I haven't yet told you how to formally calculate

Shannon information content; I've only

told you intuitively that it's the amount

of surprise that a receiver has when

receiving a message from a message

source. So intuitively, we can say that

the message source, the one-year-old who always

says "Da", gives you absolutely no surprise, wherereas the second

one-year-old who says "Dada Mama Baba" gives you

some surprise; you don't know which of those three choices

the one-year-old going to say next. So, this one has higher information content

And similarly, the message source that reports the fair coin

has only two messages, heads or tails, whereas the message source

that reports the fair die has six possible messages, so it's less predictable and has more

information content.