Power-based pricing available (r1284)

[Pete Mack]

Eddie got it right--the value of any equipment depends enormously on where you are in the game, and what you are already wearing. I think the current mean-field approach is the only way to go; the hard part is determining the valuation.
(And valuation shouldn't be linear with effects--a single resist is worth much less than 3 or 5.)

[Rizwan]

Eddie got it right--the value of any equipment depends enormously on where you are in the game, and what you are already wearing. I think the current mean-field approach is the only way to go; the hard part is determining the valuation.
(And valuation shouldn't be linear with effects--a single resist is worth much less than 3 or 5.)

How about adding a rarity component to the price value. A rarer item being more valuable than the more common items. So in the ring of speed example if a ring of speed is rarer than a ring of acid then ring of speed should be more expensive regardless of where or when anyone uses it.

[Pete Mack]

Rings of Speed are not rarer than rings of Acid; they are just deeper.

[Zyphyr]

Rings of Speed are not rarer than rings of Acid; they are just deeper.

He wasn't saying that they are rarer. He was using the two rings that were already in use in the discussion as placeholders instead of arbitrary variable names. You could change what he said to :

if "Clean Underwear" is rarer than "Loincloth of Skid Marks" then "Clean Underwear" should be more expensive regardless of where or when anyone uses it.

That wouldn't change the meaning of what he was saying.

[PowerDiver]

if "Clean Underwear" is rarer than "Loincloth of Skid Marks" then "Clean Underwear" should be more expensive regardless of where or when anyone uses it.

That is in complete opposition to "power based pricing", the subject of this thread.

[Zyphyr]

I wasn't saying that I agreed with it, just restating it for clarity.

[zaimoni]

How do you plan to get "true value" when, not only are you not dealing with a total order, but a pair of items can change drastically in comparative value?

E.g., I would always choose a ring of speed +5 over a ring of acid in the early game. And I would nearly always choose a ring of acid over a ring of speed +5 in the late game. How can any of your automated methods cope with that?

The least-squares fit is over a *very* large state-space.

To put things bluntly, for armor/weapons calculating the least-squares fit can be rotely calculated for any specific class/race/level/stat combination; the hard part is the survivability estimator. The discrete variables are the equipment in each slot.

It's a lot of memory-intensive number crunching, and a naive exhaustive implementation will easily exhaust 2GB of RAM. But it'll catch the speed +5 vs. Ring of Acid paradox just fine.

[RogerN]

Just a few points to consider (which you probably already have):

* Early-game shopping is all about opportunity cost. There are lots of useful items to choose from (!CCW, ?Phase, ?Enchant, etc...) and you can only afford a few of them. Should I enchant my weapon a bit more, or bring some extra !CCW?

* Mid- and late-game shopping is a lottery. You must get lucky in order for stores to stock a powerful item that's better than what you've already got. When you see a powerful object you want, either you can afford it or you can't. Rarely is it necessary to choose between competing items, because there usually aren't any.

* If an item is too expensive for the player to buy then it serves no gameplay purpose other than providing atmosphere. Therefore overpriced items don't serve much of a purpose... by the time you can afford them, you probably don't need them any more.

* Underpriced items, on the other hand, can be interesting. Lower-level players can actually afford them and therefore get to choose between buying a powerful item or buying staples. Stores are a lottery anyway, right? So why not let low-level characters play, too?

* I find early-game shopping to be far more interesting because of the available trade-offs

* Conversely, I don't think it's possible to make late-game shopping more interesting without significantly increasing the availability of powerful items in stores (to provide for opportunity cost). But that would lead to more store-scumming, and would decrease the emphasis on finding good equipment in the dungeon.

My conclusion: I don't think you should spend too much time trying to price powerful items. It doesn't really matter that much. The low-level items (anything less than 3k gold, IMO) are where you should be focusing your efforts, because those are the items which are most likely to have tangible opportunity cost associated with them.

