[Retros] How many (S)PGs?

[Francois Labelle]

Andrew Buchanan wrote:


> It's all about finding questions at the right level of difficulty. How

> hard is the following one to answer?

>

>     Which of the billion-odd at-home positions are (S)PGs?


Here's how far I am toward that goal:

My "7.0 moves or less" search visited 196221 distinct at-home diagrams, 
and found 10300 PGs and 9983 SPGs.

My "massacre x=5" search visited 375780 distinct at-home diagrams, and 
found 26170 PGs.

Combined, there are 567674 distinct at-home diagrams that were tested, 
still far from 2^30.

It might be possible to test a significant portion of the total, but I'm 
afraid the missing ones will be extremely hard to find or test. At least 
as hard as computing massacres with x=8 or so.

Christoph Fieberg wrote:


> You could extend the question to the ultimate question:

>

>         Which of the maximum 30,3*10^45 chess positions are (S)PGs?


The probability that a random legal diagram is a SPG isn't negligible. 
It's safe to say that there exists at least 10^30 (S)PGs, too many to 
enumerate.

On the other hand, *one-sided* (S)PGs seem much rarer. I wouldn't be 
surprised if there were only about 10^9 of them.

 	Francois