a

From page 487, The Gambler’s Ruin Problem The gambler starts with a stake of size s and plays until their stake reaches the value M or the value 0 (absorbing states). pic1

b

If he wins, the sequence of cash flow will be 1, 2, 4, 8 ie. he has to win in the next 3 attempts with a probability of 0.4

(p_bold <- (0.4)^3)
## [1] 0.064

c

Definitely bold strategy as the probability is higher compared to timid strategy.