Until someone actually performs real tests with 64 or more threads it's a bit premature to label one formula naive or outdated.
Your adoption of Amdahl's law is as much an extrapolation as the other formula - the data you used only goes to 8 or 16 threads.
I can easily give you some experience with 24 threads that counters your Amdahl formula.
If one plays a match on a 12-core Xeon with 12 threads running against 24 threads, the 24 (hyper-)threads are running at 0.65x the node speed.
Let's put the formula [speed-up = 1 / (1 - 0.955 + 0.955/n_cores)] to the test:
- for 12 threads the formula predicts a speed-up of 8.0.
- for 24 threads the formula predicts a speed-up of 11.8. Running at 0.65x the node speed, the real speed-up is 11.8 x 0.65 = 7.7.
This means that your formula predicts the 24-thread engine to lose. In fact, using Houdini 5, it wins the match by about 10 Elo as mentioned here:
http://www.cruxis.com/chess/manual/core ... gement.htm .
If even for 24 threads your formula doesn't give any useful prediction, how can you make any claims about 224 threads?