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Tuesday, Sep 11, 2012 - 23:04 SGT
Posted By: Gilbert

Downtime

Another end to a long day calls for some serious unwinding:



Me: Haven't had anything crack me up like that for weeks! Why don't some pets entertain like this? Oh, not Mr. Robo, who's had nearly all his fur drop off from the stress of preparing experiments. Yes, I mean you, Mr. Ham.

Mr. Ham: How undignified - and that's backed by the research you two seem so big on, which is not even the proper killer robot or Big Brother sort. Just so you know, I had my own projects, such as sowing strife and discord between two of hamsterdom's greatest enemies, cats and humans, and keeping competitors off my turf.

Me: Aren't the pandas safely landed?

Mr. Ham: See, I gave it as good as it got, but I got distracted by some crushing news from Korea. Poor things, they've gone from tragedy to tragedy in short order.

Me: Can't understand what people see in Gangnam Style either.

Mr. Ham: What? No! I'm talking about the fall of a G-V star among stars. Months after losing a Dear Leader, they now also mourn a Celestial Leader - he was my Sun, he was my Moon, he was my Sun Myung Moon! Cherished head of our partner organization the... uh... where are my notes... *fumbles in pocket* um... 日月神教. Yeah, that must be it. And oh, he's your Dad too. Myself, I'm up to being Great-Grandfather.

Me: ...

Mr. Ham: *sniffs* Ingrates! History will remember him as the Messiah, or at least among the top five! ...Ok, top ten minimum. O miserable are those who doubt his messiahness, for they are as the discarded popcorn buckets trampled underfoot! Those who mock us do not understand, for many raisins we shall partake of in the Light of his face, both solar and lunar, which come to think of it is solar too... never mind. Tremble in the presence of the once and forever Kim! His considerable will, subject to legal interpretation and behind-the-scene wranglings by his brood of kids, be done!

Me: I think you're mixing up both your clients and your passive-aggressive implorations very badly.

Mr. Ham: Darn, knew I had taken on too many of them. Still, Lil' Kim's exceeded my expectations - it seems like he's quite the beefcake up there. Which may not be quite that impressive when you consider that he can have competitors thrown into gulags, but Hollywood's kinda unforgiving too. And he's snagged himself a wifey as well! Dear thing must have been over the moon, maybe even the Sun, and the only thing that could have made the union even more perfect would have been the addition of a couple thousand other couples who had barely even met each other!

Me: I don't know about that...

Mr. Ham: Many are the things you do not know, human. Like the fact that you're doomed if you do not join the One True Quadrilateral. That's one of the problems you lot have - Korea's got K-pop, your artistes run off to Taiwan and Malaysia if they're any good. Korea's supported Samsung and Hyundai, your last hit was the SoundBlaster. Korea's got on the world stage with Sun and his multibillion-dollar empire, and you imbeciles shut down your best hope for the future, and for what? A mere fifty million and change. Ho ho.


Best Furry Pals

I then got into a heated altercation with Mr. Ham on his business methods, and it got to the point where he suggested we patch it up by watching Ted together.

Me: So what do you think of it?

Mr. Ham: For a film based wholly on adolescent wish-fulfilment, it wasn't too bad.

Me: Uh huh, the premise was pure fantasy, but it did work.

Mr. Ham: Yup, the whole bit about a 35 year-old used-car peddlar hitching up with Mila Kunis, then fronting for Norah Jones - what an utter fairytale! Thank goodness the director had the good sense to throw in a teddy bear coming to life as a Christmas wish to make the plot slightly plausible.

Me: Kunis doesn't really do it for me...

Mr. Ham: Yes, yes, elbows too pointy, I've been there. Ted, though, is a bear after my own heart - in different circumstances, one in which I hadn't tried to sabotage his black-and-white cousins, we might have become fast friends.


Now you're talkin', baby!
(Source: Somewhere on the Internet)


Me: I can well believe that.

Mr. Ham: Just curious, what would you do if you were caught in that predicament? Bros before hos, surely?

Me: Oh, I've got the nearest animal shelter on speed-dial for that eventuality.

Mr. Ham: That would have been funnier, you know, had I not been earning like a hundredfold your piddly income from my personal Cult. But hey, look, we're buddies, there's always a place for you in my organization, man. Whaddya want to be? A Cousin? I think an opening for Grand-Uncle rank just opened up, interested? There's been a long history of such sinecures for connected folk since the Middle Ages and before, so don't think too badly of it.

Me: Thanks for the concern, but there are still some things I will not do, my friend.

Mr. Ham: *shrugs* Alright, probably wouldn't have worked out anyway, you got a crap singing voice.


