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Timid strategy

$35.00

Timid strategy

Smith is in jail and has 1 dollar; he can get out on bail if he has 8 dollars.
A guard agrees to make a series of bets with him. If Smith bets A dollars,
he wins A dollars with probability .4 and loses A dollars with probability .6.

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Timid strategy

Smith is in jail and has 1 dollar; he can get out on bail if he has 8 dollars.
A guard agrees to make a series of bets with him. If Smith bets A dollars,
he wins A dollars with probability .4 and loses A dollars with probability .6.
Find the probability that he wins 8 dollars before losing all of his money if
(a) he bets 1 dollar each time (timid strategy).
(b) he bets, each time, as much as possible but not more than necessary to
bring his fortune up to 8 dollars (bold strategy).
(c) Which strategy gives Smith the better chance of getting out of jail?

Timid strategy
$35.00
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