The Soviet sit back and do the math and realize their Moon rocket isn't going to work. They then put their money into developing unmanned interplanetary probes
USSR actually had a semi-decent space probe program OTL. Venera probes were fairly successful in exploration of Venus, but Mars probes failed almost completely which basically sums it. Perhaps if Mars missions in 1970-s were a success there would be more ambitious projects. Soviet problems though - highly unreliable electronic components - made this rather unlikely. You need better electronic technology in USSR to successfully fly anything to outer planets but that requires a better economy which leads to rather general PODs