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Related to the current discussion here is a conjecture I made back in the year 2000 while I took Calculus in high school.
Conjecture:
dn/dxn x1/x has exactly n positive real zeroes, all simple.
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Here is a nifty problem about polytopes. I and another member of AOPS have analyzed it and came up with the answer. Here it is.
Let p0 and p1 be two parallel (n-1)-dimensional hyperplanes in Rn that are a unit distance apart. Let A be a unit (n-1)-hypercube in p0 and B be a regular (n-1)-orthoplex in p1 such that the orthogonal projections of B's vertices onto p0 are at the centers of the (n-1)-cells of A. Let C be the convex hull of (A U B). Find the formulas for following features of C:
(a) It's n-Volume Vn.
(b) It's Surface (n-1)-Volume Sn.
(c) It's circumradius Rn.
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rhebus wrote:
Patashu wrote:
1) Think about the central limit theorem - the normal distribution you get from summing infinitely many uniform distributions.
Now think about what kind of distribution you get from summing finitely many uniform distributions. For n = 2 you get a triangular shape, for n = 3 you get a shape that looks like parabolic sections stuck together and so on.
How do you generate the formulas that create these curves for each value of n? (For normalization purposes, let's say that the domain is x >= 0, x <= 1 and the integral of the curve should be equal to 1.)
If we take the special case of the discrete uniform distribution with exactly two possibilities, you've just described the binomial distribution.
EDIT: and in fact for general discrete uniform distributions, you have a multinomial distribution.
Actually, the multinomial distribution is defined as follows:
Parameters:
n - Number of trials.
k - Number of Categories.
p - vector of probabilities (pi = P(ith category).
Support: k-dimentional vectors of nonnegative integers. The sum of the integers in the vector is always n.
Basically, you perform n independent trials and in each one, you select one of k categories, where all categories are equally likely. The outcome is a vector in which for i=1,...,k, the ith component is the number of times you chose the ith category.
Some properties of the vector X~Mult(n,k,p):
E(X) = np
Var(X) = n(diag(p) - ppT)
Xi~Bin(n,pi)
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I think that the idea posted by thatguy is similar, but here is my idea.
My idea is to start with a uniform prior on each digit and update the distributions with Bayesian approach while making guesses according to the following scheme.
For both pright and pwrong being >=1/2 do the following.
Make a random guess and update the probability distributions.
From then on, keep generating random combinations, but using the updated distributions. If the generated combination was already guessed, reject it and try again. Otherwise, guess it, and use the lock's response to update your distributions.
For any other case. whichever probabilities is <1/2, do the same as above, but assume the light display is wrong when red if pwrong<1/2, and wrong when green if pright<1/2.
This method will inevitably still give the unavoidable expectation of 5000 guesses if pright=pwrong=1/2, but the expectation should lower dramatically as you increase pright and pwrong from those values.
I will run some tests on this method using R.
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I can look at that. For now, the save - state corruption is the leading route, however, in case multiple completion methods wind up submitted for publication, I can finish the optimized version of the AGDQ run.
Also, the boss fight in the save - state corruption route should be interesting, provided we don't wind up with a TAS that skips it straight to the credits. Based on the available demo, it reminds me of the final fight in Ironsword, which is comparable in complexity, but for a somewhat different reason.
EDIT:
I analyzed the campfire route using the LUA script. Based on the RTA friendliness of the AGDQ version of the game, and the fact that there are too few rooms with zombies at good positions, the pickup lineups displayed by the script shows that it is not worth it to changing the order of the kills over the winning TAS. Things would be different on the original version of the game that has the unmodified RNG though.
So we should just stick to the save-state corruption route for now.
BrunoVisnadi wrote:
I'm currently noting how many frames each of the zombie boosts saves. Then, I'll test how many we can do with the given amount of life, so that only the worse boosts are avoided. When I finish it I put here the link for the WIP.
I would like to give a crack at the boss fight once you post the next WIP.
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link_7777 wrote:
I wanted to bring this thread up to date quick. I was able to get the ACE route to work. My unoptimized run was a bit slower. I think an optimized version would be faster than the campfire route, but it would be close, you'd need to optimize both to be sure.
It is somewhat moot though since with some brute forcing I was able to get ais523's save corruption route to work and it is definitely faster. http://tasvideos.org/userfiles/download/28266011834849095
I notice that in most rooms, you go through in a noticeably sub-optimal time. Is that part of your attempt to corrupt RAM, or is only the the last room you entered used for RAM corruption?
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link_7777 wrote:
I think before we dive too deep into optimizing we need to settle on a route. This submission is the campfire route of course, but I think the ACE route can be faster. It works for sure, but I would need to do a little more optimizing to make sure it is faster. ais523 also proposed a save-corruption glitch which I don't really understand the details of.
Probably the save corruption would be shortest if it works and if not it will be between the other two
I agree. Let's try both, of these alternatives. At least one must be better than the campfire. Either way, it would be particularly cool to watch a "game-end glitch" edition of such a game.
This one will ultimately be an "any %" run. I also would like to see a separate movie under the "100%" category, which would open all chests, collect all 6 keys, and enter the final boss area legitimately. But that would be for later on.
ALAKTORN wrote:
rchokler wrote:
As a result, along the current route, we pretty much must kill the zombies in the same order as in the winning AGDQ run, even though it sacrifices many frames relative to killing zombies in a different order.
If it’s decided that the TAS should be made on the original unmodified version then your TAS may still be applicable to it. AGDQ version’s RNG was changed to be RTA-friendly.
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I am nearly back to square one with my attempt to improve the run. It turns out that I overlooked a crucial detail about the game mechanic. The detail being that which enemies are killed and in which order, also affects the item drops. I noticed it when on entering the store, the "sell" menu showed only one gem and a few pieces of cloth instead of three gems.
