δ-badly approximable numbers form (1/3, 18δ)-winning sets and (1/2, 18/δ)-ubiquitously losing sets with Hausdorff dimension strictly less than 1.
Fishman,Schmidt’s game on fractals,Israel J
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$\delta$-Badly approximable numbers and ubiquitously losing sets
δ-badly approximable numbers form (1/3, 18δ)-winning sets and (1/2, 18/δ)-ubiquitously losing sets with Hausdorff dimension strictly less than 1.