  We address two bottlenecks for concise QBF encodings of maker-breaker
positional games, like Hex and Tic-Tac-Toe. Our baseline is a QBF encoding with
explicit variables for board positions and an explicit representation of
winning configurations. The first improvement is inspired by lifted planning
and avoids variables for explicit board positions, introducing a universal
quantifier representing a symbolic board state. The second improvement
represents the winning configurations implicitly, exploiting their structure.
The paper evaluates the size of several encodings, depending on board size and
game depth. It also reports the performance of QBF solvers on these encodings.
We evaluate the techniques on Hex instances and also apply them to Harary's
Tic-Tac-Toe. In particular, we study scalability to 19$\times$19 boards, played
in human Hex tournaments.
