 But until recently, logical games were connected with rational behaviour in a quite different way. On the surface, the logic in question had no direct connection with behaviour. But logicians and mathematicians noticed that some ideas could be made more intuitive if they were linked to possible aims. For example in many applications of logical games, the central notion is that of a winning strategy for the player \(\exists\). Often these strategies (or their existence) turn out to be equivalent to something of logical importance that could have been defined without using games—for example a proof. But games are felt to give a better definition because they quite literally supply some motivation: \(\exists\) is trying to win.