There's still a small chance BA.1.1 "wins", it seems.
Unlike BA.2 which is a lineage separated from BA.1 by at least a couple of months, BA.1.1 is just BA.1 with an additional R346K mutation also found in the Mu variant.
According to atomistic models, that additional mutation makes Omicron almost entirely resistant to neutralizing antibodies elicited by the Wuhan-type virus, perhaps no more than one or two mutations away from such.
I'd guess BA.1.1 might not be transmissible like BA.2 but it scores more wins with breakthrough infections and reinfections.
BA.1.1 triumphing would also be good for the Omicron vaccines, which are using BA.1 and would otherwise have to contend with BA.2's dramatically different N-terminal domain.