@11540
"five candidate moves earlier (a couple of weeks since) but I also mentioned that to do the job properly, maybe nine candidate moves"
++ Chess is full of transpositions.
There are 10^38 legal positions without underpromotions to pieces not previously captured.
An average ICCF WC draw lasts 39 moves.
10^38 = 3^80
There are no more chess positions than there are chess positions.
So in 40 moves with 3 choices per ply that do not transpose we have the whole of Chess.
In some positions there are more possible legal moves: 20 to start with.
In some positions there is only 1 legally forced move, e.g. Qxd8+ requires Kxd8.
The number of 3 choices is that low, because there are so many transpositions.
I quote Schaeffer: 'The perfect Alpha-Beta search will halve the exponent'
That is where the square root comes from.
He's trying to use mathematical evidence (which is what I'm talking about ) when I say no evidence