 100 levels, then the artifacts are 'uncreated' and the uniques are 'revived' and the sim starts again at level 0. The artifact totals are provided from Clearing sims.

Diving mode is accurate for levels < 50 for a fairly adept player that will kill few uniques and discover few artifacts. After level 50, it more often does stupid things like create the phial several times per level, so is less trustworthy in this region. Clearing mode should be fairly accurate for newer players who progress slower for lack of knowledge, and play styles that spend more time on levels.

Of course, if anyone has more suggestions over features to add, I'll be glad to put them in. The next thing I will do is get standard deviations on the number of artifacts you find, and the levels that you are first likely to find certain items.

[ewert]

I think you are missing something basic. Suppose you have two artifacts and two base types. Say each base type is 50% and each artifact has rarity 10%. Then if both artifacts are in the same slot, you have a 50% chance to choose that slot, then whatever chance to decide to try for an artifact [depending on DROP_GOOD etc], then a 19% chance to generate an artifact [.1 + .1 - .1*.1 since each possible matching artifact type is checked until one matches]. If one artifact of each base type, whatever chance for artifact, then a 10% chance. So you are comparing proportionally 9.5% to 10.0% until one is created. After one is created, the time to generate the second artifact would be the same in either scenario.

Will have to check the creation code, since I am working on the assumption (yeayea ) that it is not a cumulative or multiplive chance to go from base to artifact based on how many artifacts are in that base, but just _a_ chance to go from base to _an_ artifact.

Thus no matter how many artifacts of the base item exist, there is no extra chance increases to start the artifact creation process. Thus double/triple/multiple "slotted" artifacts reduce the overall artifact creation rate compared to an even spread.

Of course if multiple base item artifacts increase the chance to go from non-artifact to artifact-testing, then it is a near-moot point. As I said in one of the earlier posts, we ARE talking of slightly different things. Need to check the code itself for this.

[ewert]

I think you could add a "farming" option, that clears dlvl 98 for x times, where x could be set somewhere. I know I like to farm some at the end. Would give some info on that too, so the rare items can be balanced (like the superrare rods etc., so people could realistically get them if patient in the deep end).

[fizzix]

I think you could add a "farming" option, that clears dlvl 98 for x times, where x could be set somewhere. I know I like to farm some at the end. Would give some info on that too, so the rare items can be balanced (like the superrare rods etc., so people could realistically get them if patient in the deep end).

Endgame consumables and ego items do not vary to any significant quantity based on how many ego items/uniques are left. So if you want to know what your endgame consumables are like on dlevel 99, I can already give you that info with reasonable accuracy.

you have roughly an 18% chance of finding a rod of speed/healing. And a 8.6% chance if you limit yourself to non-monster drop, non-vaulted items.

You will on average find 0.81 !life or !*healing* but ~2/3 of those are from monster drops. Similarly, you will find on average 5.1 stat gain potions (not including !Chr, !Aug counts as 5 potions) about 70% of which come from monsters and 15% are found in vaults.

[ewert]

Endgame consumables and ego items do not vary to any significant quantity based on how many ego items/uniques are left. So if you want to know what your endgame consumables are like on dlevel 99, I can already give you that info with reasonable accuracy.

you have roughly an 18% chance of finding a rod of speed/healing. And a 8.6% chance if you limit yourself to non-monster drop, non-vaulted items.

You will on average find 0.81 !life or !*healing* but ~2/3 of those are from monster drops. Similarly, you will find on average 5.1 stat gain potions (not including !Chr, !Aug counts as 5 potions) about 70% of which come from monsters and 15% are found in vaults.

Thats a 0-99 clear though? I'd be more interested in the chances of high end stuff from clearing a dlvl98. Since I can't see how one could have an 18% chance to find rod of speed/healing in a single level clear ... I'd be swimming in those with most of my chars with such chances. =P

[d_m]

Thats a 0-99 clear though? I'd be more interested in the chances of high end stuff from clearing a dlvl98. Since I can't see how one could have an 18% chance to find rod of speed/healing in a single level clear ... I'd be swimming in those with most of my chars with such chances. =P

I think it assumes you kill all monsters generated. Do you completely clear dungeon level 98 a lot? (without banishment, *destruction*, etc)

[fizzix]

Thats a 0-99 clear though? I'd be more interested in the chances of high end stuff from clearing a dlvl98. Since I can't see how one could have an 18% chance to find rod of speed/healing in a single level clear ... I'd be swimming in those with most of my chars with such chances. =P

no, the stats I cited were *only* for dlevel 99.

[fizzix]

Here are some results with the mean and standard deviation for the first level you are likely to find equipment with specific resists (assuming standarts) along with the mean and standard dev for artifact total counts.

randarts to come. After discussion with Magnate, there are some errors with how I'm been generating randarts.