From bytes of risk...

See if you can identify the pattern here: If the odds are 50:50 that something bad won't happen, then that happening carries only one bit of surprisal. If the odds against are 3:1 (i.e. "three to one"), then the surprisal is two bits. Make sense yet? Odds against of 7:1 means surprisal is 3 bits, 15:1 against means 4 bits of surprisal, etc.

If you think you've got it now, suppose the odds against something bad happening are 255:1. How many bits of surprisal does that unlikely event carry?

Those of us into computers may have noticed that when the odds against are something:1, then something+1 = 2^#bits. Since 255+1 = 2⁸, the surprisal of such an unlikely event (same as the surprisal of throwing heads on eight coins at once with a single toss) is 8 bits or one byte. If you prefer probabilities over odds, then the probability of an unlikely event is just 1/2^#bits.

OK, so why am I bothering you with this? The reason is that everyday we all make decisions which weigh one tiny risk against another. Very few of us, however, are either taught to or interested in multiplying a set of ridiculously small probabilities every time we decide to eat an apple, cross the street, or (heaven forbid) smoke a cigarette.

But what if weighing our alternatives just involved adding a few numbers typically smaller than two dozen? This is about the surprisal in bits of winning the lottery with a single ticket. More folks could then easily make (and take responsibility for) informed decisions about the risk of unlikely events, and they could enjoy the unavoidable gambling involved in the process at the same time.

For example will you risk the 16 bit surprisal of getting a disease whose surprisal of doing you in is only 2 bits, or will you go for the vaccination whose surprisal of bad consequences is up at 22 bits instead? If you pick the first, you are living more dangerously than necessary (by 4 bits of surprisal) but you will also most likely gain some satisfaction from dodging the bullet. Either way, the decision was informed and it was yours.

If you like this approach, then how can we get media and product labelers to give us numbers about risk so that we can: (i) stop being scared by one broadcast after another and (ii) be more informed about the responsibilities that we shoulder?