Editing Openai/692664f7-a230-8000-833c-663a29f9f4d1 (section)

=== Keep a two-column ledger counting plys played by each side. Start at zero. ===

When players move normally, increment their column by 1 for each ply.
When a Double Move occurs, increment that player’s column by 2 in one row (or two rows if you prefer).
When a player is skipped, do not increment their column on that scheduled turn.

Because the granter sacrificed one future ply (their next turn is skipped) and the grantee gained one extra ply (Double Move), the running totals remain equal after the skip occurs. You can always check fairness by confirming that after each pair of scheduled opportunities (a “cycle”), the running counts differ by at most 0 or 1 depending on timing — and after a skip+double resolves they equalize.

Worked ledger example (ply counts):

Initial: White=0, Black=0
# White plays (not spending token): White=1, Black=0 1... Black plays (normal): White=1, Black=1

... later:
# White spends Sacrifice Token on White’s move: White moves → White=K (increment by 1) 11... Black uses Double Move on Black’s turn (plays two plys): Black increments by 2 → now Black = previous + 2
# White’s next scheduled turn is skipped → White does not increment.

If you compute totals after the skip, totals will match (the +1 Black got from the Double Move is offset by White’s skipped ply).