...but in answer to your question, and perhaps someone here can confirm, but I don't "think" those old Bally's are polarized. So, aside from the ground, it shouldn't matter which wire connects where.

I did some research on this a while back when I got my Paragon. Realized the hot and common were reversed when compared to my other Bally's when some Led's I popped in didn't work. But, the game boots up and plays fine. No issues and all test points check out okay. I replace the power cords on all machines I buy. Generally with the older Bally's, I go with the original cord, but I'm a bit of a purist with that stuff. A more modern day cord will work as well. For home use, either is fine.

I can take a closer look when I get home from work tonight and let you know which wire goes where, normally.

Aaron

I know the cords themselves have a polarized marking, but I'd like to know if the game requires it. My hunch is no given my experience to date, but I'm not positive.

Not sure if this helps anyone or not, but if you're looking for the original cord for these machines...

Flat 10' cord @ $8.09
http://www.mouser.com/ProductDetail/Kobiconn/173-33102-E/?qs=sGAEpiMZZMvl4Mm6MN%2fmBLlRU%252b7IfrbuelKVz%252bqek%2fM%3d

Or a more modern day cord...

Standard 8' cord @ $6.13 - SVT : Uninsulated/thinner & cheaper as quantity rises ($5.57 @ 10+)
http://www.mouser.com/ProductDetail/Kobiconn/173-53102-E/?qs=sGAEpiMZZMvl4Mm6MN%2fmBLlRU%252b7Ifrbu2hg9KCAe3mU%3d

Standard 8' cord @ $6.83 - SJT : Insulated/thicker
http://www.mouser.com/ProductDetail/Kobiconn/173-73102-E/?qs=sGAEpiMZZMti11uKQaALGcnE4BsanUdI

You have to pay shipping, which obviously makes these more expensive, but who doesn't need to order from Mouser every now and then. The Pinball Resource also sells both these cords.