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Saturday, Nov 28, 2009 - 19:47 SGT
Posted By: Gilbert

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Quite Hamsterly Done

changelog v1.15a
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* Issue with Google Friend Connect showing up uninvited fixed.

It's Mr. Ham here again, after taking the hour off from my job of getting dropped on the head (see previous post). Being productive is the only way for us hamsters to gain our rightful place in the world, especially with artificial creations gaining in popularity. I'm all for robot hamsters, as long as they don't nick my hard-won position. Scary possessed-looking little buggers they can be, but let's see how tough they are after plummeting to the hard floor a few times.

I'm not sure how the human caretaker got into graduate school, as it was almost painful watching him struggling through his algorithms problems; I mean, it was so obvious that deceit can be profitable in the Stable Marriage problem, and that a minimum bottleneck tree is not necessarily a minimum spanning tree over a graph, and that's just up to Chapter Four. As it is, I think it's pointless tutoring him on the nuances of computational theory.

And even in more practical problems, such as the issue of whether it is best to claim an Energy Pack in Mafia Wars (and similar clones - e.g. Chakra Pack in Naruto Shippuden) immediately after it becomes available, he's not the sharpest. Oh, it is simple enough to show that the answer is a big fat no in general, using a counterexample, but he got stuck on how to decide whether to claim one, and in the end fell back on his unsubstantiated and inferior human intuition.


I am sorry that you saw fit to bother me with such trivialities


It is so obvious that the Mafia War Energy Pack problem can be easily solved, given the parameters of Energy (flow) per hour, Maximum Energy, Time Between Energy Packs, Average Energy to Experience conversion rate, Experience per level etc etc, and making a few trivial assumptions (such as conversion of Energy to Experience taking negligible time).

First, it is easily noted that it is impossible for waiting an entire Energy Pack cycle to result in a higher Level-cum-Experience score than using the Energy Pack immediately (proof left to the reader). Therefore, we need but consider T possibilities at each decision point, where T is the Time Between Energy Packs (in hours).

This is just a dynamic programming problem, and to determine the highest Experience level that may be obtained after any H hours, and the times at which Energy Packs should be claimed to achieve that, we simply construct the H by T matrix and populate it column by column by referring to the appropriate previously computed entries.

Of course, the plan that is best for H may very well be incompatible for H plus or minus a bit (easily noted by considering that the optimal maximization when an Energy Pack arrives at H is to use it immediately - a parallel with the last step in a repeated game), but no problem: just compute for a sufficiently large H (beyond the typical human or online game lifespan, in hours), and we are set.

Well, this is at least my intuition - I'm a big idea kind of hamster - and of course we could fall back on simulated annealing or something if this is too difficult for our graduate student to comprehend... unhand me! Stop squeezing me!

Okay, okay, no more comments on your academic failings... they are beginning to be overshadowed by your pretend football punting ones anyw... *Glurk*

$829/$1000 after a few unfortunate weeks, with the Gunners slipping up, and Villa only managing a draw.

$100 on Tottenham to beat Aston Villa (at 2.60)


Bonus Riddle of the Day:
Where are Ferguson and Benitez on the same side?





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