Epiphany in the Game of 21

Does performance in strategic settings depend on whether players realize that an optimal way to play is feasible? We introduce a zero-sum game of perfect information, simple enough to allow computation of optimal play yet sufficiently complicated that most participants initially fail. This borderline solvability-by-humans makes it a suitable research tool for experimentally evaluating if play is affected by whether it dawns on a subject that an analytic solution may be possible. Our design includes a way to control for such insight. We also examine how learning transfer across games affects subsequent learning towards optimization. Applications include the facilitation of learning how to plan ahead when actions are needed today but the consequences are temporally distant.