2081681993819799846994786333448627702865224538845305484256394568209274196127380153785256484516985196439072599160156281285460898883144271297153193175577366203972

208168199381979984699478633344862770286522453884530548425639456820927419612738015378525648451698519643907259916015628128546089888314427129715319317557736620397247064840935 to be precise. Which is more than even the square of the number of atoms in the universe, showing how silly that comparison is... Btw, the quoted "the average 150-move game contains" makes no sense at all, since such a game contains only 151 positions.