Manipulative waiters with probabilistic intuition

The probabilistic intuition is a surprisingly successful heuristic which links the theory of positional games and the theory of random graphs. Positional games are finite, perfect information two player games with no chance moves and no possibility of a draw. It is known from classical game theory that both players have deterministic optimal strategies for each such game. The probabilistic intuition suggests that a good way of predicting the outcome of such a game under optimal play, is to study what happens when both players play randomly. In this talk I will present several new results of this type.