How can I think of (visualize) 0.5 bits of information?

Question

I was studying Shannon's Entropy function and for a 35% chance of a particular event, the formula produced the answer 1.5 bits.

log2(0.35) = 1.5 bits(approx.) of information.

I know it's pretty trivial in context of practical applications, but how can one visualize 0.5 a bit of information. I mean a bit could be one or zero but 0.5? Analog values ?!?!?

Answer 1

Thank you to Jyrki Lahtonen in the comments for answering it convincingly.

You seem to be confusing the set of possible values of a bit (as information stored in some device) and the use of bit as a unit of information. A single coin flip contains one bit of information because the two possible outcomes are equally likely. But if the coin were heavily loaded, say with 99 per cent chance of getting tails, then the outcome of flipping such a coin surely contains less information than that of flipping a fair coin.

Answer 2

One bit of perfect information will allow a person to double their money. The simplest idea, is if you had a tipster than knew who would win the football game, you could go to a bookie, place a wager and double your money.

Suppose you have a tipster that is right 55% of the time. It is still worth following your tipster's advice, but you are not going to reliably double your money. And, you are not going to wager all of your money on one bet. You have a partial bit of information.