I'm a beginner with R and I am trying to design a coin flip simulation. I want it to start by having a dollar amount of x. When I flip the coin and get heads I add one dollar. When I flip the coin and get tails, I lose a dollar. I want the simulation to end when I get a certain amount of money. Then, how do I run it several times to find the probability that I will end with that certain amount of money.

Hi! Welcome!

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Here is what I came up with:

x=1

out <- c(x+1, x-1)

flip <- sample(out, size=5, replace = TRUE)

flip

I can't seem to figure out how to add on to previously generated numbers and then stop the program when I reach certain numbers. And of course, figure out the probability as well

Try this:

```
x <- 1
x + 1
#> [1] 2
# But x hasn't changed
x
#> [1] 1
# Reassign new value to the old variable name to keep it
x <- x + 1
x
#> [1] 2
```

Created on 2018-09-03 by the reprex package (v0.2.0).

Before worrying about this part, you might want to revisit your problem statement. Part of it doesn't quite add up, at least as far as I can tell:

If the simulation always flips coins until you've got your target amount of money, then the probability that a given run reaches that amount will be 1 because you designed it that way — it's going to keep flipping as long as it takes to get there, every time. So I suspect what you wrote down isn't quite what you want to do.

Setting aside for a moment exactly how it might be done, what's the overall goal of the simulation? Is it to determine the probability of winning a certain amount of money given a certain number of coin flips? Something else?

Here's an approach using a matrix, for which you'll have to decide the maximum number of flips beforehand. It checks if each run *ever* goes above the amount within the maximum number of flips (*not* the probability of *ending up* with the amount). Packaged up in a function so we can rerun it easily,

```
flip_coins <- function(n_runs, n_flips, amount, prob = 0.5, seed = 47, plot = TRUE){
set.seed(seed) # so sampling is reproducible
# make an n_runs x n_flips matrix of 0s and 1s
flips <- matrix(rbinom(n_flips * n_runs, 1, prob), nrow = n_flips)
# replace 0s with -1s so flips is now the amount won/lost for each flip
flips[flips == 0] <- -1L
# take a cumulative sum of each column to track total made/lost
winnings <- apply(flips, 2, cumsum)
if (plot){
# plot cumulative winnings, with opacity
matplot(winnings, type = 'l', col = "#00000022", lty = 1, xlab = "flip")
abline(h = 0) # break-even line
abline(h = amount, col = "red") # amount tested line
}
# check if winnings ever go above amount and divide by n_runs to get probability
sum(colSums(winnings >= amount) > 0) / n_runs
}
flip_coins(n_flips = 100, n_runs = 10, amount = 5)
```

```
#> [1] 0.7
flip_coins(100, 100, 5)
```

```
#> [1] 0.57
flip_coins(100, 1000, 25)
```

```
#> [1] 0.36
```

Messing with the probability of getting heads even a little (3%) can impact the result enormously:

```
flip_coins(100, 1000, 25, prob = 0.53)
```

```
#> [1] 0.95
```