A gambler has an opportunity to play a coin tossing game in which he wins his wager with probability .49 and loses his wager with probability .51.Suppose the gambler's initial stake is $40 and the gambler will continue to make $10 bets until his fortune either reaches $0 or $100 (at which time play will stop).Which of the following statements is true?
A)Increasing the amount of each wager from $10 to $20 will increase the expected playing time.
B)Increasing the initial stake to $50 will increase the expected playing time.
C)Reducing the initial stake to $20 will increase the expected playing time.
D)Increasing the probability of winning from .49 to 1.0 will increase the expected playing time.

Question

Quizplus · Accepted Answer

Increasing the initial stake to $50 will increase the expected playing time. This is because with a larger initial stake, the gambler has more chances to make a winning bet and reach the $100 goal before running out of money. The probability of winning each individual bet does not affect the expected playing time, as the expected number of bets to reach $100 or lose all the money is the same regardless of the probability of winning (as long as it is less than 1). Increasing the amount of each wager or reducing the initial stake will decrease the expected playing time, as the gambler will either lose all the money faster or reach the $100 goal faster with fewer bets.

A Gambler Has an Opportunity to Play a Coin Tossing