The term "high octane" sounds like it should be better than regular octane; so if it's better, it should give better gas mileage -- or so you'd think. Actually, high octane isn't "better," it's just different. Octane is the rating of the fuel to resist knocking. Most cars on the road are designed to run just fine on regular octane and that's what you should use. If your car doesn't knock and ping when using regular gasoline, giving it gasoline with a higher resistance to pinging is a waste of money. Very few cars require the higher ping resistance of high-octane gasoline. Check your owner's manual to find out what octane the manufacturer recommends for your car.
When an engine knocks and pings, it's running poorly. It has less power and you may damage your engine if you continue to run it in that state. In a case where the car is designed to run on high-octane gasoline and you give it high-octane gasoline, you will get better gas mileage than you would if you gave it regular gasoline and let the engine run poorly.
Don't use high-octane gasoline unless your car's manufacturer says it's okay to do so. Sometimes, using the same octane but switching to a different brand of gasoline can eliminate mild pinging in your engine.
