Rather the standard blue or the luxurious Gold all Mineral Patches have 1500 Minerals.
Your first base (the one you start with) will always have 8 Mineral Patches. That is 12000 Minerals. The optimal worker efficiency is approximately 2.5 workers per patch. With that presumption 20 workers is the optimal number for each main base.
-Net Worth of 8 Mineral Patches: 12000
-Net Worth of 7 Mineral Patches: 10500
-Net Worth of 6 Mineral Patches: 9000
After producing these workers that is 50 Minerals every 17 seconds (in Game Time) that can be spent on other things. Now of course you it's generally best to continue production of workers even after reaching this economical critical mass to transfer to your Natural Expansion but for now I'm just talking about that single base's optimal harvesting.
-The Natural Expansion will have either 8 or 7 Mineral Patches depending on the map and how easy it is to defend.
-Other Expansions aside from your natural have 7 Mineral Patches.
-Island Expansions have 6 Mineral Patches.
-Gold Expansions have 6 Mineral Patches.
These facts may become false as map evolution changes and more or less Blizzard maps make up the professional scene when the game actually comes out. But for now these statements are accurate assessments of the state of the game.
It's plain to see that any other base except Island Expansions have higher net Mineral values than Gold Expansions. And if their color was the only difference to between a Gold Mineral Expansion than a standard blue one it would make much less sense to take it. Fortunately, however, color is not their only characteristic.
-Workers harvest Standard Minerals at 5 per trip .
-Workers harvest Gold Minerals at 7 per trip.
That is 40% faster.
And if for mathematical simplicities sake the optimal worker/mineral-patch ratio is 2.5:1 then 15 workers for a Gold Expansion is preferable.
In Game Time it takes 85 less seconds from beginning to end to saturate a Gold Expansion than a main base if you are building from one Hach/Nexus/CC.
Plainly put: Less Workers, Less Time, Faster Income.
However, because a Gold Expansion has 6 Mineral Patches compared to 8 for a standard base a fully saturated Gold Expansion does not produce a full 40% more income than a regular base, but rather less than 40%. To do the math:....
Summary:
Rate comparison:
assumptions: saturation ratio is 2.5 workers for 1 mineral patch.
8 mineral patches = 20 workers
7 mineral patches = 18 workers (rounded up)
6 mineral patches = 15 workers
Fully Saturated:
gold expansion (6 patches) VS 8 mineral patches
(6 x 1.4 = 8.4) VS 8
8.4 / 8 = 1.05
5% faster
Fully Saturated:
gold expansion (6 patches) VS 7 mineral patches
(6 x 1.4 = 8.4) VS 7
8.4 / 7 = 1.20
20% faster
Same Number of Workers:
saturated gold expansion (i.e. 15 workers) VS
(15 x 1.4 = 21) VS 15
21 / 15 = 1.4
40% faster
To sum that up very neatly:
Expansion at blue minerals good; Expansion at gold minerals better.
Now what does that mean now that you did all the mathcraft? Should you just expand to the gold right away? Well the answer to that is depends.
General rule of thumb about expanding is that if you can't keep an expansion up for 3 minutes fully saturated then it is not cost effective (correct me if I'm wrong but that's what I remember reading somewhere on TL). In terms of a Gold expo I'm sure the time for that is slightly less.
So when should you actually expand to a Gold expansion instead of a normal one? There are several situations:
1) Sneaking an expansion at the gold
You take the gold expansion and hope your opponent doesn't find it. However, this works on some maps better than others and also depends on your spawn location. For example, If you are on the same side of the map on Kulas Ravine directly North or South, sneaking a gold expansion on the other side of the map early/mid game would be easier then say Metapolis,
2) Gold expansion is logical course with map
Lost Temple is a perfect example of this (depending if its inbetween you and your opponent). Your 3rd would be close by to your main so its very safe to expand there.
3) Aggressive play
The age old tactic of being aggressive towards your opponent while expanding. In some cases, being aggressive can make you look like you are doing some kind of an all in build which your opponent needs to defend. If you make it look like you're pushing instead while expanding at the gold then you set yourself up for a more macro intensive game. Remember that the best defense is offense.
Hopefully this adds to the post! These types of timings are more for early/mid game as you should have already have mass expos should you enter into late game.
