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I searched Leela website for some statistics about its self-training, the number of games it played with itself in order to assess its progress or to be able to predict whether it is going to win the next Sufi, for example, but I did not find any information.
What is the number of self-games it played before TCEC S19 or TCEC S20, for example? Where can this information be found? Are there any other characteristics to be used to measure its improvement?
The number of games doesn't really effect improvement.
Let's say that in the 500th game that is discovers the common Nf7 fork. This knowledge isn't useful until it plays enough games to discover that the rook is worth mort than a knight. Both pieces of information is needed, plus and ability to associate them, to understand that the fork is a positive play. And we also have to discover when there is an exception to the general rule, ie when castling pins the knight or the wasted moves justify a viscous attack.
The improvement is randomly found, so this play could discover the usefulness and exceptions within 500 games, or it may never stumble across it within 1,000,000. I've seen people make master before they ever saw the Scholar's Mate, which he fell into that trap, so number of games, intelligence, nor strength of the player are any indication of knowledge of any position.
