#----------------------------------------------------------------------
# Monty Hall game SIMULATION

# This function generates 3 random doors where 2 are set equal to 0 (the goats) and
# 1 is set equal to 1 (the car)
generate_random_3_door <- function()
{
    sampl = c(0,1)
    probvec = c(.5,.5)
    a <- sample(sampl,1,prob=probvec)
    b <- sample(sampl,1,prob=probvec)
    c <-sample(sampl,1,prob=probvec)
    if((a|b|c==1) & (a&b)!=1 & (b&c)!=1 & (c&a)!=1)
    {
        vect <- c(a,b,c)
        return(vect)
    }else
    {
        return(generate_random_3_doors())
    }
}

# Library needed to plot the pie chart
library(plotrix)

# This function simulates n games both changing and not changing door
trialswsw <- function(n)
{
# We generate our sample matrix
first <- c(1,0,0)
doors <- matrix(first,ncol=3)
for(j in 1:n){
        doors <- rbind(doors,generate_random_3_doors())
}
#View(doors)

# Choices matrix, choice 1: no change, choice 2: change
choices <- matrix(ncol=2)
for(i in 1:nrow(doors))
{
        # Since there's no reason to pick a particular door, we always choose the first
        choice1 <- doors[i,1]

        # Now Monty gets rid of one of the remaining wrong doors (either number 2 or 3)
        if((doors[i,2] == 0) & (doors[i,3] == 0))
        {
            doors[i,2] <- NA
        }
        else if(doors[i,2] == 0)
        {
            doors[i,2] <- NA
        }else if(doors[i,3] == 0)
        {
            doors[i,3] <- NA
        }

        # We switch door, while being careful not to choose the open one! (NA) ;)
        if(is.na(doors[i,2])){
            choice2 <- doors[i,3]
        }else{
            choice2 <- doors[i,2]
        }

        # This vector contains the choice
        choicevec = c(choice1,choice2)

        # we add each vector (game) to the result matrix
        choices <- rbind(choices,choicevec)
    }

    # A small adjustment, not relevant if n is big enough
    choices[1,]= c(1,1)

    # We calculate relative frequencies
    freqrelchoice1 = sum(choices[,1])/nrow(choices)
    freqrelchoice2 = sum(choices[,2])/nrow(choices)
    data = c(freqrelchoice1,freqrelchoice2)
    labels = c("% win without changing","% win changing")
    names(data) = labels

    # View(scelte)
    pie3D(data,labels=labels,explode=0.1,main="Monty Hall % chance of winning")
    return(data)
}

# Let's try our function and go for the simulation
generate_random_3_doors()

# we test our random doors generator
trials(10000)              # Please ignore this function which I have integrated in the trialswsw()
trialswsw(10000)           # We simulate 10000 games