Tuition Tut

Perspectives From A Private Tutor has been making the rounds, which led me to question myself why I am not out there corrupting the young. Given that even China is banning Math Olympiad prep classes, there might be even more business spillover here, not that custom was ever lacking.

For those who may prefer reading about doing math than doing it, like me, I recommend You Failed Your Math Test, Comrade Einstein, about how politics can interfere with the purest of sciences. I was about to check it out from the library, when I realised that there was a full PDF copy floating about, with a number of superficially-attackable problems. After looking at them, I decided to tackle Calc II first, if ever.

I must also remark that I was flabbergasted at Harvard probing half the class of Government 1310: Introduction to Congress for cheating. Shouldn't they be given extra credit, considering the subject matter? At the very least, it is an extremely important matter that deserves detailed personal attention by worthy officials.


How Would One Do It?

One cannot help but run across all manner of challenges in daily life, of which this xkcd comic (N.B. They have a wiki dedicated to explaining the strips now) stuck in my head. From the hover text:

"FYI: If you get curious and start trying to calculate the time adjustment function that minimizes the gap between the most-used and least-used digit (for a representative sample of common cook times) without altering any time by more than 10%, and someone asks you what you're doing, it's easier to just lie."

Before moving on, however, I popped on to the corresponding forum thread to check if anyone had already done it; seems not, but there were a lot of eye-openers, such as some microwaves allowing freer interpretations of times (e.g. entering 0:90 is accepted for 1 min 30 seconds), alternate input methods (e.g. a button for +30 seconds, which had some users simply pressing it in multiples) and users having quirky habits (e.g. being predisposed towards multiple mashing approximations, such as entering 0:22 for 20 seconds)

So, on to an actual solution sketch. There remain some assumptions to be made, of which the most basic is probably what sort of valid times the microwave accepts (i.e. can 0:90 be entered, or must it be 1:30?). Since there seems to be no particular justification for either without holding a survey, I'll just go with the former from here on (ironically, the microwave I have at home has but a dial)

With this decided, every input time T (in seconds) can be translated into a set of actual inputs RT={RT_1, RT_2, ...}, subject to the constraint that 0.9*T<=RT_i<=1.1*T for all i. Consider a concrete example: When T=90, R90={0:81,...,0:99, 1:21,...,1:39}, |R90|=38.

It is then time to set a second assumption - is the time adjustment function allowed to take its previous outputs as an input, i.e. is it allowed to have a memory? If not (disregarding randomization for now), then every T always maps to the same output, and the problem can be cast as optimization on the given distribution of input times, with the objective function being min(gap(sum(RTi_j))), on a mapping of each i to some j.

Now, the optimization problem has a long and storied history that I am neither qualified nor inclined to enter at depth. There are, however, a few things to note. First is that checking all possibilities always reveals the right answer - but in many practical instances, such as this one, takes far too long.

So is there some efficient way to minimize the gap? While I have neither found one nor am ready to state that one does not exist either, I thought it instructive to compare this to some classic problems. Take the subset sum problem, which asks, given any set (or bag) of integers, whether there is a subset that adds up to zero (trivially extended to any integer)

First, the similarity and good news - here, the size of the subset is fixed as the number of unique inputs times N, and in addition, there is a constraint that each element in that subset must come from a different subset in a given partition (also of size N) of the entire set, so the search space is (far) smaller than an equivalently-sized subset sum problem.

But even so, does this make the problem intrinsically easier? Not really, with the yet-more-similar multiple-choice knapsack problem (MCKP) known to be also NP-hard - no efficient solution is known for it in general. Note that while the microwave problem is not exactly MCKP, in that there is an additional gap-function covering the "profits" (the RTi_j values, themselves multi-dimensional histograms of ten elements corresponding to the ten digits), I am hard-pressed to see how this would make the computation substantially simpler.

All this points to a heuristic solution, in which the search space is scoured using some technique like simulated annealing, parameters extracted, and results reported (disappointing, I know)


Simple example of exhaustive greedy search with
T=10 (50 times), T=30 (100 times), T=60 (200 times)
Note normalised gap (NGap) = 1 if the natural inputs "10", "30" and "60" were chosen; static mappings were "9", "27", "81"


The results can be improved with the allowal of memory and/or randomization. Consider the case where the cooking times were all T=50 - then, any static mapping would forever produce the same two digits, i.e. the normalised gap must be 1, whereas if randomization were allowed, the digits used would be able to spread over the entire 0-9 range (since allowable R50={45...55}, for a normalised gap of less than 1. With memory of past choices, the average-gap-over-time would be further minimized, since the best mapping option could then be selected at each input time.

