I am surprise this thread is this calm here
On some forums 'type of fuel' discussions get very heated.
The subject is complicated, you could google and read for hours and still not know who to believe.
In a nutshell higher octane buys you more resistance to combustion, nothing more, nothing less (a more stable fuel is one way to look at it).
The BTU content from premium to regular is about the same depending on what is used to increase the octane (so in some cases it is slightly less with premium)
BTU content is really what drives your MPG, energy doing work. Unless you add more energy (BTU) you are not going to get more work done (drive more miles).
If your engine is designed to run on premium, this basically means it has a higher compression ratio (or has forced indcution) than an engine set to run on regular.
Your cylinders can compress the fuel further before sending spark in an effort to get more power. You want higher octane to make sure the fuel/air mixture doesn't explode upon just compressing it. Higher octane helps ensure the mixture waits for the spark before exploding.
Engines that recommend premium, but can run on regular, generally have electronics that retard the timing to compensate for the more sensitive lower octane fuel, so the engine will make a little less power (no more than a couple HP on a dyno) as a result. You still go the same # of miles, but your 1/4 mile times might be 1/10 of a second off
I personally don't see any benefit to running premium in the Ody.
Running premium in an engine that isn't designed for it MIGHT cause extra carbon build up to happen.
I will also say that meaningful measurements of MPG can't really happen using pump gas from a retail pump gas station and using your odometer vs gallons purchased as the basis.
You MIGHT be accurate to 2-3mpg at best.
Retail gas is another problem. The wholesale distributors mix and match so often, that you really have no idea what you are buying at the pump. I don't buy into 'top tier fuels' anymore, it is a thing of the past. Our EPA regulates fuel so heavily that all are pretty much the same from brand to brand. Additives that one brand may add aren't enough volume to matter in the long run and you don't have sensitive enough equipment at home to really measure (and you can't closely enough control the environment the car is driven in from tank to tank)
Best advice here is follow the owners manual and use what Honda recommends and you will be safe.