First a detour: Making choices under uncertainty

Expected value is a simple enough notion, and critical for our discussion.

Suppose we play a game. Heads I give you a dollar, tails you give me a dollar. The coin is fair, so what we do is we multiply the outcomes (plus and minus one) with the probabilities (one half for each) and add. We get zero.

So this game, in the long run, you expect to make zero dollars playing this game.

Suppose now we play a new game. Heads I give you a dollar, tails you give me nothing. The coin is fair.
We perform the same arithmetic and arrive at 50 cents is the amount you would expect to make per play.

Thus if i charge 50 cents, you would be indifferent between playing and not playing.

This was quite quick, but what we need to understand here is only the basic element of how we can go about making decisions under uncertainty.

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