EPTI like the experimentation by d3_crescentia, suits perfectly to my engineering mind, haha.
Maybe someone should try the thing with zealots, yes, more protoss love please~
Math in Starcraft pt.1 - Page 2
| Blogs > ShinyGerbil |
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OpticalShot
Canada6330 Posts
I like the experimentation by d3_crescentia, suits perfectly to my engineering mind, haha. Maybe someone should try the thing with zealots, yes, more protoss love please~ | ||
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ShinyGerbil
Canada519 Posts
@ d3_crescentia, wow it's awesome that you went though all the trouble to get those results. I think it's really cool to have an experimental aspect to these ideas, to compliment the theory. Many thanks! | ||
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d3_crescentia
United States4054 Posts
I ended up taking data for 13v12 and some other instances. Have some graphs: ![[image loading]](http://img.photobucket.com/albums/v312/vdraconis/zerglings5-1.jpg) A short explanation: since it's difficult to evenly spawn the two symmetric parallel lines of zerglings since one is odd and the other is even, the 13th zergling was added to either the top or the bottom of the line. I tried these instances with both Linear2 and 3 line separation distances (refer to my earlier attempts for a better idea). Looking at the graph of Linear3.1 specifically it's here where we start to realize that 100 trials is definitely not enough to give us accurate data. Still, it seems to suggest a peak at either 4 or 5, which is close, given the imperfect nature of the experiment. ![[image loading]](http://img.photobucket.com/albums/v312/vdraconis/zerglings6.jpg) To see if anything interesting would happen, I added the results from Linear2.1 and 2.2, and 3.1 and 3.2 together and plotted them, though this would compound the experimental error significantly if I was doing this seriously (for that matter, if I was doing this seriously, I wouldn't be using Excel). Again, suggestion of a peak at 4-5, but we need more trials to be accurate. ![[image loading]](http://img.photobucket.com/albums/v312/vdraconis/zerglings8.jpg) Lastly, some other trials for people that are interested. These are runs of 101 trials of Linear2 setup (with the exception of 18v15) - enough to suggest peaks, but we're starting to get to the point where 100 trials is not enough. We have a predicted peak for 17v15 at 8 and an actual at 9-10. For 20v16, this is simply a multiple of 10v8, which should give a peak at 12, but more trials are necessary to see if it does indeed occur there. It could also be that the mathematical model fails at larger numbers of zerglings for whatever reason. *The run of 18v15 was entirely a mistake - I set my triggers to spawn an extra zergling in the 17v15 run. By the time I had noticed, it was already >70% completed. Truth be told, this data doesn't look too bad, as the peak should be at about 10 (root(99) to be exact), but again - more trials to be sure. + Show Spoiler [Speculation] + Discounting the points at zero, it seems that the distribution climbs more gradually before the peak and falls more steeply after the peak. Having been trained as a physicist, I've only encountered such a graph once before. If we reverse the x-axis and define it in terms of zerglings lost for player 1 (with the surviving zerglings simply being added to the 'lost' count), then we can get something that looks like: ![[image loading]](http://upload.wikimedia.org/wikipedia/en/5/5d/Maxwell-Boltzmann_distributionPDF.png) The Maxwell-Boltzmann distribution for particle speeds in gases. Of course, more trials may end up telling us that this is not entirely the case, and I can't discount the fact that I'm just pulling things out of my ass right now. But, if there's a connection between the two (as unlikely as it is), I'll see if I can't find it. I also tried experimenting with different concave formations in the 10v8 scenario to see if the 8 could win, but none of them turned out very well. Some conclusions/possible improvements: - Probably a good mathematical model for 1-2 control groups of lings under ideal circumstances. - The next possible avenues of inquiry involve different zergling formations (clumps, perpendicular lines, concave) or with larger groups of lings and more trials. - Zergling AI, while not as bad as Dragoon AI, can still be pretty bad. - Possible UMS improvement - having an internal counter of each trial, as I double-checked the leaderboard after every engagement (not difficult, just tedious). This is rather difficult/boring with StarEdit alone, but I don't think it will be too much better with SCMDraft. This was a lot of fun - I miss doing scientific-ish things, so it was refreshing and entertaining to do it for SC. It was also nice to work on a UMS map again, especially since I have a tendency to set projects too big for me to finish quickly. If you come up with other things to experiment, let me know and I'll see if I can give it a shot testing it. | ||
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figq
12519 Posts
On January 10 2010 20:22 ShinyGerbil wrote:So as we can see, if an army of ‘a’ Zerglings engages an army of ‘b’ Zerglings with a>b, the remaining number is speculated at sqrt(a^2-b^2), which I found very interesting because it maps out the sides of a right angled triangle (Pythagorean Triples). Some interesting applications include: Indeed, due to fragmentation of armies most calculations are based on L2-normed space (or Pythagorean metric), adjusted to include standard deviation, due to non-deterministic randomness. The volatility factor is quite high, so this makes the outcomes of most evenly matched battles fairly unpredictable. Therefore, people shouldn't be too quick to conclude anything from the outcome of a Starcraft battle.5 vs 4, 3 survive 13 vs 12, 5 survive 17 vs 15, 8 survive | ||
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G3CKO
Canada1430 Posts
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Garrl
Scotland1975 Posts
If anyone can give me a clear rules of what perfect micro is, I could try it (and probably fail, but that's besides the point). | ||
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Impervious
Canada4216 Posts
+ Show Spoiler + For individual controls, I'd guess that they should retreat before dying (with 1 hit left on them, waiting for their health to return), as well as retreat from 1v1 battles where they will lose (ie, they have less health than the enemy unit). They should run from 2(+)v1 battles (unless they will win them), and attempt to engage in 2(+)v1 battles (unless they will take any casualties). Target priority should go to the enemy units with the least health left. Attempt to prevent overkill somehow as well..... After that, you'll have to incorporate multi-unit positioning into it, to form concaves, and trap running enemies. That will be much, much trickier..... And then, there are times where taking some damage gets multiple units into better positions, allowing the combined group to do much more damage than if the individual followed the set rules..... There will also be times where one needs to retreat, to give another room to retreat to prevent it from dying..... this part will be next to impossible to code, if not impossible..... Of course, if you were to do this with the group with less lings, and have normal micro on the group with more, I would fully expect them to win without taking any casualties (assuming a large space to work with, and more than 1 ling is involved for them)..... If it was done right, I doubt Jaedong could win with 2X the lings..... It might be powerful enough that it could eventually defeat hundreds of lings under his control with only 2 under perfect micro. | ||
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illu
Canada2531 Posts
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Megaman703
Canada688 Posts
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Exteray
United States1094 Posts
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nosliw
United States2716 Posts
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Ivs
Australia139 Posts
2F.F' - 2G.G'=2F.(-kG) - 2G.(-kF) = 0 gives you that F^2-G^2 is constant and the rest follows. | ||
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illu
Canada2531 Posts
On June 01 2010 10:59 Megaman703 wrote: the US has stolen enough of our doctors, scientists and engineers, they don't need to steal our SC players, thank you very much. We steal those from Third World countries... | ||
]343[
United States10328 Posts
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meeple
Canada10211 Posts
On June 01 2010 10:26 illu wrote: let this guy go to berkeley... Edit: I was mistaken... Also... I love this theoretical gaming stuff. I was working with my game theory prof to do some simplistic starcraft analogies a little while ago. | ||
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