Abstract. An online Ramsey game is played between Builder and Painter on an infinite board [Formula: see text]. In every round Builder selects an edge, then Painter colors it red or blue. Both know target graphs [Formula: see text] and [Formula: see text]. Builder aims to create either a red copy of [Formula: see text] or a blue copy of [Formula: see text] in [Formula: see text] as soon as possible, and Painter tries to prevent it. The online Ramsey number [Formula: see text] is the minimum number of rounds such that the Builder wins. We study [Formula: see text], where [Formula: see text] is fixed and [Formula: see text] is large. We show that [Formula: see text] if [Formula: see text] is even, while [Formula: see text] if [Formula: see text] is odd.