An anomalously strong increase of nuclear fusion gains for laser driven compression and thermal ignition of hydrogen-boron11 has been discovered from computations by using the latest results of Newins and Swain about details of a resonance maximum of the astrophysical S-function at 148 keV for the reaction cross-sections. Extensive computations based on volume ignition showed some usual improvements of the fusion gains. However, for a very narrow range of parameters, the increase of the gain was found to be higher by more than a factor 6. This is very unusual in all similar computations and is related to retrograde properties which were known for other parameter values. On top it is most important that the anomalous range is in the practically very interesting range for incorporation of laser pulse energies of few megajoules. The gains of up to 20 may be of interest for power generation in future by the high density fusion scheme.