Octal games may allow splitting a heap into two parts without removing any tokens, by use of the digit 4 to the left of the decimal point.
This is similar to the move in Grundy's game, which is to split a heap into two unequal parts.
Standard octal game notation, however, does not have the power to express the constraint of unequal parts.
The game Kayles is usually visualized as played with a row of n pins, but may be modeled by a heap of n counters.
[3] The puzzle was posed as involving opposed rows of pawns separated by a single rank.
Although the puzzle is not posed as an impartial game, the assumption that captures are mandatory implies that a player's moving in any file results only in the removal of that file and its neighbors (if any) from further consideration, with the opposite player to move.
The octal notation may also be extended to include hexadecimal games, in which digits permit division of a heap into three parts.
The analysis of an octal game then consists in finding the sequence of the nim-values for heaps of increasing size.
[4] A complete analysis of an octal game results in finding its period and preperiod of its nim-sequence.