  We propose a new version of formula size game for modal logic. The game
characterizes the equivalence of pointed Kripke-models up to formulas of given
numbers of modal operators and binary connectives. Our game is similar to the
well-known Adler-Immerman game. However, due to a crucial difference in the
definition of positions of the game, its winning condition is simpler, and the
second player (duplicator) does not have a trivial optimal strategy. Thus,
unlike the Adler-Immerman game, our game is a genuine two-person game. We
illustrate the use of the game by proving a nonelementary succinctness gap
between bisimulation invariant first-order logic FO and (basic) modal logic ML.
