He can avoid being captured in this way: If he is on square A, while a piece moves from square X to A intending to capture the Karate Man, he can move away from square A to square B. For this, square B must be vacant.
Then we look at the original radius of the attacking piece from square X. If square B is outside this radius, then the Karate Man survives. If square B is inside this radius, then the Karate Man is taken and the attacking piece ends on square B. This avoiding move counts as a separate move and it is the opponent's turn again. This avoiding move is optional. The owner of the Karate Man can choose to let the Karate Man be captured and do another normal move instead.
Despite the above general rule, the Karate man cannot dodge the capture by an enemy Karate man, Time Thief or Time Traveler.
This is an unrated Chess game with Karate man and Time Traveler.
General rules for this game:
https://www.chess.com/clubs/forum/view/rules-for-bulldog-chess-with-witch
https://www.chess.com/forum/view/chess960-chess-variants/correspondence-chess-rules-for-variant-chess-proposal
Rules for pieces:
https://www.chess.com/clubs/forum/view/list-of-pieces-used-for-bulldog-and-infinite-chess
Rules for Time Traveler:
https://www.chess.com/forum/view/chess960-chess-variants/letrsquos-invent-some-very-weird-pieces?page=20
#383
Rules for Karate man:
The Karate Man can move and capture like a King
He can avoid being captured in this way:
If he is on square A, while a piece moves from square X to A intending to capture the Karate Man, he can move away from square A to square B. For this, square B must be vacant.
Then we look at the original radius of the attacking piece from square X. If square B is outside this radius, then the Karate Man survives.
If square B is inside this radius, then the Karate Man is taken and the attacking piece ends on square B.
This avoiding move counts as a separate move and it is the opponent's turn again. This avoiding move is optional. The owner of the Karate Man can choose to let the Karate Man be captured and do another normal move instead.
Despite the above general rule, the Karate man cannot dodge the capture by an enemy Karate man, Time Thief or Time Traveler.
Rychessmaster1 plays White. Enjoy the game.