Infinite Armada Chess

This variant is humorously proposed in this XKCD comic. It introduces a chessboard with an infinite number of squares, only a finite number of which are empty, giving each player an infinite armada of queens.

Setup

The FIDE chess board is extended with an infinite number of ranks on both players's sides, i.e., beyond the starting positions of the black and white pieces. All added squares on white's side are filled with white queens, while all squares added on black's side are filled with black queens. Hence, each player has an infinite number of queens, in addition to the standard set of FIDE pieces.

The setup is illustrated by this diagram, where dots denote an infinite continuation:

| . | . | . | . | . | . | . | . |
+---+---+---+---+---+---+---+---+
| q | q | q | q | q | q | q | q |
+---+---+---+---+---+---+---+---+
| q | q | q | q | q | q | q | q |
+---+---+---+---+---+---+---+---+
| r | n | b | k | q | b | n | r |
+---+---+---+---+---+---+---+---+
| p | p | p | p | p | p | p | p |
+---+---+---+---+---+---+---+---+
|   |   |   |   |   |   |   |   |
+---+---+---+---+---+---+---+---+
|   |   |   |   |   |   |   |   |
+---+---+---+---+---+---+---+---+
|   |   |   |   |   |   |   |   |
+---+---+---+---+---+---+---+---+
|   |   |   |   |   |   |   |   |
+---+---+---+---+---+---+---+---+
| P | P | P | P | P | P | P | P |
+---+---+---+---+---+---+---+---+
| R | N | B | K | Q | B | N | R |
+---+---+---+---+---+---+---+---+
| Q | Q | Q | Q | Q | Q | Q | Q |
+---+---+---+---+---+---+---+---+
| Q | Q | Q | Q | Q | Q | Q | Q |
+---+---+---+---+---+---+---+---+
| . | . | . | . | . | . | . | . |

Pieces

All pieces move as in FIDE chess. There are different possibilities to handle pawn promotion on this type of board:

Pawns do not promote.
Pawns promote as in FIDE chess when they reach the starting rank of the opponents non-pawn pieces.

Rules

Except for the unusual board, number of pieces, starting position and potentially pawn promotion, FIDE rules apply.

Notes

Even though this board is infinite and there is an infinite number of pieces present, there is only a finite number of moves allowed at any time. In particular, in the starting position, only the 20 opening moves from FIDE chess are possible, since all queens are blocked by other pieces. After any finite number of moves, only a finite number of pieces has moved, and thus unblocked only a finite number of additional queens.

One possible strategy could be to play offensively and capture as many opponent pieces as possible, and then move one's own pieces out of the way. The infinite armada of queens will then give check on large areas of the central part of the board, where the opponent king is located. However, note that this may also expose one's own king. It is quite likely that this variant will lead to an aggrssive "capture race" between both players, which either ends in a checkmate, or possibly continues forever.

Due to the likely aggressive nature of the gameplay, the choice of the pawn promotion rule probably has no large effect, since pawns are unlikely to ever reach the opposite side of the board.

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