Jon is at a blackjack table. He can place a bet of $20 or do nothing. His odds of winning a bet are 49.5%. Jon wants to maximize expected value. a) What should he do? b) Suppose that before placing a bet, Jon will be told whether he will win or lose with 100% accuracy. How much is this information worth to him? c) Now suppose that Jon counts cards. If the deck is "good", his odds of winning are 52%. If the deck is "bad", his odds of winning are 49%. The deck is good 20% of the time. What is the value of this imperfect information for Jon?

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
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Jon is at a blackjack table. He can place a bet
of $20 or do nothing. His odds of winning a
bet are 49.5%. Jon wants to maximize
expected value.
a) What should he do?
b) Suppose that before placing a bet, Jon will
be told whether he will win or lose with 100%
accuracy. How much is this information worth
to him?
c) Now suppose that Jon counts cards. If the
deck is "good", his odds of winning are 52%. If
the deck is "bad", his odds of winning are
49%. The deck is good 20% of the time. What
is the value of this imperfect information for
Jon?
Transcribed Image Text:Jon is at a blackjack table. He can place a bet of $20 or do nothing. His odds of winning a bet are 49.5%. Jon wants to maximize expected value. a) What should he do? b) Suppose that before placing a bet, Jon will be told whether he will win or lose with 100% accuracy. How much is this information worth to him? c) Now suppose that Jon counts cards. If the deck is "good", his odds of winning are 52%. If the deck is "bad", his odds of winning are 49%. The deck is good 20% of the time. What is the value of this imperfect information for Jon?
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