Strategy Transformation Proof

Patrick Traill I think this is a handy concept, but if anybody knows a different term, perhaps this could be made an alias (after merging any content not covered there).

A strategy transformation proof is a proof of a statement of the form “if one can achieve result ``R`` in position ``P`` then one can achieve result ``S`` in position ``Q``” by showing that if there is a strategy to achieve ``R`` from ``P``, this can be adapted to a strategy to achieve ``S`` from ``Q``.

An particular case is a proof of a statement of the form “it is optimal to play ``M`` in position ``P``” by showing that any strategy for winning from ``P`` can be adapted for use after playing ``M``.

See also

• Difference game — Another strategy for determining optimal plays (when two positions are competing for attention)