The transition from algorithmic to memory-based performance is a core component of cognitive skill learning. There has been debate about the temporal dynamics of strategy execution, with some models assuming a race (i.e., independent, capacity unconstrained parallel processing) between algorithm and retrieval, and others assuming a choice mechanism. The authors investigated this issue using a new approach that allows the latency of each algorithm step to be measured, in turn providing new insight into (a) whether there is slowing of 1 or more algorithm steps on trials immediately preceding the 1st retrieval trial for an item, as might be expected if there is a competitive strategy execution process of some type other than a race, and (b) whether there is partial algorithm completion on retrieval trials, as would be expected if the 2 strategies are executed in parallel. Results are uniquely consistent with a strategy choice mechanism involving a competition between the retrieval strategy and the 1st step of the algorithm.