“Stockfish and Lc0, Test at Different Number of Nodes”, 2021-03-08 ():
[chess time-travel experiment] …From the graph, it can be seen that less than 100,000 are sufficient to allow Stockfish to defeat Fruit [200420ya] or an equivalent top rating human player (a fraction of a second with modern PC), and less than 1,000 (!) to defeat an average/good club player. As a comparison, Deep Blue defeated Kasparov in 1997 by analyzing an average of 200,000,000 nodes/move. Continuing the analysis, it can be seen that as the number of nodes double, the corresponding increase in terms of Elo, decreases more and more until it almost flattens out (diminishing returns). It’s worth noting that matches with 256M nodes are limited to few hundreds, therefore the error margin, in this case, is bigger. But the trend seems quite clear.
…In the case of Lc0 [Leela Chess Zero] the situation is still more surprising. For those who don’t know, Lc0 is a chess engine that combines a search based on Monte Carlo tree search method (MCTS) with a self-learning neural network, and the project is inspired by the AlphaZero program made by DeepMind. This is a different approach to Stockfish, which uses a classic minimax algorithm with alpha-beta pruning, and with the NNUE neural network used only for the evaluation. Lc0, with only 1 node/move (therefore without any knowledge of the opponent’s counter-play) is above 2200 Elo points, more than enough to create troubles even to a human master. 100 nodes/move are enough to annihilate any human player on the planet (around 3,000 Elo points). [at tournament time controls, that allows roughly 2 seconds per node]
From the graph above it can be seen that Lc0 scales better than Stockfish 13 increasing the number of nodes, even if when the number of nodes exceeds 10,000/move, the inflection of the curve appears accentuated up to nearly flattens out.
Unfortunately, the hardware requests to use Lc0 properly are huge and it was impossible for me to test the program over 100,000 nodes/move…From the first impressions, supported also by the recent victories of Stockfish over Lc0 in the TCEC and other tournaments, is that the flexion is real and that Stockfish remains a notch above even with great hardware advantage for Lc0, for long times.