Monty Hall game in R with base functions

Just for fun and to train R, I tried to proof the Monty Hall Game rule (changing your choice after one gate opened gives you more probability to win), I made this reproducible code (The explanation of every step is within the code):

## First I set the seed

set.seed(4)

## Then I modelize the presence of the prize as a random variable between gates 1,2,3


randomgates <- ceiling(runif(10000, min = 0, max = 3))

## so do I with the random choice.

randomchoice <- ceiling(runif(10000, min = 0, max = 3))

## As the opening of a gate is dependent from the gate you chose (the gate you chose cannot be opened)
## I modelize the opening of the gate as a variable which cannot be equal to the choice.

options <- c(1:3)

randomopen <- rep(1,10000)

for (i in 1:length(randomgates)) {
  realoptions <- options[options != randomchoice[i]]
  randomopen[i] <- realoptions[ceiling(runif(1,min = 0, max = 2))]
}

##Just to make data more easy to handle, I make a dataset

dataset <- cbind(randomgates, randomchoice, randomopen)

## Then I creat a dataset which only keeps the realization of the games in which we carry on (
## the opened gate wasn't the one with the price within)

steptwo <- dataset[randomopen != randomgates,]

## The next step is just to check if the probability of carry on is 2/3, which indeed is

carryon <- randomopen != randomgates

sum(carryon)/length(randomgates) 

## I format the dataset as a data frame

steptwo <- as.data.frame(steptwo)

## Now we check what happens if we hold our initial choice when game carries on

prizesholding <- steptwo$randomgates == steptwo$randomchoice

sum(prizesholding)

## creating a vector of changing option, dependant on the opened gate, in the dataset that
## keeps only the cases in which we carried on playing (the opened gate wasn't the one with the prize)

switchedchoice <- rep(1,length(steptwo$randomgates)) 

for (i in 1:length(steptwo$randomgates)) {
  choice <- options[options != steptwo$randomchoice[i]]
  switchedchoice[i] <- choice[ceiling(runif(1,min = 0, max = 2))]
}

## Now we check how many times you guess the prize gate when you switch your initial choice

prizesswitching <- steptwo$randomgates == switchedchoice

sum(prizesswitching)/length(steptwo$randomgates)

When I check the probability without changing my initial choice in the cases in which the game carried on (the gate opening didn't match the one with the prize) I obtain what I exepected (close 1/3 of probability of winning the prize), which refers to the following instruction:

carryon <- randomopen != randomgates

sum(carryon)/length(randomgates) 

My problem arises when I check the probability of winning the prize after changing my choice (conditionate, obviously to not having opened the door which holds the prize), instead of getting 1/2 as Monty Hall states, I get 1/4, it refers to the following instruction:

prizesswitching <- steptwo$randomgates == switchedchoice

sum(prizesswitching)/length(steptwo$randomgates)

I know that I am doing something bad because it is already more than proofed that Monty Hall holds, but I am not able to detect the flaw. Does anyone know what it is?

If you don't know what Monty Hall problem is, you can find easy-to-read information at wikipedia:

Monty Hall Game