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Background
Most TvP games today feature the Terran going for a 1 Factory, 2 Factory or 1 Factory & 1 Starport opening. The standard build orders for the 1 Factory build try to maximize the mineral mining rate for faster CC and the like and as such tries to optimize the amount of SCVs on Gas in the early phase. Anything more agressive like 2 Factory or 1 Factory & 1 Starport requires more gas and thus 3 SCVs on Gas all the time after its completion. A regular Protoss player exploits and is most often able to read the Terran on how he will tech depending on the amount of SCVs on Gas.
Afterall by the time the second Factory will go up or a Starport is being built proper marine and SCV micro can deny the scouting information, but he will still know something fishy is going on if he saw 3 SCVs on Gas and will prepare accordingly.
The question is, how many minerals do you gain from putting SCVs back to minerals and then back on gas. And is there any more "optimal" way of managing your SCVs?
Definitions
* We let t denote the ingame Starcraft time-unit that is independent of the game speed and s denote real time in seconds that is dependent of the game speed.
The following holds approximately at the fastest game speed: 1 s = 1.6 t or 1 t = 0.625 s equivalently. Henceforth we will stick to the ingame time unit.
* Let m/t denote the gathering rate of minerals per time-unit and m/s the gathering rate of minerals per second.
Assuming that any worker could have 0 travel path from the CC to a mineral patch the maximal gathering rate is then 1.5 m/t or 1.5*1.6 m/s = 2.4 m/s. The reality is different and as it turns out; at the standard mineral distance one SCV will gather 0.68 m/t which is about 45% of the maximal mining rate one mineral patch can deliver.
Data
The data is taken from a future post of mine that will discuss optimal mining in detail. It represents the amount of minerals mined per time unit on a "general" 9 mineral patch main @ Python. I will not go into detail of what the different data represents or how I obtained it but will rather just present the results.
Also note that the almost horizontal section around 13 (1.5 SCVs per patch) to 23 (2.5 SCVs per patch) is due to worker wandering. Also note that 1
This represents the marginal benefit to the mining rate of adding one SCV. For example if we have 12 SCVs mining then our mining rate would be 8.1 m/t as seen in the upper graph. Adding an additional SCV would increase this rate with about 0.8 to 8.9 m/t. Which is the mining rate of 13 SCVs.
One can readily see that you gain an negible amount mining by adding SCVs when you have 12 to 22 SCVs mining. And you gain the most between 0 to 9 and then 22 to 26. After 26 you've fully saturated your mineral patches and gain nothing from additional SCVs.
Mechanics
Max Mineral Mechanic: (16 Fac - 1 Gas)
The current widely used mechanic consists putting 3 SCVs on gas at the rafinery completion and then building a Factory on 16 supply. At 16 supply you will have 1 SCV scouting, 1 building another supply and 1 on gas (removing 2). Then at 20 supply when the Factory is complete you will have 17 SCVs mining and you transfer 2 SCVs to gas again, totalling you 15 mining SCVs.
Max Gas Mechanic: (16 Fac - 3 Gas)
This consists of always having 3 SCVs on gas and thus only having 11 mineral SCVs at 16 supply.
Optimal Mechanic: (16 Fac - 1 Gas, 17 - 2 Gas, 18 - 3 Gas)
The difference between this and the mineral mechanic is that you take away 2 SCVs on gas at the start of the Factory but then each new SCV built is being put on Gas instead of on minerals up to 3 SCVs on gas.
Results
Max Gas vs. Max Minerals.
Max Minerals has a total mineral gain of 33.2 + 17 + 0.2 + 3.1 = 53.5
Max Gas vs. Optimal
Optimal has a total mineral gain of 33.2 + 16.9 + 0 + 0 = 50.1
Conclusion
The "Optimal Mechanic" is obviously optimal because not only does it give you more gas if you would decide to change gears and change your build order instead of say expand but also does it allow you to fool your opponent into thinking you're going for a gas heavy build, or at best leave him in the dark.
Any comments are appreciated!
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A terrible terrible day for protoss.
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if i understood this right, taking 2scvs off gas, until factory is done only gives you a plus of 3 minerals in comparison to your optimal solution? i find that sort of hard to believe, that would mean that the scvs that are built in the time the factory is made, only mine 3 minerals until its done?
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Wurzelbrumpft. That's correct. The reason is worker wandering in SC.
