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On February 11 2011 09:28 Dragar wrote:Show nested quote +On February 11 2011 07:20 natewOw wrote:
It's just fact? Where are you getting this "fact" from? Because I ran a simulation comparing 24 workers to 27, and 27 was netting me more minerals. Can you offer any evidence to back up your fact? Simulation? What happens in the game? I don't know either way, but surely it's better to look?
Just to put a nail in this one, I decided to actually test the minerals mined over a 1 minute period at 24, 25, 26, and 27 probes. I did the test on Steppes of War and allowed the probes to settle over a 2 minute period before taking any numbers. I also didn't test any number of probes less than 24 as I believe that range has been tested before.
24 Probes - Top starting position
Minute 1 = 785 minerals
Minute 2 = 790 minerals
25 Probes - Bottom starting position
Minute 1 = 810 minerals
Minute 2 = 785 minerals
26 Probes - bottom natural
Minute 1 = 815 minerals
Minute 2 = 810 minerals
27 Probes - top natural
Minute 1 = 815 minerals
Minute 2 = 810 minerals
Given these numbers, I don't think it's safe to say that 27 probes produces any more minerals than 24 probes. The variance in mining rates can easily be accounted for by the time I pressed pause and wrote down the numbers. If I had waited a fraction of a second longer or paused a fraction of a second sooner, the numbers would undoubtedly be different as probes are constantly dropping off minerals at the Nexus.
So yeah...sorry to say but I think 24 probes is the point of maximum saturation.
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There are way too many variables to even bother calculating the exact number of workers for optimal output. When you factor in time away from mineral gathering, such as constructing buildings (or sac'ing yourself to make a bldg, read: drones), scouting, losing workers to harassing, transferring to for efficient expo'ing, proxy pylons, making bunkers, repairing mech, it's simple to reach the conclusion that in 99% of occurances (with the 1% being a planned 1 base all-in without getting harrassed,scouting, or using the workers to attack at the end), more workers are better, until you can blatantly see that you're oversaturated) regardless of what economic principles you want to apply. Factor in the opportunity cost of building workers instead of your army, and what you're left with is a strategy game..not an economics game.
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On February 11 2011 10:26 supernovice007 wrote:Show nested quote +On February 11 2011 09:28 Dragar wrote:On February 11 2011 07:20 natewOw wrote:
It's just fact? Where are you getting this "fact" from? Because I ran a simulation comparing 24 workers to 27, and 27 was netting me more minerals. Can you offer any evidence to back up your fact? Simulation? What happens in the game? I don't know either way, but surely it's better to look? Just to put a nail in this one, I decided to actually test the minerals mined over a 1 minute period at 24, 25, 26, and 27 probes. I did the test on Steppes of War and allowed the probes to settle over a 2 minute period before taking any numbers. I also didn't test any number of probes less than 24 as I believe that range has been tested before. 24 Probes - Top starting position Minute 1 = 785 minerals Minute 2 = 790 minerals 25 Probes - Bottom starting position Minute 1 = 810 minerals Minute 2 = 785 minerals 26 Probes - bottom natural Minute 1 = 815 minerals Minute 2 = 810 minerals 27 Probes - top natural Minute 1 = 815 minerals Minute 2 = 810 minerals Given these numbers, I don't think it's safe to say that 27 probes produces any more minerals than 24 probes. The variance in mining rates can easily be accounted for by the time I pressed pause and wrote down the numbers. If I had waited a fraction of a second longer or paused a fraction of a second sooner, the numbers would undoubtedly be different as probes are constantly dropping off minerals at the Nexus. So yeah...sorry to say but I think 24 probes is the point of maximum saturation.
I think you just pointed to the opposite of your conlusion. You have an overall increase which seems to be fairly small but linear from 24-27 workers. Then you attribute that variance purely to error (which is random) and then you jump to the conclusion that error variance explaining your results means that 24 is optimal? I dont understand your logic. Plus if you are going to show me that your data is statistically non-significant i will point out that it is really not very applicable here for various reasons.
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If I may offer a suggestion: I believe you are not taking in to account the fact that all scvs cannot be mining simultaneously. This theory makes sense assuming an unlimited amount of patches to mine from and to account for this I think you are assuming a base expansion. Is that correct?
