people still earn money in a socialist society. it is just harder to grow because as well as helping yourself you help society. the rich still exist in socialist countries. richard branson isn't exactly starving due to labour's tax laws. and the ikea man isn't living on the streets of sweden.
lets take two people. bill and ben. bill is intelligent and is of very good ability. his father is a lawyer and his mother a doctor. bill wants to go to vetinary college to be a vet (a well qualified job). he can do this because a. he has the ability. b. his parents have the money.
ben could be bill's twin. he has the exact same IQ received the exact same grades in the exact same classes. but ben has a problem. his father disappeared when he was 3 and his mother suffers from mental problems and hasn't worked in years. but through that ben managed to achieve excellent grades. and with these grades ben wants to become a vet. but he can't do this. he has the ability and intelligence but the one thing holding him back is his parent's wealth.
so here we have an example where we have to exact equals except for wealth and that is the defining trait which means these people will succeed or fail in live. and this wealth isn't their fault or gain. but circumstance that has nothing to do with them.
they do not have an equal chance. ben never had one.