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 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. 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:....
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
gold expansion (6 patches) VS 8 mineral patches
(6 x 1.4 = 8.4) VS 8
8.4 / 8 = 1.05
gold expansion (6 patches) VS 7 mineral patches
(6 x 1.4 = 8.4) VS 7
8.4 / 7 = 1.20
Same Number of Workers:
saturated gold expansion (i.e. 15 workers) VS
(15 x 1.4 = 21) VS 15
21 / 15 = 1.4