Also, mineral patches eventually run out. Maybe 27 workers should be the optimal level of saturation for one base but only 8 workers can mine at once. Perhaps in this situation all workers are not getting their optimum level of mining time because of the latency created when they have to wait to gain access to a mineral patch.
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MC is wrong and so is MR.
MC = 50
MR = the expected total minerals harvested by the end of the game from having that 1 extra drone.
At best MR is zero when all mineral patches are fully saturated and an extra drone just does nothing. It can never be negative.
By this method, I think you'll get the 'conventional' result that we should fully saturate our mineral patches. Most games will last long enough to be worth that.
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to expand on my post from the previous page, with a income advantage of only 20 minerals per min, it will take you 7:30 game time to pay for the 3 probes. as I mentioned earlier unless you chrono boost while building #25, 26 or 27 (which would be impractical to say the least) you will have a mineal lead over 24 probes for a maximum of 2:48 game time, at which point you will be completely mined out. Again as I said in my previous post these are perfect world no gas no downtime numbers, doing ANYTHING you would do in a normal game will result in fewer minerals being left when you get to 27 probes on minerals, making the margin even worse.
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5003 Posts
@OP: the reason why you're getting such bad responses is because you convoluted the entire thing in unneeded econ terms. Not that there's actually econ in this -- there's zero economics involved in your model which is why it's just confusing people
if you just stated it for what it is ("At what point do you stop getting positive returns for adding a probe") then no one would have an issue.
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I liked to read the OP. The usefulness in regards to actually playing the game can be discussed, but that doesn't make it irrelevant. Some people might enjoy relating StarCraft to economic theory and discuss it.
If people want to nitpick whether 24-27 (or another number) workers is optimal saturation, they should at least carefully consider the things which comes into play. I haven't, but stuff such as mineral formations on different maps comes to mind. That certainly plays a minor role when nitpicking.
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On February 11 2011 10:48 Genovi wrote:
I think you just pointed to the opposite of your conlusion. You have an overall increase which seems to be fairly small but linear from 24-27 workers. Then you attribute that variance purely to error (which is random) and then you jump to the conclusion that error variance explaining your results means that 24 is optimal? I dont understand your logic. Plus if you are going to show me that your data is statistically non-significant i will point out that it is really not very applicable here for various reasons.
How is it linear when 26 and 27 are exactly the same? Even 25 probes shows a range of 785 to 810 versus a range of 810 to 815 for 26 and 27.
You could argue that there is a small increase from 24 to 25 but my feeling is that this is attributable to variations in timing rather than some increase in efficiency. Minerals increase in increments of 5 only when the probe drops off the minerals. A probe that is a one pixel from dropping off minerals accounts for zero minerals exactly as a probe that is half done or a quarter done with his mining path. We have no way of accurately determining partial values so we have to accept some flex in the mining numbers.
In other words, if I had waited another half second, the numbers would be different.
My conclusion that the differences are insignificant is based on the range of values found even within a single probe count and small sample size.
I'll concede that I might be jumping to conclusions when saying that there is no difference between 24 and 25 since I'd need to do alot more iterations to rule out the variance but I'm comfortable saying there is no difference between 25, 26, and 27.
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Basically, the OP can be summed up like that:
Assuming that every probe mines forever and minerals never run out even the slightest increase in income (eg 0.001 minerals per minute) will result in a probe paying for itself.
All the ecobabble is completely irrelevant given the basic assumption.
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I have to criticize this analysis for the sole reason that the OP states at the end of the post that the results show how to get the most minerals from one base. This is an example of a statistical analysis that does not take game mechanics into account.
Getting the most minerals from one base (in the shortest amount of time) cannot be achieved by constantly making workers. I don't have the exact numbers handy, but as a few people have previously shown getting more than 25/26 workers does not increase your minerals per minute.
More importantly oversaturating the mineral line will increase the amount of time it takes to completely mine out one base. Even though the workers should mine out a base above saturation in the same amount of time, it seems that the increased frequency of "mineral bouncing" that happens when a probe reaches a saturated mineral patch actually decreases mining efficiency. In numbers above 28, oversaturation can increase the amount of time it takes to fully mine one base by 20-30 seconds (which is pretty significant if you are staying on one base).
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Thanks for taking the time supernovice007. 
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Hah, in economics when you have uncertainty about a variable you don't just assume its infinity and call that taking an expectation!
