I’ve played about 6 AAZ game sessions now. I love the affordability/simplicity aspect of the game for many reasons, but as a consequence it doesn’t ship with a large surplus of units or chips. You do have enough pieces to play a quick aggressive game, but if you want to stack up a lot of units you can find yourself short of pieces. Particularly I found myself frequently short of UK and US land units and transports, and short of round chips. I never ran short of money or air units.
After looking at HBG I decided it might be more economical to buy an additional complete game set, especially considering that the complete set is so affordable anyway. Low and behold I found a damaged set on Amazon, it was at a discount and claimed to be an intact set with a damaged outer box.
I received it today and it has nothing more than one finger sized hole punched into the center of the back side of the box. The plastic tray and all of the components inside were undamaged and intact. So I now have plenty of units and chips to play AAZ big unit stacker style, and even have an extra map, battle board, etc if I spill too much beer on the original ones.
TL;DR: If you want more AAZ units/pieces, look around the intertubes for used or damaged sets, and you might get a good deal on a second set of components.