[MichaelDickens]

Wouldn't human^2 chess be similar to regular chess? The human-chess AI is guaranteed never to play the regular-chess optimal move, so you can get a checkmate by always playing the optimal move (according to the engine). And unlike human chess, there's nothing preventing you from checkmating your opponent.

(I believe a chess engine could play human^2 chess exactly like it plays regular chess. A human couldn't because a human doesn't know what moves the chess engine would pick.)

[a1369209993]

Presumably human^2 chess would prohibit both the top engine move from human^1 chess and the top engine move from human^0 chess. That is, it's human^1 chess with the added restriction of not playing top engine moves.

[janalsncm]

The problem is that there may not always be 3 possible moves in a given position.

[a1369209993]

There may not always be 1 possible move in a given position either; how does regular chess handle that? (Presumably you'd use the same rule by default for human^n chess.)

[Leherenn]

It's called a stalemate, and results in a draw.