# Posts for numerics

##### numerics
Posted: 1/10/2014 5:24:47 AM Off topicsome math challenges.
Experienced Forum User,Published Author,Player   (230.4)

Joined: 11/17/2013
Posts: 9
I just finished commenting on that video. Fancy that. Some of the assumptions I noticed: 1) 1-1+1-1... = 1/2 (wild theorycrafting about the nature of infinity) 2) The power series for 1/(1-x) being valid at x=-1 (the power series is only valid for |x|<1) 3) Using analytic continuation to say the Reimann Zeta function converges for s<=1 ("Well the definition says P, so let's assume Not P and see where that gets us"). I can use analytic continuation to find factorials for negative numbers, it doesn't mean my result has any meaning. 4) That it kind-of makes sense because you go "all the way to infinity" instead of using partial sums. If you're going to make me include infinity as a number in my calculation, then you're working in the Extended Reals and all bets are off. You can use 1-1+1-1... and creative use of parentheses to prove that 0=1. You have to be careful when doing anything with non-convergent series, and I don't see any of that in the video. I'm okay with non-mathematicians skimping on the mathematical rigor in favor of application, and under normal circumstances I would have been fine with a non-intuitive answer if there was real world evidence backing it up. But this is an extreme case of that and I'm going to need something a little more "real world" than string theory or quantum field theory to accept it. And honestly, if you need a non-convergent series to have a finite value for your theory to work, maybe the proper response is to take a step back and question whether or not the universe really has 26 dimensions.
##### numerics
Posted: 1/7/2014 1:50:14 AM The Newbie CornerDTM files (Dolphin Emulator)
Experienced Forum User,Published Author,Player   (230.4)

Joined: 11/17/2013
Posts: 9
A frame with no controller input looks like this: 00 00 00 00 80 80 80 80 There's a couple of them in your screenshot starting at 0x100. If you just put a bunch of nulls then it translates to mashing down left on the joysticks, so that could be messing you up. I'm not exactly sure what you're going for though. If you're removing frames it might be causing desyncs with the RNG, or maybe you accidentally edited the header or misaligned the frames. You might also miss an input if it gets shifted into a lag frame, which would probably happen pretty often if the game has a lot of pauses.
##### numerics
Posted: 1/4/2014 11:03:48 PM Off topicsome math challenges.
Experienced Forum User,Published Author,Player   (230.4)

Joined: 11/17/2013
Posts: 9
Oh snap a math thread. I'm in. The probabilities are different but the decision is the same because in neither case is it a disadvantage to switch. If the issue is random goat vs. standard Monty Hall then you're decision is always to switch. That said, there are host strategies where it's better to stay, like you said. Suppose he had the following strategy: 1) If the player picked a goat, open the player's door (2/3 chance) 2) If the player picked the car, open a different door (1/3 chance) In the 1/3 chance that the host didn't open the player's door, you are guaranteed to get the car if you stay. In this case it looks like the standard Monty Hall problem but you're actually better off staying. Even though the individual round looks identical to Monty Hall, knowing the host's strategy greatly affected the probabilities. Likewise in the random goat vs Monty Hall strategies, knowing that the host could have picked the player's door makes the random strategy a 50/50 instead of the Monty Hall's 33/66.
##### numerics
Experienced Forum User,Published Author,Player   (230.4)

Joined: 11/17/2013
Posts: 9
Oh okay, no worries then. I was under the assumption that Time displayed == Time to finish.
##### numerics
Experienced Forum User,Published Author,Player   (230.4)

Joined: 11/17/2013
Posts: 9
I'm glad you brought this up, because this is something that bugged me when I wrote up the submission info. I considered both "time" and "entertainment" primary goals, but at the end of the day I went with "time" because I would have considered the TAS a failure if it didn't beat every existing run. Based on other submissions and the default prefill text, I interpreted "Game Objectives" as "what kind of categories would the run fall under." If I were to write them based on what I had intended the run to be, it would look like this:
- Make a run that is entertaining to both the TAS crowd (who value creative optimization strategies) and the Smash crowd (who value style). - The run must be acceptable for publication on this site (that is: beats all existing records, contains no obvious optimization flaws, etc). - KOs should involve a high degree of variety. Use items and stage hazards whenever possible. - Entertainment tradeoffs are only acceptable if the optimum solution is boring. Nobody wants to watch Samus down tilt everything in a team battle. - Optimal play. That is, if I'm going to perform a certain combo, it should not be possible to do it faster.
I'd rather have this as the Game Objectives section because I think it's more descriptive of my actual objectives. I wouldn't be surprised if it was too late in the submission process to change it though. I'd also like to change the branch to "Adventure Mode", but again, probably too late. Unrelated: I noticed the time was changed to 10:23.48. I really don't think the post-Giga Bowser content should count towards the official time. None of it is necessary to beat the game (the game finishes by itself after you press Start after beating him), and since I didn't skip anything there would be a solid 2 minutes of wasted time at the end. If you need a trimmed version of the input file for official timing purposes I can get you one.
##### numerics
Experienced Forum User,Published Author,Player   (230.4)

