Skip to comments.St Petersburg Paradox; Games and Statistical Decisions;
Posted on 07/17/2010 6:55:34 AM PDT by mattstat
The estimable Daniel Bernoulli gave us this problem, one of the first creations of decision theory. You have to pay a certain amount of money to play the following game:
A pot starts out with one dollar. A coin is then tossed. If a head shows, then the amount in the pot is doubled. If a tail shows, the game is over and you win the pot, else the coin is re-flipped repeatedly until a tail appears. How much should you pay to play?
Suppose you pay ten bucks and the coin shows a tail the very first throw. You win the dollar in the pot, but it costs you a bundle. You wont make any money unless a tail waits until at least the fifth throw.
The standard solution begins by introducing the idea of expected value. This is usually a misnomer, because the expected value is often one that you do not expect or is impossible. Its formal definition is this: the weighted sum of everything that can happen multiplied by the probability of everything that can happen.
For example, the expected value of a die roll is:
EV = 0.167*1 + 0.167*2 + 0.167*3 + 0.167*4 + 0.167*5 + 0.167*6 = 3.5,
where 0.167 is 1/6, the probability of seeing any result. This says we expect to see 3.5, which is impossible. The dodge we introduce...
(Excerpt) Read more at wmbriggs.com ...
Thereby defining federal bureaucracy...
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