Coin Toss Surprisal

Surprisals, defined by probability = (1/(2^(#bits))), add when probabilities multiply.  To refine your taste for surprisals, try the following experiment. Toss a single coin a few times, each time trying to predict which side of the coin will land facing up. The predictions (of ordinary folk, at least) are often wrong. That pleasant surprise we feel when our prediction comes true (after some practice) is associated with one bit of surprisal. Next, toss two coins. Occasionally both coins will land "heads up", and the surprisal associated with that happening is two bits. Now imagine (or sample) the surprisal associated with three coins landing "heads up", or four, or ten. The twenty bits of surprisal associated with throwing "heads" on twenty coins on the first try will be better appreciated after you've tossed those twenty coins hundreds of thousands of times, without finding all heads up even once. Thus a few coins in your pocket can give you a feel for what a given amount of surprisal means, anytime you need a reminder.

DETAILS

http://www.umsl.edu/~fraundorfp/egsurpri.html

Contributed by: P. Fraundorf

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