So I didn't bother to try more than just this, but this will work for you:
With relatively little micro (I only moved the first Colossus back at 50% health) I was able to keep all three Colossus alive against Marines with both Stim (which you have to use manually) and Combat Shield.
Edit: I also found
- 4 Sentries and 2 Templar are enough, but that requires more micro
- 1 Mothership and 3 Templar (Vortex into Storm)
You're almost on the right track, but some of your math is a little off.
First I'm going to define effective DPS:
100 * Damage / (Attack Cooldown * (Minerals + Gas * 2.5))
Next let's look at the Marine and the Marauder:
Marine: 100 * 6 / (0.86 * 50) = 13.95
Marauder: 100 * 10 / (1.5 * (100 + 25 * 2.5)) = 4.10
So the Marine has about 3.5 times as much effective dps.
For the Marauder to win out against the Marine you'd need at least 3.5 times as much HP.
The Marauder to Marine ratio is 125 / 45 = 2.7
Ultimately, the opinion on TeamLiquid has almost nothing to do with this calculus and everything to do with real world experience. In real world scenarios groups of Marines beat out Groups of Marauders, not only because the Effective DPS ratio is higher than the Hit Point ratio, but also because Marines take up less space; this means that more Marines will be able to attack at the same time. Ultimately that math trumps just about any theory crafting you and I could perform.
Note, that in Marauder vs Marine, Marines only do 5 damage, which reduces their effective dps to 11.6, and the dps ratio to 2.8. While this still gives the advantage to the Marines, it is paltry compared to the size advantage.
Best Answer
A marine is spawned each time you make a move, i.e. remove three jewels. The only way you could make more marines is to make more moves.
As in Starcraft itself, StarJeweled makes you pay attention to different things - the jewel game and the tug of war. It usually helps a lot if you are able to focus on jewels. One way to do this is to just spam one unit in tug of war and never think about it again. Another way is to ask another person to play tug of war while you concentrate on jewels.
As for the game itself, try to make moves in different parts of the field, or go top to bottom, to ensure there are no falling jewels in the area you are looking at. If you can't see a move for a second or two, just shuffle the board, there's no time to look closer.