The Borel determinacy theorem establishes Borel determinacy. It guarantees that one player has a winning strategy
in every two-player game on a tree
with a Borel set of winning paths. Let 
be a Borel set of infinite sequences of natural numbers
in the product topology. Two players alternately
choose the terms of such a sequence, and the first player wins if the resulting sequence
belongs to 
.
Then one of the players has a winning strategy.
Borel Determinacy Theorem
See also
Game Theory, TreeExplore with Wolfram|Alpha
Cite this as:
Weisstein, Eric W. "Borel Determinacy Theorem." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/BorelDeterminacyTheorem.html