EPT************ADDED SOMEWHERE ON PAGE 2************
Timings on 6pool through 14pool, using the various orders. Supershort results: 12pool with double extractor before overlord, 11pool with single extractor before overlord, but 13+pool should always be with 9OL. Also, never ever ever overpool. 11pool with extractor trick is superior in every possible way.
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tl;dr version:
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I used the AI to test the various builds in a very consistent manner, to try to answer the question once and for all.
The 9 overlord is the best economic build, period.
Minerals at 2:15: 370
10 overlord can be used for 10pool and overpool, but is inferior to 9OL in every other possible respect to the tune of 10 minerals, and loses the small window of advantage it gets by building the 10th drone sooner by the time 10OL finishes its 11th worker.
Minerals at 2:15: 355
A single extractor trick doing the trick before building the overlord (11 drones then overlord) gives a small time window of about a 15 mineral advantage, between workers 11 and 14, but there's a cost, of around 5-10 minerals. Best case, you *might* be able to break even when compared to 9OL, but most of the time you'll lose 5-10 minerals.
Minerals at 2:15: 364
Single extractor trick after the overlord (10 drones, overlord, trick to 11 drones) is inferior to 10-T-OL in the 11-13 worker range, and is inferior to 9OL in the 14-15 range, so I honestly see no reason to ever trick this way, UNLESS you meant to 9OL, but forgot the overlord. In that case, this is your best way to try to catch back up, because the cost is 0-5 minerals instead of 5-10.
Minerals at 2:15: 369
The double extractor trick provides such a small advantage over the single extractor trick during even a smaller window that it should probably only be used exactly to 12 pool, and even then, there is an extra cost over the single extractor trick. It probably compares to the single extractor trick much like 10OL compares to 9OL, meaning that if you're doing something exactly on drone 12, you might use it, otherwise, the single trick is probably strictly superior.
Minerals at 2:15: 353 (imprecise, but again, likely strictly inferior to single trick except for fastest 12pool)
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BTW, are you concerned yet that the tl;dr version is that long?
Full version
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In an attempt to put this question to rest once and for all, I decided to set up a computer player to perform everything at as close to the exact correct timing as possible. There are many advantages to testing this way rather than testing on your own, the primary reason being that the computer can be much closer to perfect than you.
Computer players do a pretty dang near-perfect 3/3 split (a lot better than any 3/3 split I've ever seen in a replay), and with some manual rally-point management as well as spending a *lot* of time trying to figure out exactly when the best time to trigger the extractor trick was (and how to do it to begin with in the map editor, which definitely was not easy), I was able to get truly consistent timings. What I ended up with was the as near-perfectly as possible for the first 15 drones, and certainly performing much better than any player could, especially performing the extractor trick, where the AI is able to perform a number of completely separate actions at the exact same time. (build a drone, cancel an extractor, put a worker back on minerals)
Note that there was actually some amount of variation here. This shocked me at first, because the timing numbers would come through and match EXACTLY, even for entire sequences up to 15 drones, down to the one-sixteenth of a second that it looks like the timer resolution might be. Which makes perfect sense, because the computer player is going to make the exact same decision at the exact same time *every* time.
But there turned out to be quite a lot of variation. I'd only see 2-3 patterns of timing, and once the pattern was established, it would match exactly, but there was as much as a full second's difference in later drone start timings. I puzzled over this for a really long time, and then as I was watching a sequence and saw a cocoon pop up, it hit me.
Larva movement is random, and the start position of your larva determines how far the drone has to move once it's been created. What's surprising is that this one little thing can make a rather large difference.
Since there was quite a bit of variation, I ran through a number of times, and picked out the most consistent timings for each variation. Anyway, the point here is that although this test was not absolutely consistent (even though I thought when I started that it should be), it's definitely going to be more consistent than testing by hand.
With no further ado, here are the results. sdXX is when drone number XX was started, and FDXX is when it completed building. Each point records the exact time, as well as the number of minerals that the player had at that point. sovl and FOVL represent the overlord, and EXTR and CANC are the extractor when doing an extractor trick. I also printed the number of minerals at 2:15 (135 seconds), by which time all 3 builds were complete. Time measurements are all in gametime, not real time.
