I only figured this out LATE in the game playing as the allies. As I looked longingly upon the Axis armor getting two strikes, I learned that I could double the Soviets' strikes by reaching level 1/1 of Armored Warfare -- a no-brainer, one-time investment of 100mpp, at least for the Soviets, probably also for the US.
A better general understanding of supply also is hugely important, but the only specific piece of advice here would be to use the overlay, which I discovered halfway through my first game.
What were your ah-HA moments, as you played your first few games?
“I can no longer sit back and allow Communist infiltration, Communist indoctrination, Communist subversion and the international Communist conspiracy to sap and impurify all of our precious bodily fluids.”