A bstract A measurement of CP -violating observables in B ± → D * K ± and B ± → D * π ± decays is made where the photon or neutral pion from the D * → D γ or D * → D π 0 decay is not reconstructed. The D meson is reconstructed in the self-conjugate decay modes, D → $$ {K}_S^0 $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msubsup> <mml:mi>K</mml:mi> <mml:mi>S</mml:mi> <mml:mn>0</mml:mn> </mml:msubsup> </mml:math> π + π − or D → $$ {K}_S^0 $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msubsup> <mml:mi>K</mml:mi> <mml:mi>S</mml:mi> <mml:mn>0</mml:mn> </mml:msubsup> </mml:math> K + K − . The distribution of signal yields in the D decay phase space is analysed in a model-independent way. The measurement uses a data sample collected in proton-proton collisions at centre-of-mass energies of 7, 8, and 13 TeV, corresponding to a total integrated luminosity of approximately 9 fb − 1 . The B ± → D * K ± and B ± → D * π ± CP -violating observables are interpreted in terms of hadronic parameters and the CKM angle γ, resulting in a measurement of γ = ( $$ {92}_{-17}^{+21} $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msubsup> <mml:mn>92</mml:mn> <mml:mrow> <mml:mo>−</mml:mo> <mml:mn>17</mml:mn> </mml:mrow> <mml:mrow> <mml:mo>+</mml:mo> <mml:mn>21</mml:mn> </mml:mrow> </mml:msubsup> </mml:math> ) ° . The total uncertainty includes the statistical and systematic uncertainties, and the uncertainty due to external strong-phase inputs.