Optimizing altitude for a given motor is an interplay between rocket length, nose weight, and fin size and critical assumptions about stability caliber, among a number of other variables. For a given rocket length (shorter with less skin drag is better) fin size should be continually reduced until, eventually, the additional nose weight needed to reach the desired stability caliber exceeds optimal mass thereby reducing altitude. **Adding additional fins of smaller size at that point would not be helpful. **Of far more importance is deciding what is the minimal stability caliber you are willing to accept (is 1 necessary, how about 0.7 or 0.6?).

Anyone playing seriously with the available variables in a simulation program such as OR will arrive at the optimization process you describe.

You state the bolded part as a simple, unsupported assertion. That is actually the question under discussion in this thread. The point is to pull on every available thread and try to figure out whether it's a valid assumption or not.

The minimum acceptable stability factor is obviously of critical importance in the optimization process. I've written elsewhere about why I believe discussing stability in calibers rather than percentage of airframe length is an error in denominator selection.

Also, in the original post the statement that 3 fins are more likely to induce rotation than 4 is incorrect. Properly placed fins should induce no rotation but with 4 fins you have more chance of messing one up than with 3.

In a perfectly still atmosphere without any disturbances to the flight, this would be true. There is extensive discussion and even published literature about four fins having less roll moment than three fins when angle of attack is not equal to zero, due to the asymmetry (varying periodically with rotation) of three fins.

With robust fin tooling, I am not worried about messing one up. Doing everything by hand, it may be nearly impossible to get them close enough to right (even just the same) that fewer fins isn't the best answer.

Make that equal CP. That should be close to the same thing, but what with one thing and another it might not be exactly the same.

As far as I can tell, this is the source of the advantage I'm seeing in OR for four fins. Making the fins smaller (equal area) moves their contribution to CP farther aft, which allows them to be made even a little more smaller and arrive at the same CP. It's a small difference, on the order of a small single digit percent.

Smaller fins generate smaller moments due to landing impacts and should have an edge in durability.

There should be an additional advantage for high-speed rockets in that smaller fins have a higher flutter velocity for the same material thickness/stiffness, so it may be possible to reduce fin thickness and stay clear of flutter.

There is another thread with currently ongoing discussion of the aerodynamic virtues of fillets on model rockets.

Testing the difference between fully optimized three- and four-fin designs (otherwise as close to identical as can be built, obviously) to a level of statistical significance acceptable in various engineering fields would require 30 flights of each configuration in conditions as close to the same as possible. That is likely the biggest barrier to getting it done. It's likely that the total difference between the two would be less than production variation in motor output and variation in conditions from launch to launch that defied measurement and normalization against a sim (bringing sim accuracy back into it, if one went that way).

I won't deny the possibility that, as a practical matter, the real-world performance difference that might be available due to the theoretical difference between fully optimized three- and four-fin designs for model rockets is less than the real-world performance differences of reduced potential for performance-inhibiting variation and reduced construction labor that lie in the three-fin court, especially with low-power altitude competition models.

Further questions (probably best addressed in a different thread) are, how good are we at really optimizing our models with construction technique, and how consistent are we from build to build? How much maintenance is required on an ongoing basis to keep models at peak performance? i.e., filling scratches/dings from landings, maintaining polish, cleaning out ejection charge material buildup, etc.