I want them to use the chessboard as their item, probably a Gold Chessboard. They'll play one side on any board in the range of their main chessboard. They'll criticize a player if they play poorly, or give advice if they seem to be taking too long in the area. If a player plays the Savant's side, they'll whack the player, and yell at them and may reset the board. When chess pieces can be collected, they'll trade for pieces.

Players can improve the qualities of trades not through trading, but through playing well against the Savant (making good moves, not cheating, not taking too long). I like how this creates a social enforcement of the rules vs. a technical one.

I'm tempted to allow the savant to troll you through bound boards.

Medieval chess players have traditionally been rather poor players compared with the 20th century. As MC has a semi-medieval theme, perhaps the villagers could have a very simple AI. This would keep the game from lagging any more than necessary.