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It would be very interesting with a few follow-up simulations under similar conditions but starting at different ELO-levels.
Warmest Thank You for for efforts and interesting findings!
The point of the endgame pill is that you can reference it continually throughout the middlegame, knowing which trades and pawn structures will or wont favor you.
If the endgame pill only kicked in once you reached a 7 man position, then maybe only a small raise in rating for a 1400. But if you can reference these positions throughout the middlegame, it would be a huge boost (and why endgames are touted as so much more important than openings).
I would suppose the player would be about the same strength in both scenarios; the only difference being that one player had wasted more time then the other which might then be applied to something else that could increase playing strength. Still a decent foundation of common lines does help one's game. At the very least it keeps more time on your clock to solve tactics that can alter the games outcome.
I actually had the same thought about the different base elo levels the other day. My guess is that the elo advantage for the opening book would increase slightly as the base elo increases; The only question is by how much.
After I finish the 1400 elo test, I could try another test at a different base elo. (What base elo would you like to see for the second test?)
I would like to continue the 1400 test a while longer to get the error margin down a bit more. Unfortunately, the testing takes time, as I run the games at 40 moves in 4 minutes. (I don't like to test at faster time controls.) For information, I'm using the Ufim 8.02 engine (pondering off and using "delay on weak levels" setting) and evaluating the results with bayeselo.
The next base elo should be much higher, i would think about 2000
Talk about coincidence. I didn't hear from the OP, so I had already arbitrarily picked 2000 elo to test. (2000 elo is Ufim's highest reduced-strength setting. So the only higher setting with Ufim would be full strength.)
At 1400 elo, 1000 games: Ufim with book is +32 elo with possible error of plus or minus 10 elo at a 95% confidence interval.
At 2000 elo, 800 games: Ufim with book is +27 elo with possible error of plus or minus 11 elo at a 95% confidence interval. (During the 2000 elo test, the elo difference had recently spent much time around the 20 to 22 level.)
It would be interesting to do more tests at 1000 elo and full strength, but I have other testing that I'd like to get on with, so I can't promise that I'll do any more testing on this book issue.
Interesting! Your research os the closest to a cure for openingphobia I have ever seen!
1400 chess engines are so terrible that that figure is useless. They make moves that are bad in unpredictable and often absurd ways. With weak humans you look for underlying patterns behind the bad moves, that's not the case with weak computers.