Gah, it'll probably be easier to use a scramble keypad.


One In A Million

It had to happen.


It must be the best public housing in the world!
(Source: SGAG.SG)


The best tip that I got for the week was to immediately renew my library books upon checking them out, which should save me a pretty penny on fines. The other big tip, from one of my reads, was never to pay more than 15 years' fair rental value for a property, with 150 months an ideal. This does seem to hold here, using the S$2560 average of median rents, which points to prices of S$384k to S$460k for five-room flats.

There was to be more here, but it deserves its own post.


Viva la Résistance!

Having done what I had set out to, and gained a few Paragon levels on my Demon Hunter, I resolved to return to Oboham the Monk and get him to Inferno difficulty (the cousin's now on Dragon Force, of all things). To this end, I found out that I had lost sight of my original vision of a nigh-unkillable grinder-tank, and boy, does it lend itself to a whole new experience when he's built properly.

First, the gearing. Following the idea outlined in this forum post, I stacked All Resist and Arcane Resist stats on Oboham's items with highest priority, and then Life Regeneration, only taking Dexterity and Vitality when they came along for the ride. With the One With Everything and Time Of Need-runed Mantra, a mere 265000 gold (again, could have been less with more patient spending) bought 1370 in every resistance, 5912 Armor, 2368 Life regenerated per second and *ba-dum* a mere 968 Dexterity, 10k DPS and, most startlingly of all, 12000 Life.

Wait, wasn't the Monk supposed to be a meat-shield class? Why then does he have less than half the Life points of the glass cannon Demon Hunter, despite having only 40% more Armor?

Well, the magic lies in those resistances, of which Physical Resistance is one - as with the Dexterity bonus and Critical Hit Damage (exploitatively stacked by Demon Hunters), they are mutually multiplicative. In this case, 1370 resist would mean that all incoming damage is reduced by about 81%. This remaining 19% has another 65% chunk taken out of it by the 5912 Armor if physical, which then has a 30% discount applied for being a melee class, leaving only 4.5% of the original damage, assuming it's not dodged outright (30% chance) or blocked (18% chance) in the first place.

Okay, so a monster hits for 4500 damage down from 100000 raw - isn't that still a large percentage of Oboham's health? Well, to begin with, Oboham would heal that back in less than two seconds passively, no questions asked - while the Life on Hit affix is popular, why bother with it when one can just run about for five seconds and be back at full health?

This is just the beginning of Oboham's survivability toolbox. Breath of Heaven, on a 15 second cooldown, becomes close to a full heal; Serenity, on a 20 second cooldown, is three seconds of invulnerability plus a full heal. Blinding Flash gets enemies off his back, Mantra of Healing is yet more regeneration (perhaps overkill), and there are always health potions on top of all that, of course. To cap it all, the dirt-cheap breastplate I picked out happens to have Health Globes grant a bonus 10k Life (plus 6k from the boots)


Here, everybody gather around and hit me, it'll save time in the long run


The practical upshot of this is that Oboham is practically immortal in the course of normal play on Hell difficulty - basically, he can be left in a mob of Elites and Champions for a toilet break, smile through taking their attacks on his face indefinitely, stand in multiple Plague or Desecrator pools, and probably kill them eventually through his Thorns aura, all the while not even seeing his health pool do more than twitch.

There are drawbacks, certainly, the most glaring being that killing monsters actually takes time now. Run-of-the-mill mobs that Mysdeth one-hits take multiple punches, bosses that she shoots down in seconds can take minutes, Lashing Tail Kick can't be spammed like Chakrams and is less powerful besides due to the huge difference in base damage, and Oboham has no mobility skill on a par with Vault.

In conclusion, for efficiently farming items (which was the whole point, wasn't it? Even games need to crunch numbers one eh) I'll still take a Demon Hunter over a Monk any day (though I haven't gotten anything worthwhile other than a poor Ageless Might that would probably be most valuable broken down into a Fiery Brimstone - well, at least Exquisite Essences still sell for something), or at least until I can afford a lot more damage for Oboham, and maybe gear him more towards Armor.

For the record, Mysdeth is doing the Festering Woods -> Halls of Agony (1 and 2) -> Cursed Hold -> Halls of Agony (3) run, which takes about half an hour on average, and gives 50k gold/2.75M exp, and a crapload of unsellable magic and rare items that gets turned into essences or sold to the in-game vendor for maybe 25k gold. Yes, paying cash would be far more efficient, but that defeats the whole purpose, doesn't it?



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