HIV-1 broadly neutralizing antibodies (bnAbs) require high levels of activation-induced cytidine deaminase (AID)-catalyzed somatic mutations for optimal neutralization potency. Probable mutations occur at sites of frequent AID activity， while improbable mutations occur where AID activity is infrequent. One bottleneck for induction of bnAbs is the evolution of viral envelopes (Envs) that can select bnAb B cell receptors (BCR) with improbable mutations. Here we define the probability of bnAb mutations and demonstrate the functional significance of key improbable mutations in three bnAb B cell lineages. We show that bnAbs are enriched for improbable mutations， which implies that their elicitation will be critical for successful vaccine induction of potent bnAb B cell lineages. We discuss a mutation-guided vaccine strategy for identification of Envs that can select B cells with BCRs that have key improbable mutations required for bnAb development.