= Covering of an infinite game
= Game covering
{synonym}
A covering consists of a new game tree, a length-preserving prefix map to the original tree, and maps taking strategies of each player to strategies of that same player. Every play following a projected strategy lifts to a play following the original strategy, with identical projection or a premature terminal loss for that strategy's player. Terminal outcomes inherited from the original tree are respected. The strategy maps are local in depth. These conditions transfer every winning strategy, for any payoff pulled back by the prefix map. A $k$-covering leaves all positions, outcomes and strategy choices through depth $k$ unchanged.
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