A knightly tussle for two
on a chessboard

Knightcap was Set-up one of my entries to a competition set by the late Canadian magazine Abstract Games in what was to prove its final issue, so it never had a chance to get published. The specification was for a two-player abstract with neutral (common-ownership) gaming pieces.

Two players designated Black and White place 63 identical knights on 63 squares of a chessboard. (To represent knights you can use Go stones, checkers, or counters all of one colour). Initially, Black chooses which square to leave empty and White moves first.
To capture the most knights.
At each turn you move any knight to capture one or more knights from squares of your designated colour. A knight moves like a Chess knight to any attainable vacancy. In doing so it naturally passes over two intervening squares, one of each colour. White captures only a knight occupying the intervening white square, Black only a knight occupying the intervening black square. For example: examples
Left - If it's Black's turn, moving from A captures 3 knights on black squares. Centre - If it is White's turn, moving from A captures 3 knights on white squares. Right - More profitably, White captures 4 knights by starting from B.
You must move and capture if you can, and must then, if possible, keep taking with the same knight till you cannot capture any more. Given a choice of captures you may choose freely. Captured knights are removed immediately so that the capturing knight can land on thereby vacated squares later in the same turn. If you cannot capture you cannot move, but this doesn't prohibit you from moving and taking on a subsequent turn when possible.
Score (simple)
Play ceases when neither player can capture by jumping. You each then add to your captures any and all knights left isolated on squares of your designated colour. Whoever captured the majority of knights scores 1 point per knight taken in excess of 30. (Thus the minimum possible score is 2 points).
Alternative score (compound)
The knights you capture on each turn are kept together in a group separate from those captured in previous turns. At end of play you will have a number of groups each consisting of one or more knights. The score for each group is the triangular number of the number it contains. That is: a singleton scores 1, a group of two scores 3 (1+2), of three 6 (1+2+3), of four 10 (1+2+3+4), and so on (5 = 15, 6 = 21 etc). Captures made on the last move (mopping up singletons) count as one group.
In subsequent games players keep to the same colour but take turns to move first. The first mover's opponent always chooses which square to leave initially empty. Play up to any agreed target, such as 10 points (simple) or 100 (compound).
Copyright © 2017 by David Parlett