Let two integers such that 1<a<7 and 2<b<5.We play the following game: We start with a euros and we roll a dice.If the result of the dice is at least b we earn 1 euro and we lose 1 euro otherwise. The game ends if we reach 8 euros (winners) or in 0 (losers). We prefer to be ?
A) Rich: we start with a equals 6 euros , but unlucky because b equals 5. B) Mediocre: we start with a equals 4 and b equals 4 C) Lucky: we start with a equals 2 but b equals 3.
How can I do it in R using simulation in order to decide If I want to be rich ,mediocre or lucky?
My effort
gamble <- function(a,n,p) {
stake <- a
while (stake > 0 & stake < n) {
bet <- sample(c(-1,1),1,prob=c(1-p,p))
stake <- stake + bet
}
if (stake == 0) return(1) else return(0)
}
a <- 6
n <- 8
p <- 1/3
trials <- 100000
simlist <- replicate(trials, gamble(a, n, p))
mean(simlist) # Estimate of probability that gambler is ruined
a <- 4
n <- 8
p <- 1/2
trials <- 100000
simlist <- replicate(trials, gamble(a, n, p))
mean(simlist)
a <- 2
n <- 8
p <- 2/3
trials <- 100000
simlist <- replicate(trials, gamble(a, n, p))
mean(simlist)
We could define a function f() that uses recursion.
f <- \(a, b) {
s <- sample(6, 1)
l <- length(a)
a <- c(a, a[l] + ifelse(s >= b, 1, -1))
if (a[l + 1] %in% c(0, 8)) return(a)
else return(f(a, b))
}
R <- 1e5
set.seed(42)
r0 <- replicate(R, Map(f, c(6, 4, 2), c(5, 4, 3)))
rowMeans(matrix(rapply(r0, \(x) x[length(x)] == 8), 3))
# [1] 0.24668 0.49885 0.75435