[Polyonymous]

I was contemplating a long post where I described how there are at least six axes of power and that for the price of an item to accurately reflect it's power it would need to be the product of at least six different components. Then I realized that it's all moot. Roger hit the nail on the head.

Cash in pocket is a function of where you are relatively in the game and how slow you have gone. So long as it's possible to easily generate more objects on the floor that are saleable, cash is a function of gameplay choices. The cost of something (and the options for raising the cash) only matter if the game is cash constrained and it's not unless you're minimizing turncount (as then you have a tradeoff between the time to farm more cash for marginal turncount improvement through the Black Market).

If I were pricing objects, I'd first define a power curve throughout the dungeon that I expected typical players (sorry divers) to progress through {player eq dependant speed = max(0, (dungeon level - 10)/3, damage/round = ...., etc}. Once you have the power curve of the player defined, you can divide up the gear provided components of player power among the equipment slots (maybe body armor is worth a bigger percentage of the total power pie than about armor, etc).

Then you can quickly examine the stats on an item and assign it an appropriate dungeon level. You then can determine the appropriate price based on your assumptions about cash earned (speed of dive) and how often you want players to buy items versus find them (if you want them buying things that are 10 dungeon levels better than current equipment instead of things that are 20 dungeon levels better, it induces a different pricing function).

But the first step in all of this is determining the cash inflow assumptions, the frequency of item purchase that you would define as optimal for gameplay, and the power curve of the player over the dungeon levels. You can even calibrate for the fact that balanced items are worth more than specialist items.


PS the six axes of character power (doubling of one of these halves the turncount independant of the others) that I could determine were energy/turn, damage/attack(or missile or spell), attacks (or missile or spell)/100 energy, hit chance, defensive be hit chance (halving this doubles power), and regeneration speed. The last two factors depend on an assumption that resting is a significant portion of turn count, which is partially invalidated for divers, but then again the game isn't balanced for them. (Although maybe it is, loot improving by dungeon level without mobs improving is a gigantic boost to diving as optimal, I'd make item level = mob level, you go deeper to get better monsters to kill, not to get better loot from the same monsters)

PPS Here's why balanced items are more powerful than specialist items. Consider a 2 attack/round +0 speed character. Which would they prefer to be? 4 attack/round +0 speed (double attacks/round), 3 attack/round +5 speed (+50% to attacks and energy/turn), or 2 attack/round +10 speed (double energy/turn). They'd prefer to be 3 attack/round +5 speed as over 100 game turns, they'll have 45 attacks (15 energy/turn 3 attacks/100 energy = 45 attacks/100 turns), while both of the versions would get only 40 (10 energy/turn * 4 attacks/100 energy and 20 energy/turn * 2 attacks/100 energy). An accurate pricing method would make the +1 attack/round +5 speed item more expensive than either of the two alternatives. This actually means that the speed scale in the spreadsheet is wrong. Each additional energy/turn is worth less, +10 speed isn't more than twice as good as +5 speed, it's actually less.

It's really about the same, but if you give me the choice above, I'd pick the +1 attack/round and +5 speed item rather than the +2 attack/round or the +10 speed item for combat which is likely the balancing situation

If balancing for minimized turncount the speed item looks better than the combat math shows as it minimizes movement turns, etc, How much depends on how much resting to regenerate hp is done as if a turncount game is constrained by hp regeneration, then it's also balanced by the combat case as ending the combat sooner means less hp to regenerate, means a faster game.

[Pete Mack]

@zephyr-
I was trying to point out that object rarity doesn't have much to do with object power, which is the point of this thread. I regret that my post was perhaps obscure on that point, though I thought the comparison of Rings of Acid and Rings of Speed made it obvious that object rarity has nothing to do with valuation. Individual feature rarity has something to do with it, but only insofar as going without that feature has significant effect on character power.

