On an infinite board, which pieces are needed to checkmate? Most of the winnable endgames require cornering the opposing king to checkmate, often using zugzwang. However, if you have an infinite board (infinite in every direction), you won't be able to corner the opposing king as easily, as they will be able to retreat unless there is a threat behind them. For example, queen vs king will be a draw in this scenario, as the king and queen will never cover all escape routes. I also believe that two rooks will be unable to deliver mate, as you cannot force opposition. However, queen and rook will be able to checkmate, by using the queen to create a &quot;corner&quot; and checkmating using rook and king. In general, if a combination mates in a regular board, that combination plus a queen will be able to mate here; but I'm looking for more interesting combinations.
So, which piece combinations will be able to mate in this scenario?
In fact K+R+R can force checkmate against K on an open board.
First move both Rooks away from the King and to different rows and columns.
Then check the King with one Rook, say on a row.
Whichever side the King goes, move the other Rook to limit it to a single row.
Now the Rooks, moving only horizontally,
can limit the defending King to just four squares on that row,
with enough spare moves for the attacking King to approach:
[Title &quot;RR keep K boxed in&quot;]
[FEN &quot;R7/5k2/2R5/8/8/8/8/K7 w - - 0 0&quot;]

1. Rh8 Kg7 2. Rch6 Kf7 3. Kb2 Ke7 4. Rc8 Kd7 5. Rhc6 Ke7 6. Kc3 Kf7 7. Rh8

Once the King has joined the fray, mate can soon follow.  For example:
[Title &quot;KRR mate K on infinite board&quot;]
[FEN &quot;7R/5k2/2R5/8/3K4/8/8/8 w - - 0 0&quot;]

1. Ke5 Kg7 (1... Ke7 2. Rc7#) 2. Rch6 Kf7 3. Kd6 Kg7 4. Kd5 Kf7 
5. Ke5 Kg7 (5... Ke7 6. R6h7#) 6. Kf5 Kf7 7. R6h7#