Problem 12.1.Rmd

---
title: "Problem 12.1"
output: html_notebook
---

# 12.1.1
```{r}
0 * 1/2 + 1 * 1/2 * 1/2 * 1/2+ 1 * 1/2 * 1/2 * 1/2 + 2 * 1/2 * 1/2 * 1/2
```
```{r}
1 * 1/2 * 1/2 * 1/2 + 1 * 1/2 * 1/2 * 1/2 + 2 * 1/2 * 1/2 * 1/2
```


#12.1.2
Single Run:
```{r}
ifelse(rbinom(n=1, size=1, prob=1/2), sum(rbinom(n=2, size=1, prob=1/2)), 0)
```
Expected Value of Winnings
```{r}
mean(replicate(10000, ifelse(rbinom(n=1, size=1, prob=1/2), sum(rbinom(n=2, size=1, prob=1/2)), 0)))
```
## 12.1.3
```{r}
myplay <- function(wealth, price){
  noGames = 0
  while (wealth > 0) {
    wealth <- wealth + ifelse(rbinom(n=1, size=1, prob=1/2), sum(rbinom(n=2, size=1, prob=1/2)), 0) - 1
    noGames <- noGames + 1
  }
  return(noGames)

}

mean(replicate(1000, myplay(10,1)))
```