[Rizwan]

@zephyr-
I was trying to point out that object rarity doesn't have much to do with object power, which is the point of this thread. I regret that my post was perhaps obscure on that point, though I thought the comparison of Rings of Acid and Rings of Speed made it obvious that object rarity has nothing to do with valuation. Individual feature rarity has something to do with it, but only insofar as going without that feature has significant effect on character power.

Well that's my mistake then because I thought that rarity DID have some effect on power as it was my understanding that suppose a flail of westernesse was rarer than a flail +0+0 and hence the westernesse was more powerful than the ordinary flail. Therefore my suggestion to use rarity as a part of the price calculation feature. Rarity and price are directly related in the real world. So maybe in Angband world we can also apply the same rule. That was my suggestion.

[Magnate]

@Rizwan: rarity only affects pricing in the real world because it (artificially) alters desirability. The whole point of proposing power-based pricing is to base prices on desirability. So no, rarity isn't taken into account at all. If it were ever to do so, it would be based on overall attribute rarity (i.e. the chance of finding rnether), rather than base item rarity - because the former affects desirability and the latter doesn't.

Roger hit the nail on the head.

Cash in pocket is a function of where you are relatively in the game and how slow you have gone. So long as it's possible to easily generate more objects on the floor that are saleable, cash is a function of gameplay choices. The cost of something (and the options for raising the cash) only matter if the game is cash constrained and it's not unless you're minimizing turncount (as then you have a tradeoff between the time to farm more cash for marginal turncount improvement through the Black Market).

If I were pricing objects, I'd first define a power curve throughout the dungeon ...
(snip)
... But the first step in all of this is determining the cash inflow assumptions, the frequency of item purchase that you would define as optimal for gameplay, and the power curve of the player over the dungeon levels. You can even calibrate for the fact that balanced items are worth more than specialist items.

I'd be interested to see such an approach - it sounds more flexible than the mean-field approach of power-based pricing, but also a lot more work. The only reason I've proposed this is because the power evaluation function already existed!!

I'd also be very interested to see the outputs of the least-squares iterative approach suggested by Camlost/Zaimoni. I suspect this too would be quite a bit of work, though perhaps it could be added to the existing borg code.

This actually means that the speed scale in the spreadsheet is wrong. Each additional energy/turn is worth less, +10 speed isn't more than twice as good as +5 speed, it's actually less.

Well, the scale does show individual points of speed gradually declining in value, but only after +10. In most cases +10 speed *is* more than twice as desirable as +5 speed, because you have a very limited number of equipment slots with which to reach the speed necessary to defeat Morgy. That said, speed has been by far the hardest thing to value in the power calc, so I'm always interested in other views.

@Pete: totally agreed about multiple resists being more valuable - for the same limited-slots reason as above. It's the very next thing on my to-do list.

Er, actually it's next-but-one, after adding power for activations. Ho hum.

CC

[Polyonymous]

I'd be interested to see such an approach - it sounds more flexible than the mean-field approach of power-based pricing, but also a lot more work. The only reason I've proposed this is because the power evaluation function already existed!!

Prices are only meaning as long as cash is a constrained resource for players (given what cash they have, they have to make meaningful choices about what to buy). This is generally true only for divers as they can always buy out the BM for a chance at an item that might help. "Normal" players see the whole buying out the BM as a waste of time and too much RSI and quickly have excess cash. For the nondiver, any pricing scheme will work as the majority of nonconsumable items come from the dungeon. My point was that pricing isn't the big win from standardizing item power. The big win is being able to generate an item of arbitrary power and to measure the power of each item.

Well, the scale does show individual points of speed gradually declining in value, but only after +10. In most cases +10 speed *is* more than twice as desirable as +5 speed, because you have a very limited number of equipment slots with which to reach the speed necessary to defeat Morgy. That said, speed has been by far the hardest thing to value in the power calc, so I'm always interested in other views.

