Simulating a dice game in R; doesn't seem random - r

Question

I'm trying to simulate a dice game, with the following criteria:
(1) You are allowed to roll a die up to 6 times;
(2) At any time during the game, after observing the outcome of the roll, you may stop the game, and you win the dollar amount shown on that roll. For example, your rolls are 5, 1, 3, 4, and you
decide to stop the game, then you win $4; your rolls are 5, 1, 3, 4, 3, 2, with no decision to stop the game, then you win $2.
The function I have at the moment is
stop_on_6 <- function() {
nrolls <- 0
# set.seed(0)
n <- 1
# generate 1 random integer from uniform distribution on [1,6] with
# equal probability.
while (n <= 6){
roll <- sample(1:6, size = 1, replace = TRUE, prob = rep(1/6, 6))
if (roll == 6) {print('A 6 was rolled')
return (roll)}
n <- n + 1
}
sprintf("You've rolled ", n, " times.")
}
The function I'm aiming for will compute your expected winnings over n game plays, assuming that you stop the game only if you get 6 on your roll.
At the moment, when I call the function, prints either "A 6 was rolled", or "You've rolled 7 times". I'm not sure how to make the function roll up to 6 times, but stop if roll == 6.

Answer 1

First part of the answer, you have either both answer because :
1- 6 happens very often when running a dice 6 times.
2- the while loop will stop when n == 7, so you will always have 7 times.
To fix the second case you can either print n-1 or go with n initialised at 0 and while n < 6.
I used the first one below.
stop_on_6 <- function() {
n <- 1
memory = 0
while (n <= 6 & memory != 6){
roll <- sample(1:6, size = 1, replace = TRUE, prob = rep(1/6, 6))
if (roll == 6){
print('A 6 was rolled')
}
memory = roll
n <- n + 1
}
sprintf("You played %d times and won %d", n-1, memory)
}
stop_on_6()

Answer 2

stop_on_6 <- function(episode) {
reward <- c()
for(i in 1:episode) {
n <- 1
while (n <= 6){
roll <- sample(1:6, size = 1, replace = TRUE, prob = rep(1/6, 6))
reward[i] <- roll
n <- ifelse(roll == 6,7,n+1)
}
}
return(paste0("You played ", episode," episode.Your expected reward is ",mean(reward)))
}
stop_on_6(1000)
gives,
"You played 1000 episode.Your expected reward is 4.944"

Answer 3

This question just nerd-sniped me, so here's a loop to give you the optimal strategy each roll. If you get a 5 in the 2nd roll or later, or a 4 in the 5th roll, you should quit, since you'll likely do worse staying in.
dice <- 1:6
breakeven = 0 # no value of rolls after the sixth one
for(i in 6:2) {
next_roll_EV <- breakeven
values_over_future_EV = dice[dice > next_roll_EV] # stop if you get one of these
settle_chance = length(values_over_future_EV)/6
settle_EV = mean(values_over_future_EV)
keep_going_chance = 1 - settle_chance
breakeven = settle_chance*settle_EV + keep_going_chance*next_roll_EV
stop_rolls = dice[dice > breakeven]
print(paste0("roll ", i, " has EV of ", breakeven,
", so stop in the prior roll if you have any of ", paste(stop_rolls, collapse = ", ")))
}
[1] "roll 6 has EV of 3.5, so stop in the prior roll if you have any of 4, 5, 6"
[1] "roll 5 has EV of 4.25, so stop in the prior roll if you have any of 5, 6"
[1] "roll 4 has EV of 4.66666666666667, so stop in the prior roll if you have any of 5, 6"
[1] "roll 3 has EV of 4.94444444444444, so stop in the prior roll if you have any of 5, 6"
[1] "roll 2 has EV of 5.12962962962963, so stop in the prior roll if you have any of 6"