Your views wanted on artifacts in V

[Nick]

Speaking of which, the iPhone port would be a real win on the bus....

... and this (or some successor to it) might help solve the interface problem.

[Pete Mack]

I just reread what you wrote, and I don't understand it. My memory is that you observe the first N/e and then take the first one better than the best observed. I don't remember the chance of success, but I thought it was more complicated than 1/e. For a counterexample, calculate prob[do not observe 1 & 2 & 3] in which case success is less than 1/3 which less than 1/e. For sufficiently large N, that prob approaches 1 given your limited inspection range, which seems to contradict what you wrote.

Aaah! I have no idea how I thought N/e and wrote 1/lnN, but somehow I did it. I blame the tiny screen on my iPod, which is what I use on the bus.
Yeah, that's it.

Speaking of which, the iPhone port would be a real win on the bus....

[PowerDiver]

Is it possible that your changes messed up the final drop?

M just dropped a massive iron crown [0,+2] and mighty hammer (3d9) (+3,+5) with no special abilities. r1858

Psi reported something similar fairly recently.

[PowerDiver]

I can't recall the exact answer, but this book has an amusing discussion of the question.

That looks like an amusing book, but it's usually easier to me to solve the problem than to look it up.

If you inspect A out of N and then take the first one better, I get a success rate of (A/N) * (H_{N-1} - H_{A-1}). That approaches Pete's 1/e success rate as N increases, when using the A = N/e I remember.

[Nick]

I can't recall the exact answer, but this book has an amusing discussion of the question.

[PowerDiver]

@Eddie: and if you know there are N items, and you're betting on the best one in order, don't take the first 1/lnN items, then take the first item better than the best you've already seen. This is the optimal strategy, with odds 1/e

I've never been able to figure out a real life situation, including playing games, where I could apply anything remotely similar to that theorem. Usually the difference between 1st and 10th [much less 2nd] is much smaller than the difference between 10th and nothing at all.

The coupon collector theorems come up over and over again.

I just reread what you wrote, and I don't understand it. My memory is that you observe the first N/e and then take the first one better than the best observed. I don't remember the chance of success, but I thought it was more complicated than 1/e. For a counterexample, calculate prob[do not observe 1 & 2 & 3] in which case success is less than 1/3 which less than 1/e. For sufficiently large N, that prob approaches 1 given your limited inspection range, which seems to contradict what you wrote.

[Pete Mack]

@Eddie: and if you know there are N items, and you're betting on the best one in order, don't take the first 1/e items, then take the first item better than the best you've already seen. This is the optimal strategy, with odds 1/e

edit: fixed really stupid math error.

[PowerDiver]

If you have an ordering on a set of N items, and you pick them one after another at random, you only expect to get a better item a total of about ln N times.

[edit] That can't be exactly right. It's been too long since I solved these problems. I must have forgotten the right constants.

[For those who are unfamiliar with the ln function, ln grows very slowly, and ln 400 is about 6.]

If anyone cares, I remembered correctly. This loop

n = 400;
while (n > 0)
{
n = random() % n;
sum++;
}

gets executed an average of about 6.6 iterations. The exact expectation is the 400th harmonic number.

[Magnate]

Right, but egos and normal enchanted items are less painful to discard because they are not unique. That's like stack of forks in local pizzeria. You don't care if you pick up just one and leave rest of them there. You use it when you need it and discard it when you don't. That's just natural. It is different with unique items. Unique item that is junk just feels wrong.

Hmmm. I must say I don't share this view. I understand Eddie's logic that there ill *always* be junk items, and since there are 136 artifacts I don't see any choices except deleting most of them or just accepting the fact. Personally I don't see it as my place to delete artifacts - if Takkaria instructs me to, that's different, but I'd rather spend my time tweaking their abilities and depths and rarities to make sure that they're useful as often as possible. Yes, they'll be junk sometimes, but I strive to avoid them being junk every time they're found (or even most of the time).

[Timo Pietilä]

Isn't this isomorphic to the current situation, with the exception that artifacts are only generated once? You will still find just as much junk... but instead of junk artifacts you'll get junk egos (since artifacts will be rarer and thus generated less often), right?

Right, but egos and normal enchanted items are less painful to discard because they are not unique. That's like stack of forks in local pizzeria. You don't care if you pick up just one and leave rest of them there. You use it when you need it and discard it when you don't. That's just natural. It is different with unique items. Unique item that is junk just feels wrong.

You don't want to discard Edvard Munch Scream even if you are offered Leonardo Da Vinci Mona Lisa. You want to keep them both. You don't care if you discard map of London Metro for better map of London Metro.

[d_m]

There is one way to prevent this and it is to make artifacts rare enough that you simply don't find many of them, and when you do they should all be powerful ones. Just get rid of all of the weak ones. *ALL* of them. Play with ego-items until you find that rare powerful artifact.

Isn't this isomorphic to the current situation, with the exception that artifacts are only generated once? You will still find just as much junk... but instead of junk artifacts you'll get junk egos (since artifacts will be rarer and thus generated less often), right?

[Timo Pietilä]

You are going to find many artifacts that are junk. It can't be helped.

There is one way to prevent this and it is to make artifacts rare enough that you simply don't find many of them, and when you do they should all be powerful ones. Just get rid of all of the weak ones. *ALL* of them. Play with ego-items until you find that rare powerful artifact.

Of course better weapon obsoletes weaker weapon, but that is only if those two are equal in all aspects except that one thing that makes one better than other. With ego and enchanted normal items that is constantly happening and can't be helped, but Ringil doesn't always beat Aule and Pain can compete with Durin.

With powerful artifacts it isn't always black and white and one doesn't replace another, there are gray areas, and you have to make sometimes make hard decisions which one to use and which to ditch.

[PowerDiver]

Adding +10,+5 to Elvagil still makes it junk, because you need a defender or a westerness to beat it. The point is, that at that level you are quite probably using your weapon for FA. The *thancs beat it, because for damage they are much better.

If you have an ordering on a set of N items, and you pick them one after another at random, you only expect to get a better item a total of about ln N times.

[edit] That can't be exactly right. It's been too long since I solved these problems. I must have forgotten the right constants.

[For those who are unfamiliar with the ln function, ln grows very slowly, and ln 400 is about 6.] All the rest would be junk. By mucking with rarities, so that you do not get the items randomly, you can introduce better behavior, but whatever you do most items will still be junk. If you improve one enough to be better than something else, you change the order of the list, but you do not change the junk ratio. Another approach is to give them different non-comparable powers, but even then slot limitations force you to compare one to the other anyway.

You are going to find many artifacts that are junk. It can't be helped.

[Philip]

Try playing the nightlies. It comes up a lot earlier now, and has been beefed up a bit (I forget exactly how).

Adding +10,+5 to Elvagil still makes it junk, because you need a defender or a westerness to beat it. The point is, that at that level you are quite probably using your weapon for FA. The *thancs beat it, because for damage they are much better.

[Magnate]

I found Elvagil, and in 3.1.1.1626 it is worse than a spear of slay evil. That is a weapon that needs FA, slay evil and come up earlier and more often.

Try playing the nightlies. It comes up a lot earlier now, and has been beefed up a bit (I forget exactly how).