9OL
sd07 0 0
sd08 15.9375 0
FD07 17 10
sd09 26.5625 5
FD08 32.9375 30
FD09 43.5625 80
sovl 46.625 0
sd10 54.375 0
FD10 71.375 105
FOVL 71.625 60
sd11 71.625 60
sd12 71.6875 10
sd13 78.125 0
FD11 88.625 70
FD12 88.6875 70
sd14 91.875 30
FD13 95.125 65
sd15 106.938 110
FD14 108.875 125
FD15 123.938 270
At 2:15, this build had 370 minerals
10OL
sd07 0 0
sd08 15.9375 0
FD07 17 10
sd09 26.5625 5
FD08 32.9375 30
sd10 38.9375 0
FD09 43.5625 30
sovl 55 10
FD10 55.9375 10
FOVL 80 120
sd11 80 120
sd12 80.0625 70
sd13 80.125 20
sd14 95.25 75
FD11 97 85
FD12 97.0625 85
FD13 97.125 85
sd15 110.813 140
FD14 112.25 150
FD15 127.813 290
At 2:15, this build had 355 minerals
There is exactly *one* point of time where 10OL is ahead of 9OL. From 55.9375 seconds until 71.375 seconds, 10OL has one more worker running, for a gain of about 15 worker seconds. But 9OL finishes drones 11 and 12 almost 10 seconds faster than 10OL, so this 15 second advantage begins to be lost at 88.625, and is completely gone somewhere around 96 seconds in. After that point, 9OL is ahead of 10OL in every way. It finishes the 15th drone 4 seconds faster, and is 15 minerals ahead at the 2:15 mark.
As a result of this, the only situations where it is not better to 9OL are when you are 10-pooling or overpooling.
SINGLE EXTRACTOR TRICK BEFORE OVERLORD (or 10-T-OL)
sd07 0 0
sd08 15.9375 0
FD07 17 10
sd09 26.5625 5
FD08 32.9375 30
sd10 38.9375 0
FD09 43.5625 30
EXTR 49.6875 45
sd11 50.3125 0
CANC 50.3125
FD10 55.9375 49
sovl 64.375 4
FD11 67.3125 29
FOVL 89.375 139
sd12 89.375 139
sd13 89.4375 89
sd14 91.5 44
FD12 106.375 159
FD13 106.438 159
sd15 106.563 114
FD14 108.5 129
FD15 123.563 249
At 2:15, this build had 364 minerals
This is a little more difficult to figure, so lets start with the easiest result: at 2:15, this build was exactly 6 minerals behind the 9OL build. That amount happens to be exactly what you lose from the extractor cancel, although technically it works out that you're 10 minerals behind, not 6, since there's nothing you can ever spend 4 minerals on.
Now the hard part: figuring out exactly where this has an advantage over 9OL. Drone 10 finishes at 55.9375, and drone 11 finishes at 67.3125. So we gain 15.43 worker seconds on drone 10, and 21.31 worker seconds on drone 11, for a total of 36.75 worker seconds. At 88.6875 seconds in, 9OL finishes worker 12 ahead of the extractor trick, gaining 17.69 worker seconds back on drone 12, and also finished worker 13 11.31 seconds ahead, which leaves a 7.75 worker advantage starting at 106 in seconds unaccounted for, which only builds on drones 14 and 15, becase 9OL finished them both about a third of a second later than the extractor trick. Call it 8.5 seconds for good measure.
So the extractor trick *should* be 8.5 worker seconds worth of mining ahead of 9OL, but ended up being at exactly the same point mineral-wise, minus what was spent on the extractor. Some of this is the loss of time for the worker building the extractor. This drone building the extractor is the one closest to the extractor, and it drops off minerals at 47 seconds, builds the extractor at 49, and touches the minerals after cancelling at 52 seconds, basically taking around 5 seconds to get from base to mineral patch, a trip that normally takes about 2 seconds.
So that accounts for 3 seconds, but we should still be 5 seconds ahead.
Well, it turns out that 5 seconds is less than the amount of time it takes for one worker to collect and return 5 minerals. So for a lot of extra complexity, we've made a very small gain in time, but not gained enough time to overcome the loss we take from cancelling. Again, there is quite a bit of variance here. I saw 2:15 marks from 364 to 374, with 364 being the most common.
There is a period here though, where this build has a 36.75 worker second advantage though, which works out to be somewhere around 25 minerals (or 15, after taking out the extractor trick penalty). If having an extra 15 minerals between the 11th and 14th drone speeds things up enough that it's worth 5-10 minerals later, then the extractor trick is worthwhile. So 12-14 pools could extractor trick rather than 9OL (but could also choose to 9OL if the 5-10 minerals aren't worth the slightly increase pool speed), everything else should 9OL.
If you perform the extractor trick well, that is.
