This is a game played between a team of 3 people (Ann, Bob and Chris, say), and a TV game show host. The team enters the room, and the host places a hat on each of their heads. Each hat is either red or blue at random (the host tosses a coin for each team-member to decide which colour of hat to give them). The players can see each others' hats, but no-one can see their own hat.
Some birds, including sparrows and herring gulls, lay their eggs so that the last one to come out is a shade or two lighter than the others. You might suppose that laying eggs requires some effort and that the colour of the last egg is a sign of an exhausted mother. But this practice might be of evolutionary advantage.