We can train with the algebraic notation. Feed it all the games and see how it goes. Or make the LLM self-play. ChatGPT can emit the notations, but all it generates are illegal moves.

Edit: after some corrections, it actually proposed the correct moves. Here are the prompts:

ME: The following is a series of chess moves after opening: 1. Nf3 Nf6 2. c4 g6 3. Nc3 Bg7 4. d4 0-0 5. Bf4 d5 What is the best next move?

ChatGPT: The next move depends on the playing style and strategy of both players. However, here are a few options that are often played in this position:

• e3 - This is a flexible move that allows the player to develop their bishop or castle kingside. It can also be useful to control the center.
• dxc5 - Taking the pawn on c5 can lead to a tactical or strategic advantage for White. This move can open up the c-file and create a strong pawn structure for White.
• Be2 - Developing the bishop to e2 can help to control the center and prepare to castle kingside.
• h3 - This is a prophylactic move to prevent Black from playing Bh4, which can be a nuisance for White.

It's important to note that all these moves have potential drawbacks and should be evaluated based on the player's individual preferences, the position of the other pieces on the board, and Black's response.

ME: Some of the moves are illegal. Look at the board again.

ChatGPT: I apologize for the mistake. Here are the corrected moves:

1. Nf3 Nf6 2. c4 g6 3. Nc3 Bg7 4. d4 d5 5. cxd5 Nxd5

In this position, some of the most common moves are:

• e3 - This is a flexible move that allows the player to develop their bishop or castle kingside. It can also be useful to control the center.
• Bd3 - Developing the bishop to d3 can help to control the center and prepare to castle kingside.
• Qc2 - Developing the queen to c2 can help to control the center and prepare to castle kingside.
• 0-0 - Castling kingside is a common move that helps to get the king to a safer square and connect the rooks.

It's important to keep in mind that these moves should be evaluated based on the player's individual preferences, the position of the other pieces on the board, and Black's response.

ME: No. The opening moves are: 1. Nf3 Nf6 2. c4 g6 3. Nc3 Bg7 4. d4 0-0 5. Bf4 d5

ChatGPT: Thank you for correcting me. Here are the moves as given:

1. Nf3 Nf6 2. c4 g6 3. Nc3 Bg7 4. d4 0-0 5. Bf4 d5

In this position, some of the most common moves for White are:

• e3 - This is a flexible move that allows the player to develop their bishop or castle kingside. It can also be useful to control the center.
• Bg5 - Developing the bishop to g5 can put pressure on the Black Knight on f6.
• Qb3 - Developing the queen to b3 can put pressure on the Black pawn on d5 and prepare to castle queenside.
• cxd5 - Taking the pawn on d5 can open up the center and create a strong pawn structure for White.

It's important to keep in mind that these moves should be evaluated based on the player's individual preferences, the position of the other pieces on the board, and Black's response.