Daniel Bernoulli and the St. Petersburg Paradox
L
A
T
E
X file:
StPetersburgParadox
— Daniel A. Graham, June 19, 2005
Suppose you are offered the chance to play the following game. A fair coin will be tossed until a head
appears. If a head occurs for the first time on the
n
th toss then you will be paid 2
n
dollars. How much
would you be willing to pay to play this game?
The
St. Petersburg Paradox
is that although the expected value of the payoff is infinite, 2
1
(
1
/
2
)
1
+
2
2
(
1
/
2
)
2
+ · · · =
1
+
1
+ · · · = ∞
, no one seems to be willing to pay anything approaching this sum to
play this game.
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 Spring '09
 Physics, Utility, St. Petersburg paradox, Daniel Bernoulli

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