Let’s go to the casino. You have a bankroll of $500, and play $10 *red* bets in

Let’s go to the casino. You have a bankroll of $500, and play $10 *red* bets in

roulette. Consider one *trip* to the casino to end with either surpassing $2,000,

playing 300 games, or running out of money. A *bankroll trajectory* tracks the

amount of money in your bankroll over time.

Simulate and plot one bankroll trajectory for one trip to the casino.

Hint: one of the discussion files includes a similar scenario.

“`{r simulate_casino_trip}

“`

## Question 2

Same scenario as question 1, simulate 1,000 trips to the casino. Estimate and

plot the 10th percentile, 50th percentile (median), and 90th percentile for

for your bankroll over time.

Hint 1: The “quantile“ function in R allows you to calculate any arbitrary

quantile for an input vector “x“. Assemble the trajectories into a

single matrix, then use “apply“ with the function “quantile(x, c(0.1, 0.5, 0.9))“.

Plot the 10%ile and 90%ile with a muted color and dashed lines, and the median

with a bold color and solid line.

Hint 2: use “lty“ argument in “lines“ to specify line type.

“`{r Q2}

“`

## Question 3

Same as Question 2, but change the bet type to *Street*, $lbrace 1, 2, 3rbrace$.

“`{r Q3}

“`

## Question 4

Same as Question 2, but use Martingale doubling strategy with the *black* bet.

If you can’t make the *next* bet, make the largest bet you can. Same exit conditions

as Question 1.

“`{r Q4}

“`

## Question 5

Estimate the probability of winning the pass-line bet, by simulating 100,000

games. Note: The shooter has not started the game yet. You must include in

simulation all possibilities that can happen during play (both on come-out roll,

and in point phase)

“`{r Q5}

“`

## Question 6 (Bonus)

You are playing blackjack. On a fresh deck, with no other players at the table,

you have a 10 and 8, and decided to stand. The dealer is showing a 4.

Via simulation, estimate the probability of your winning the hand. Note: In

this casino, the dealer has to hit on a soft 17.

“`{r Q5}