Quote:
Originally Posted by Driving91LX
Let's simplify.
1) Passing electricity through metal submerged in water makes flamable gas.
2) This gas gets sucked into the intake and explodes in the cylinders, thus reducing the amount of petrol you need to run the engine.
3) Using less petrol gives you better mileage.
Do we really need a bunch of complicated formulas for this? Ok, proceed with the "over-simplifying" responses 
Disclaimer: The guy in this video isn't me 
youtube]lB0Rn76kS1E[/youtube]
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You're forgetting that that electricity has to come from somewhere. If there was a magical way of producing nameless amounts of energy with no work input then that would be what powers all of the world's nations.
What actually happens is the additional electrical draw on the alternator increases the amount of energy the alternator draws from the engine via physical work (increased resistance to turn alternator over the same period of time = greater work). That's less energy going to the wheels. If the system works perfectly (all components, including engine, operating at 100% efficiency), then your fuel economy will stay the same. Since the system is non-ideal (real), then you will actually lose fuel economy in varying degrees.
What causes people to notice small increases in fuel economy after installing such kits comes down to driving style. They drive more economically, and that skews the results. If the EPA conducted their driving cycle, however, the fuel economy would drop.