With the online routing game model we can investigate the online routing problem, where each subsequent agent of the traffic flow may select different route based on real-time data. Recent investigations proved that if the agents of such system use the selfish shortest path search strategy, then in some situations sometimes the multi-agent system may be worse off with real-time data than without real-time data, even if anticipatory techniques are applied to predict the future state of the environment. We investigate the online Braess paradox, where each subsequent agent of the traffic flow may select different route, using anticipatory techniques.