If a further piece of data, Y 2 = y 2 , subsequently comes in, the probability distribution for x can be updated further, to give a new best guess p ( x ∣ ∣ y 1 , y 2 , I ) . If one reinvestigates the information gain for using p ( x ∣ ∣ y 1 , I ) rather than p ( x ∣ ∣ I ) , it turns out that it may be either greater or less than previously estimated: