the optimum fuel/air mixture with a high octane/high compression engine will still yield more power, than the optimum fuel/air mixture with a low compression/low octane engine- provided you have the high octane fuel for the high squeeze engine. You can't retune a low-squeeze engine to get the same power as a high-squeeze engine. By it's very nature a high-compression engine makes a certain percentage more power if fueled correctly.
wide open throttle performance on a 4-stroke engine is often on the rich side, dragsters make the most power a tad under hydraulic-ing the cylinders full of fuel- and raw fuel is going out the exhaust and burning in the air above the pipes on a run
my brother is into 2-strokes and has told me many times running even a tad too rich will drown out the horsepower quickly on a 2-stroke, mainly because you only have one or 2 cylinders, so they are very tune sensitive. A big V-8 can be out of tune a little and still make a lot of power, because it has so many cylinders to begin with.
octane number was boosted by adding lead years ago, because lead is so inert and doesnt' react, it slowed down the burn enough so the engine could gain some horsepower from the higher compression ratio. In this way compression and octane are a catch 22- raise compression increases pumping efficiency and cylinder pressure, but requires raising octane to avoid detonation to make the fuel burn slower- so it's like 3 steps forward, then one step backwards- but the end result is still 2 steps forward and more power
a general rule of thumb for a V-8 engine is for every 1 point of compression ratio you increase, you gain 20 horsepower- this has been proven on the dyno- with a 1 cylinder engine it would be proportionately less- one point of compression may add 1 or 2 horsepower.
but you don't want a really high compression engine with a pull start, simply because then it's very difficult to start with a pull rope ! then it requires an electric starter
so chainsaws, lawn mowers, etc. are generally low compression, regular fuel engines, that are easy to pull start- the very high compression racing V-8's are often spun on the starter without spark, then while the engine is spinning, the ignition is kicked on and the engine starts- one of the foibles of high compression is difficulty cranking the engine, and the high octane fuel costs a lot more due to additives needed to raise the octane
