This is the fourth entry in my decentralised or "Swiss" chess mini series. See bottom for a recap of the modified rules of Swiss chess.
Consider the Swiss KNN-K endgame: All pieces except for the two kings and two white knights have been traded and a neutral (no immediate threats on either side) position has been reached. In regular chess this is a theoretical draw: Assuming best play from both sides white despite being two pieces up cannot force check mate. But what about Swiss chess? Is the Swiss king + 2 Swiss knights vs Swiss king endgame winnable or a draw? Please back up your answer by summarising the successful side's strategy.
By "summarising" I mean: Give just one or two example variations demonstrating each major step the strategy may consist of. I'm not asking for an exhaustive search tree
Note: This may look rather daunting at first sight but Swiss rules actually make it much easier to analyse than the standard chess KNN vs K
Swiss chess primer:
In Swiss chess, the advantage in terms of mobility of a centrally placed piece over a piece in the corner is compensated for by opening up additional squares a marginalised piece has access to. This applies to all pieces except rooks and pawns. To keep rules simple, the queen like in standard chess is a bishop+rook even though that does mean it is a bit weaker on edge-of-the-board squares.
Credit to @AxiomaticSystem for the following streamlined description of Swiss moves:
Movements ending at the starting square are implicitly forbidden
The King may either take a diagonal step, or make an orthogonal jump. This jump can skip at most as many squares as the number of edges the King is on.
A bonk is a unit move (knight leap for the Knight, diagonal step for the bishop), except if this move would take them to a square off the board, the piece moves to the closest on-board square instead.
A Knight can always bonk. In addition, if it's in the corner, it can also take a diagonal step .
A Bishop can always move as normal. If the number of possible normal moves (assuming otherwise empty board) is smaller than the maximum, 13, then the bishop can also bonk off the nearest edge. (If the Bishop is on one of the long diagonals there are two nearest edges and both are allowed.) This extension is, however, capped at 13 possible moves total, meaning that if necessary the longest bonk moves are pruned.
The Queen moves like a Rook or Bishop.
Here are some animated gifs, showing the full set of legal moves from a representative set of squares for the Swiss knight, the Swiss bishop, the Swiss queen and the Swiss king. If you need more info, please comment or find some at the other Swiss chess posts.
Note that due to the "asymmetric" way the Swiss king moves it is sometimes possible for a Swiss king to give check to the other Swiss king. Not very royal behaviour, admittedly, but useful to know.