There's a feature possiblity in here. More pval's per item. Maybe artifact.txt looks like DEX=4 | STR=3 | SPEED=5 | ... instead of DEX | STR | SPEED with a fixed pval for all the stats. To change the example, consider a ring of Damage +x and a ring of speed +y that are each worth the same amount in combat. By a similar argument, a ring that combines the half of each effect is going to be more powerful than either specifc ring and that mix of abilities is possible without any code changes. Change it to Rings of Accuracy vs Damage vs Slaying and they are automatically made today (for those who would say that the game doesn't make dam/speed combo rings).

Speed (and every other factor) is dependant on where the character is. +10 speed to a 0 speed character doubles combat effectiveness as it doubles energy/turn. +10 speed to a +10 speed character only adds 50% to relative combat effectiveness (it still adds 100% of a 0 speed character's combat power). Essentially as long as +1 speed gives 1 more energy/turn, +1 gives +10% base combat effectiveness. It's a fixed power increase that's equal to 10% of the power the character would have if at +0 speed. [going from n to n+1 energy/game turn gives and additional player action every 100 game turns, which is 10% of the 10 actions per 100 game turns they have at +0 speed].

To put actual numbers on it, if a character does 1000 damage per attack round, each +1 speed increases total damage per 100 game turns by 100. +5 speed gives exactly five times the increase as 5 times the increase that +1 speed gives. The reason that the attacks/round and speed example I gave has the mixed item as better is that it's the relative improvement that matters, and the relative improvement of each additional tick of any linear stat is less than the prior tick. (speed is linear in energy/turn up to where it goes sublinear).

I can take an approximation to how I'd write a power calculation formula if you want. I'll have to do a good bit of code study to understand how things impact performance as I don't have a perfect handle on everything.



Tangent: Some of the things that I think are poorly balanced with items tie into how items and power are distributed throughout the dungeon. Some of this is my preferences, but it would seem to make the game cleaner/better in a lot of ways from my perspective. When revisiting how item power is distributed, I'd also check the balance on the following aspects.

0) Most character power should be derived from the character level (about half). Right now it's too much equipment and found items (stat potions). This is a personal value statement. Flags on EQ is good, combat power being EQ based not so much, although that is somewhat the genre of Angband. It's about equipment, not leveling.

1) Stat Gain is too big a power boost (scumming the same set of levels shouldn't be as valuable as it is in the 30's). This is a specific example of the prior item, but it should be fixed on it's own even if player versus equipment is not rebalanced. You can decrease the impact of stats, change the way they are gained (level up bonuses rather than drops), etc but regardless of play style, there shouldn't be a big value add from scumming levels. (regardless of if this is the floor in the 30's or snagas in 54-60)

2) Object drop quality should depend solely on monster difficulty. Just being deeper in the dungeon shouldn't make monsters drop better items as currently they're not functionally any more diffiicult. Better versions of the same monsters would be a different case, see variants that level their monsters, ToME does at least.

3) Very few objects if any should be on the floor. Monster drops should provide (almost) all items of any importance.

Note: I think diving would still be a valid strategy, it'd be about picking and choosing your kills to level up, and since power is more tied to level than equipment, divers would be able to manage with proper kill selection deeper.

[Pete Mack]

There are two benefits to speed. The first is improved damage. If you can reliably do 100% (or 50% hasted) additional damage per turn, you can handle tougher monsters. But the second is reduced chance of bad touble turn against you. And double moves are the kind of thing that kill you (800+ damage). Base speed 10 is an absolute must for thriving deeper than 3000'. (You can survive with less speed, but it requires stealth and extreme evasion.) Base speed 20 is a must if you want to be able to handle the nastiest monsters with reasonable safety.

[Nick]

There's a feature possiblity in here. More pval's per item. Maybe artifact.txt looks like DEX=4 | STR=3 | SPEED=5 | ... instead of DEX | STR | SPEED with a fixed pval for all the stats.

I am currently coding this into FAangband for the next version.