Ideally one SCV will mine one mineral patch at 45% capacity. Meaning two SCVs will mine one patch at 90% capacity, but not really because of wandering. This means, whenever one SCV arrives at a busy patch he won't always wait for the other SCV to finish but rather go to a nearby patch and try to mine it. At some SCV populations this is even amplified as you can see in the first graph around 13 to 22 SCVs. There wandering is really high and those additional SCVs spend much of their time wandering instead of mining. In fact you can see how many mineral patches at these populations are idle not being mined on.
Edit: Of course these 3 minerals won't always be 3 minerals but on average. Sometimes it can be less, sometimes more.
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GrandInquisitor
New York City13113 Posts
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Yeah, but what about if you micro all your SCVs individually to minimize wandering? 
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This was interesting, can you do it for P too? IE the economic impacts of various scout times and or build orders?
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A great read for when I occasionally screw around in TvP.
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I liked this post
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intrigue
Washington, D.C9935 Posts
pretty nifty! the limiting resource in the speed of standard 1fact cc the minerals though, so though it's less efficient it is probably better in the long run (getting your nat up faster) to do it the standard way. the timings of this could definitely confuse your opponent though.
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I would just like to know the number of trials that you took to produce the mining rate vs no. scv graph data. (I know you will post it later, but I cannot wait xd).
Thanks.
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Muff2n: I mined the 9:clock main with said number of SCVs for 2 queued battlecruiser building time. That is 2*133 time units. Then I used http://www.teamliquid.net/forum/viewmessage.php?topic_id=92971 to see how the 9:clock compares to other mains and factored that in. The reason why I used battlecruisers is that in general using a timer is inaccurate I've found and watching replay time likewise. The only accurate and reproducable result I could find was the battlecruiser's building time.
Intrigue: The mineral loss is negible on average (3 minerals)
Xe(-_-)ro: The races have different gathering rates because of different acceleration and mining animation. Roughly one worker on one patch has for P: 0.72 m/t, Terran: 0.68 m/t and for Z: 0.70 m/t. So, roughly, what is said above holds for protoss too however there are small subtle differences. Assuming it takes 60 time units to go from one main to another on a map the costs for scouting as protoss at 9 supply is 0.72*60 for one main, 0.30*60 for the other main, 0.11*60 for the third. At 13 supply it is 0.30*60 then 0.11*60 then virtually 0*60.
okum: That's really hard in practice.
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wow thanks, very interesting read
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great read, now i can fool my protoss opponents even more
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Well I have been keeping putting scvs back on gas once I have 13. If my bo needs to fast cc anways, they I'll wait until when i dump all 3 scvs back on minerals I will nw have a total of around 18. Then any more that pop get gas again. Now I dont know how much this has been 'earning me' but I do notice that less scvs wander at the start, so it does have a feeling of increased total resource mining.
What seems a little odd to me is that I need 27 scvs to max out a mineral patch! 3 to 1, I always believed it was 2:1.
I would be very interested if you could repeat the data takings 1-2 more times for comparison.
But thanks for this info.
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I don't get it 
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nice work. i didn't know it was just 3 minerals. i'll be trying your optimal mechanic from now on.
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On July 19 2009 18:23 Muff2n wrote:
Well I have been keeping putting scvs back on gas once I have 13. If my bo needs to fast cc anways, they I'll wait until when i dump all 3 scvs back on minerals I will nw have a total of around 18. Then any more that pop get gas again. Now I dont know how much this has been 'earning me' but I do notice that less scvs wander at the start, so it does have a feeling of increased total resource mining.
What seems a little odd to me is that I need 27 scvs to max out a mineral patch! 3 to 1, I always believed it was 2:1.
I would be very interested if you could repeat the data takings 1-2 more times for comparison.
But thanks for this info.
What I didn't explain in this post is that wandering depends on how many mineral patches you have. The more mineral patches clumped together the higher wandering. Since all mains have 9 tight mineral patches it makes no difference. However if you have an expansion with 8 mineral patches in groups of 4 then you will attain max at 2 SCVs per patch. Because then you will have about 93% of the max and no wandering.
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O.o so for 9 you need 3x as many (root 9), for 4 you need 2x as many (root 2) and therefore logically you need root 1 for a lone patch which is ... 1x. Damn! Thought I was onto something 
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I didn't actually manage to read this until now.
Great analysis and report Sub!
Depending on what build I do I would take SCVs off accordingly, so I have tried this way before, but I didn't know it was optimal regardless of your factory followup. Thanks.
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