Thats like saying, I don't know what the stock market will do tomorrow so we have to assume its going to go to infinity, if you invest a penny today you'll be a millionaire tomorrow.
When you have uncertainty you have to actually take a MATHEMATICAL EXPECTATION by integrating over a distribution of possible game lengths.
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hm, im a little bit confused, cause i dont see why you would need all that economics stuff to answer your question. maybe thats because i missunderstood the question you tried to answer, so correct me if this is wrong:
you are trying to find the number of workers needed to maximize your income from one base(minerals mined from 8 mineral patches per time)
assuming adding workers increases income until theres a number of x workers after which adding more workers will not increase your income(respectively income stays constant or decreases because of workers getting into the way of each other), "all you have to do" is figure out the income for 1 worker, 2 workers, and so on until you dont see an increase in income.
i think from a theoretical point of view(assuming you know the game will go on long enough and there are enough minerals) its quite intuitive that up until that number x its "worthwile" to produce workers, cause all of them add to your income, thus eventually will "pay off" (after y minutes the additional income created through that worker will be higher than the cost of that worker).
i think you tried to explain that fact with all that "economics stuff", right?
so whether x=24 or x=27 or x=something else basically comes down to the numbers for the income you used. In your first post you wrote: "I generated predicted values of income per minute as a cubic function of the number of workers currently mining", which sounds to me like you used some kind of function to simulate those income numbers. if so you should show us this function and tell us why the values generated by it are the correct numbers for the income.
later on you said something like you used ingame observations to get those numbers. in this case i doubt your observations reflect the actual income rates, because there are sources of measuring error, for example:
1. How did you make sure you were measuring the income over the exact same time( and not 60.0 vs 60.5 seconds or something?)
2. How did you make sure you did not start measuring the income for 24 workers 1 millisecond AFTER 8 workers brought in a mineral patch and the income for 25 workers 1 millisecond BEFORE 8 workers brought in a mineral patch?
these two things alone might falsify your numbers enough to bring you to wrong conclusions.
on another topic: i unterstand that you approached this from a theoretical point of view, but if you want to find applications in actual games, you probably have to consider the maximal number of minerals that can be mined. for example, the whole map is mined out except for one base. according to your numbers getting a 27th worker on minerals might be ok, because he pays of after 20 minutes, but in reality the last base will be mined out after 15 minutes, so you are actually losing minerals with the 27th worker
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Your argument that the marginal cost is 0 is obviously incorrect, because games do not last infinitely long. If you know you're going to all-in in 10 seconds, then building another probe will not net you increased income.
Also, what evidence is there that increasing your worker count from 24 to 27 actually increases your income? Your graph says it, but your graph already assumes that having more miners past 24 will increase your income. It doesn't seem to consider max saturation.
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If nothing else, OP is doing a great job at reinforcing the stereotype of economists among engineers - takes some data, applies numbingly simple analysis and covers it all in unnecessary terminology, and then fights off all and any critic to the ill-fitting model with beak and claws.
Why does the marginal revenue go down from 7 to 8? The increase in income should be 100% linear, since the 8th worker is using a patch previously unused. Why does it go down between 9 and 16? Each of those workers modify a patch worked on by 1 worker into a patch worked on by 2 workers - the increase in income should be the same for each of these. Why? Because you've applied a poor model to the data - it even goes negative at a point, something you defend by pointing to cluttering, rather than acknowledging the limitations of your model!
Also, letting time go to infinity thus saying that the expected marginal cost for adding a worker is zero is very strange - why did you even bring up the subject if you're going to throw it away by making odd assumptions? The concept really lacks meaning when you do such a thing.
Finally, please consider using a lower-case t for time, my eye twitches too much otherwise.
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Playing the game a lot and looking to actively improve through experience and getting a great feel for the game is more effective than applying overly complicated economic principles and being more mathematically analytical than is necessary. I feel like I'm in an internet poker forum.
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Didn't anaylze your formulas too much (to be honest it doesn't seem that strange that more workers = more minerals) but:
1. Workers cost supply (roughly 12.5 minerals each)
2. There aren't infinite minerals. It should be fairly easy to get a total mineral count for each map and then average them to determine a limit.
Not sure what effect these things have on your determination, but with a slightly higher probe cost, I'm guessing the extra probes take a little while longer to pay for themselves.
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EPT
