One who keeps accounts, or casts up accounts by counters. Thus, in The Winter's Tale, the Clown says, “Fifteen hundred shorn; what comes the wool to? I cannot do't without counters.” (Act iv. s. 3.)
And what was he? Forsooth, a great arithmetician, And I ... must be belee'd and calmed By debitor and creditor, this counter-caster
Shakespeare: Othello, i. 1.
Source: Dictionary of Phrase and Fable, E. Cobham Brewer, 1894