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).
print((1.5^1-1)/(1.5^8-1))## [1] 0.02030135(b) he bets, each time, as much as possible but not more than necessary to bring his fortune up to 8 dollars (bold strategy).
print(dbinom(3,3,0.4))## [1] 0.064(c) Which strategy gives Smith the better chance of getting out of jail?
Bold strategy with probability of 0.064 gives Smith better chance if getting out of jail