Let's just think about it for a moment... if electrolyzing water and burning the produced hydrogen and oxygen were able to provide ANY surplus in gas mileage at all... ANY.... then that would mean that the net result of the hydrogen production through the electrolysis of water was a slight gain of power. And if you were able to gain a slight amount of power by the electrolysis of water, then you'd have the basic building block for a type of engine... a water engine. You could have the electolysis of water producing hydrogen and oxygen, and you could have the hydrogen and oxygen burning in the engine producing power, turning an alternator, producing electricity that further electrolyzes water and continues the cycle. This is impossible, a type of perpetual motion engine. Water is inert. It would take more energy to break it down than the byproducts (hydrogen and oxygen) can provide.