Joined: 11/17/2013
Posts: 9
Dont forget the stages where I outspeed him: Stage 1-1: -3.4 Stage 2-2: -3.55 Stage 3-1: -4.41 Stage 3-2: -1.65 Stage 5-2: -5.56 Stage 5-3: -7.39 Stage 7: -23.52 Stage 8-1: -11.38 Stage 10: -6.5 Stage 11-1: -9.5 Stage 12-1: -1.03 Stage 12-2: -23.77 Even if we leave out the huge differences to account for the fact that he wasn't going for time, that's still -42.99, which comes out to -7.23 overall. Samus and Fox are different characters with different movesets who excel in different situations. Recent TASes have gotten the Escape from Brinstar stage down to 6 seconds for Fox. Perfectly optimized Samus will never be able to beat that. Likewise Fox will never be able to beat Samus' time against the cars on the Grand Prix stage. It's all about the tradeoffs from using one character over the other. Very rarely will you ever see a character outperform another in every aspect of the game. Even Pichu has some advantages over Pikachu. As for the credits, I see where you're coming from, but I disagree with removing it from publication. The audience is going to have to sit through the credits anyway, might as well entertain them. It doesn't affect the time of the run in any way. And I'm not sure, but I believe this exception has been made before. Correct me if I'm wrong. On that note, if the admins want a trimmed version of the input file to prove that the game does complete by itself after frame 31,364, I can provide that.
##### numerics
Experienced Forum User,Published Author,Player   (230.4)

Joined: 11/17/2013
Posts: 9
Most of the changes you get from having everything unlocked are trivial. The only thing I could see affecting the difficulty would be having to fight Metal Luigi along with Metal Mario. Everything else is just "substitute this character for this other character you've unlocked," and even that doesn't happen very often. You also get a couple more names in the credits, but that shouldn't matter for the overall run. I wouldn't be surprised if they came out with a version that played this game correctly since I started the run, but I doubt it would play the input file correctly. I remember reading somewhere that the core changed often between releases for the earlier versions. Some names don't show up until you've unlocked content, i.e. you wont get Marth's voice actor until you've unlocked Marth. I can guarantee you I hit all of them, I spent more time on the credits than on any other segment. The ICs spawn on a timer. No matter what you do they're always going to appear at the 3:08 mark. The best you can do is be prepared to hit them on frame 1.
##### numerics
Experienced Forum User,Published Author,Player   (230.4)

Joined: 11/17/2013
Posts: 9
Thanks for the positive responses! Yup, they spawn on a timer. When I first started this run I thought it was determined by distance covered too, but after I told a friend, he said otherwise and went home and confirmed it was a timer. And then I went home and confirmed it was a timer. There's a couple other TAS's on youtube, and the Popos always spawn at around the 3:08 mark. I went into this with every intention of using items all the time, but they just don't spawn often on Very Hard. The timing is scripted (although the actual item and its location are manipulable), so there was nothing that could be done to get more. This particular game desyncs constantly in the most recent versions of the emulator. My research told me that r7719 was the latest stable version that worked for this game, which is why I went with it. I ended up writing a program to brute force the a/v sync, manually adjusting the frame dumps after the fact. Worst case scenario, I can get a high quality dump and send that to somebody for encoding. I assume it would be preferred for the emulator to do it, though. I don't know if the source code for this particular version is publicly available.
##### numerics
Experienced Forum User,Published Author,Player   (230.4)

Joined: 11/17/2013
Posts: 9
Hey guys, I'm new to this so let me know if I missed anything. I'm sure there's something. Also I'm not sure where it got the 08:38.3 number from. The input file is 10:23.48, and the last frame of input necessary to beat the game is 08:42.73. Thanks!