One (questionable) roulette strategy is called bet doubling. You bet $1 on red, and if you win, you pocket the $1. If you lose, you double your bet so you are now betting $2 on red, but have lost $1. If you win, you win $2 for a $1 profit, which you pocket. If you lose again, you double your bet to $4 (having already lost $3). Again, if you win, you have $1 profit, and if you lose, you double your bet again. This guarantees you will win $1, unless you run out of money to keep doubling your bet.

1. Say you start with a bankroll of $127. How many bets can you lose in a row without losing your bankroll?
2. If you have a $127 bankroll, what is the probability that bet doubling wins you $1?
3. What is the expected value of the bet doubling strategy with a $127 bankroll?
4. If you play the bet doubling strategy with a $127 bankroll, how many times can you expect to play before you lose your bankroll?

In R Programming please