You can also play the latter directly under WinBoard, as a local program. It might be much stronger.
[Edit] I had a look at the PyChess FAQ, to get an idea of how that site works. It states that the "play against AI" functionality there uses a version of the Fairy-Stockfish engine that is running on the server. This means the thinking time of the engine has to be severely limited to not overload the server. The FAQ states that even on level 8 it is limited to less than 1 sec (one assumes using a single CPU thread). The time control that you can select (base time per game and increment per move) is just for the human player.
When you download and run Fairy-Stockfish on your own PC, you can have it think many seconds (or minutes or hours), using all CPU cores.
In normal Chess Fairy-Stockfish should be similar in strength to regular Stockfish. Which would be around 1500 Elo stronger than Zillions of Games (3400 Elo vs 1900 Elo on the CCRL scale). Since the rule of thumb is that doubling thinking time gains an engine some 70 Elo, you would have to make Zillions think a million times longer than Stockfish, to approach the latter in strength. Stockfish at 1msec/move should still easily beat Zillions at 10 sec/move.
The lower levels of the AI on the PyChess website are probably implemented by using Stockfish' UCI_LimitElo option in addition to reducing its thinking time. This option intentionally randomizes the evaluation, increasing the probability for the engine to play moves it would otherwise recognize as sub-optimal / blunders.
PyChess is a web version of Fairy-Stockfish?
You can also play the latter directly under WinBoard, as a local program. It might be much stronger.
[Edit] I had a look at the PyChess FAQ, to get an idea of how that site works. It states that the "play against AI" functionality there uses a version of the Fairy-Stockfish engine that is running on the server. This means the thinking time of the engine has to be severely limited to not overload the server. The FAQ states that even on level 8 it is limited to less than 1 sec (one assumes using a single CPU thread). The time control that you can select (base time per game and increment per move) is just for the human player.
When you download and run Fairy-Stockfish on your own PC, you can have it think many seconds (or minutes or hours), using all CPU cores.
In normal Chess Fairy-Stockfish should be similar in strength to regular Stockfish. Which would be around 1500 Elo stronger than Zillions of Games (3400 Elo vs 1900 Elo on the CCRL scale). Since the rule of thumb is that doubling thinking time gains an engine some 70 Elo, you would have to make Zillions think a million times longer than Stockfish, to approach the latter in strength. Stockfish at 1msec/move should still easily beat Zillions at 10 sec/move.
The lower levels of the AI on the PyChess website are probably implemented by using Stockfish' UCI_LimitElo option in addition to reducing its thinking time. This option intentionally randomizes the evaluation, increasing the probability for the engine to play moves it would otherwise recognize as sub-optimal / blunders.