SINGLE EXTRACTOR TRICK AFTER OVERLORD (or 10-OL-T)
sd07 0 0
sd08 15.9375 0
FD07 17 10
sd09 26.5625 5
FD08 32.9375 30
sd10 38.9375 0
FD09 43.5625 30
sovl 55 5
FD10 55.9375 10
EXTR 65.6875 45
sd11 66.1875 0
CANC 66.1875 0
FOVL 80 64
sd12 80 64
sd13 80.0625 14
FD11 83.1875 29
sd14 91.1875 34
FD12 97 89
FD13 97.0625 89
sd15 106.313 99
FD14 108.188 114
FD15 123.313 254
369 at 2:15
Over a number of runs, the final mineral result bounced pretty consistently from 369-374, which gives an overall cost of 0-5 minerals, which is better than 10-trick-OL by 5 minerals. If we compare this build to 10-T-OL, we can see the following:
Drone 11 comes out 15.875 seconds later, putting us behind by that many worker-seconds at 83.1874 seconds. We start to gain this back on drones 12 and 13, which are each faster by 9.375 seconds, and that both finish at 97 seconds. So at 104.9375 seconds, this build has caught back up to 10-T-OL, and at 106.375, we're ahead by 2.875 worker-seconds. We gain another .312 seconds on drone 14, and .25 seconds on drone 15, giving us a grand total of 3.4375 worker seconds advantage over 10-T-OL.
BUT....
We already know that both of these builds are behind, or at best equal to, 9OL, which is far easier to execute. The only reason to doing the extractor trick at all is to get an advantage at some point in the 10-15 worker range in order to get some building out faster. 10-OL-T has a smaller advantage over 9OL than 10-T-OL in the 10-13 range, and has a very negligible advantage over 10-T-OL at around the time we hit 15 supply.
So if we want to build in the 12-14 range, 10-T-OL clearly has an advantage in that time range, and if we're waiting til 15 supply (the only time 10-OL-T has an advantage over 10-T-OL), then we should just 9OL.
At the end of all that, 10-OL-T seems inferior to 10-T-OL in the 11-13 range, and inferior to 9OL in the 14-15 range, so there doesn't seem to be any valid reason to ever do this build. The only reason I can think of would be to be less behind if you meant to 9OL but forgot the overlord. In that case, tricking after the overlord will put you less behind than tricking before the overlord.
DOUBLE EXTRACTOR TRICK
The AI does not have enough flexibility to allow it to do a double extractor trick optimally. Specifically, I wasn't able to tell specific workers exactly where to build, and it makes poor decisions about when and where to take extractors and which workers to use in this case. What I can do though is extrapolate some numbers based on when the extractor trick would start, and the fact that we know it takes about 3 seconds of time away from the workers building the extractors.
We would be starting the double trick at around 55 seconds (the time when 10OL starts an overlord). This has drones 11 and 12 finishing at 72 seconds, giving us a 33 worker-second advantage for these two drones over 9OL. We lose some of the worker 11 advantage we got from 1 extractor trick by delaying though. We get 33 seconds for 11 and 12, but we were getting 21 seconds on just 11 before, so we gain 12 more worker seconds. 12 worker seconds is worth somewhere around 7-8 minerals, and it cost us 5 to do the second extractor trick. So we've basically gained 2-3 minerals worth of worker mining time over a single extractor trick, and that's only if we do things completely perfectly, which is a lot harder to do with a double cancel. In addition, drones 13-15 will be even more delayed, giving 9OL more of a chance to catch up or even pass us.
I would guess that the only time you should even consider doing a double-extractor trick is if you're going to double-trick, and build your pool on 12 before your overlord. The advantage simply isn't big enough compared to the double-extractor to make anything else worthwhile.
I did let the AI run a double-extractor trick, but it was fairly sub-optimal, wasting somewhere around 5-10 droneseconds due to poor choices when building the extractors. The tests that I did run though, showed it finishing drone 15 later (by many seconds) than the other builds, and showed it finishing with 343-353 minerals at 2:15, or 10-20 minerals behind the single trick. I would guess that an optimal build would bring that closer, but drones 13, 14, and 15 are all going to be later in a double extractor trick than a single, and I don't think the time gained from worker offsets that.
KICKS AND GIGGLES: 8 OVERLORD
Just for grins, I plugged in an 8OL build. Posting timings really isn't necessary, because this build is behind 9OL at every point, and ends up with a 25 mineral deficit. Basically, never build your overlord before 9. Ever.
