GAMBLER'S RUIN A gambler repeatedly plays a game where in each round, he wins a dollar with probability 1/3 and loses a dollar with probability 2/3. His strategy is “quit when he is ahead by $2”,...

GAMBLER'S RUIN
Q. A gambler repeatedly plays a game where in each
round; he wins a dollar with probability 1/3 and loses a
dollar with probability 2/3. His strategy is “quit when he is
ahead by $2”, though some suspect he is a gambling
addict anyway. Suppose that he starts with a million
dollars. Show that the probability that he will ever be ahead
by $2 is less than 1/4.
Answer:
Given- P (win) = 1/3 P (loss) = 1/3
Initial amount that the gambler has = $1,000,000
The amount he/she has when he/she quits =...