As a result, along the current route, we pretty much must kill the zombies in the same order as in the winning AGDQ run, even though it sacrifices many frames relative to killing zombies in a different order.
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The extra frames saved on the menu was a false alarm, because of the axe not being equipped. However, once I fixed that, I saved 5 frames on the first set of zombies by carefully manipulating them to move so that after I killed two of them, during the collection of the second pellet, allowing the third zombie to bump me rightward.
So I am already 7 frames ahead. Given the number of rooms traveled in the winning submission, I predict at least about a few seconds can be cut.
I am looking forward to the decision of which version of the game we should go for.
Edit:
Now 71 Frames ahead, due to change in the second fight with zombies. I am not too worried about having more health than in the submitted TAS at this stage of the game.
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caitsith2 wrote:
This run should be specifically in the vault mainly because it is the run featured in AGDQ2016.
I agree.
Edit:
I will have to come back to tweeking this TAS in a few hours, since I have to go tutor a student, but after selecting the axe and exiting the menu, I am 5 frames ahead. So the submitted TAS has it's slightly sloppy areas, but otherwise, the team has done quite well for a four hour time limit.
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Samsara wrote:
I think submitting this is fine. It puts it out in public for people to start frame-warring and optimizing, which was going to happen regardless even if this had been a far more optimized submission. The fastest campfire run I know of is 5 seconds faster than this, so perhaps that should be the first goal for the framewar (I'd post it here, but I'm not sure if I'm allowed to).
I agree. A frame war is in order for this run. Otherwise, it is not well enough optimized for publication yet. I will take a look at the current file right now.
Edit: Indeed, it can be slightly optimized on movememt, even if just a few frames. I saved a frame exiting from the beginning room already.
If there are any major optimizations possible, then it is most likely in how the zombies are approached. In particular, to have them always push the hero in a favorable direction, and in the room where multiple sharks are killed, to reach every zombie just as it spawns in.
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Speaking of this, I just ran LordTom's any% run of Metroid through FCEUX 2.2.2 using Metroid(U).nes ROM. Although it is a different dump and the published movie is FCEU, it sincs properly.
Perhaps a fresh run is in order.
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I agree, I would like a game similar to Streemerz used next time. I think that the best games for the speed TAS competition are ones that , though not familiar to the competitors, are much more oriented on just knowing how to TAS games well. If a game uses complicated maze-like map(s), it would be great if one of the files packaged with the game is a file with the map(s). Otherwise, we must draw the map(s) ourselves, relying on luck, hoping we are taking the best route right from the start. That consumes a lot of precious time that we could otherwise be using to optimize the character's movement, considering that the best expert TASer's will submit TASes so well optimized that other TASers stand very little chance to do better.
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arandomgameTASer wrote:
PM me the game so I can get a 4 day head start kthx.
(sign me up)
Nice try, but you will just have to wait until the competition.
I am not yet sure if I will be available to compete because I don't know my personal schedule for Saturday yet. However, if after the competition is over, it is chosen to further optimize the winning TAS so it can be published, like with Streemerz, then I am definitely up for that.
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I agree with others. Running a game to overflow the score display is usually only good as a proof of concept. Generally, we would only have a TAS showing an overflow published if it is a side effect of trying to beat the game efficiently, such as from large time bonuses or amazing combos to rack points up fast.
This run offers neither of these. Also, in the process, you are replaying the same small set of levels again and again. In fact, my emulator froze for half a minute just trying to load the input log you submitted.
Like the others are saying, this game can be published only if you just play all the built in levels once each and then stop there.
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I am with most other's, nominating Alyosha.
I never saw anyone put out so many quality TAS movies during a single year, especially for a player who became a member near the end of the year before.
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JVB wrote:
I think it would be nice to see so called "Perfect Run" TAS-videos of the Mega Man games, a la RoahmMythril. Or if you're unable or too lazy to watch the video, the basic jist of it is that you try to complete a stage only using the buster, no charge shots unless absolutely necessary, like knocking over the enemies that become platforms, and without taking damage.
(link above goes to the first ever Perfect Run video Roahm did, Cutman and is from 09)
While Roahm's videos are entertaining and fun, for a truly perfect run i think we need to TAS it up.
Oh and, another youtuber called Kevvl has done the same challenge in the Mega Man X games, so if someone doing the X series wants to do this, it should be possible in those games as well.
I think that may be a neat idea. But I think a TAS of the perfect runs for Megaman would be best done by AltimaMantoid's rules. His "Megaman Mantis-Style" uses RoahmMythril's rules plus the rule that you can't miss. That is, if any shot you fire flies off screen or get's deflected or absorbed by an enemy in it's invincibility frames, that counts as a failure.
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I think that now that Wizards and Warriors II and III have fresh TAS movies, it might be good to look at this first episode as well.
I just verified that both of Cardboard's movies sync on FCEUX 2.2.2.
The FCEUX times:
All Levels - 00:12:13.72
Reuse Levels - 00:09:34.47
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Thank you.
I was surprised myself that this much improvement was even possible. It's now probably much closer to a perfect fight since many of the blows dealt are fairly big, including one shot that dealt 80 HP damage to the Earth elemental and 3 shots that each hit two elementals. This latest fight may be the one to have in the publication since with such great luck with the hits, it is hard to imagine another major improvement.
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I can attempt to improve the hits with RAM watch. I do admit though that one of the complexities of this fight is that often a slightly less damaging hit is better because it allows for the next shot to be fired on a frame that makes it much more damaging. In theory, this tradeoff philosophy extends to sets of 3 or more consecutive shots, which is why I agree that this boss is a pain to optimize. If my current path is a perfect fight already, we may never find out.