= Losing position
= P-position
{c}
{synonym}
= Losing state
{synonym}
In a finite <impartial game> with the <normal-play convention> and no draws, a <losing position> is one from which the player whose turn it is cannot <force> a win against best play. It is also called a <P-position>, since the previous player wins.
A terminal position is losing. Recursively, a position is winning if it has at least one move to a <losing position>, and losing if every legal move goes to a winning position. <Induction> on the finite remaining <game tree> proves this classification. For a single <Nim heap>, only the empty heap is losing. Infinite plays and <misère play> need separate conventions and can change the <base case>.
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