######################################################################
#
# This file contains a completed function that simulates a (simplified) Yahtzee game,
#  as well as some questions to explore and plots to produce with ggplot2.
#
# Rules of Yahtzee (Simplified)
#
#  * Roll five dice, and re-roll some of them until you get a Yahtzee (meaning that all five dice show the same number).
#  * Roll five dice. Suppose we get 1,2,1,3,1.
#  * Keep the values that occur the most. In our example, we have three 1s. This is our "current Yahtzee."
#  * Re-roll the other dice. In this case, we re-roll the two dice that were not 1s. Suppose we get 1 and 4.
#  * Add to the current Yahtzee. In our example, we have 1,1,1,1,4. Return to second step and repeat until all the values are the same, in which case we have a Yahtzee.
#
#
######################################################################


##### Rolling Dice #####
# We previously wrote a function to simulate rolling n dice

myDice <- function(n){
  sample(1:6, n, replace=T)
}

##### Simulating a game of Yahtzee #####
# This function simulates a game and counts the number of rolls.
# It returns the number of rolls, the number of individual dice rolled, and the final Yahtzee (5 matching dice).

rollYahtzee <- function(){
  totRolls <- 0  # we haven't yet rolled
  indivDice <- 0  # counts rolls of individual dice
  currMatches <- c()  # no matches to start
  totMatches <- length(currMatches)  # total matches
  
  while(totMatches < 5){ # repeat while totMatches is less than 5
    # keep track of the number of rolls
    totRolls <- totRolls + 1
    
    # roll the correct number of dice
    indivDice <- indivDice + (5 - totMatches)
    currMatches <- c(currMatches, myDice(5 - totMatches))
    
    #check for matches
    matches <- rep(0,6)
    for(i in 1:6){
      # this counts how often each value i occurs
      matches[i] <- sum(currMatches == i)
    }
    max.roll <- which.max(matches)  # this is a value with the most matches
    totMatches <- max(matches)  # how many matches
    currMatches <- rep(max.roll, totMatches)  # keep only the current matches
  }
  # return the result
  c(totRolls, indivDice, currMatches)
}

# try it out:
rollYahtzee()
rollYahtzee()[1]

##### Now simulate Yahtzee many times and record the number of rolls for each simulation. #####
M <- 1000
rollList <- c()  # total number of rolls in each game
dieList <- c()   # total number of individual dice rolled in each game
for(i in 1:M){
  result <- rollYahtzee()
  rollList[i] <- result[1]
  dieList[i] <- result[2]
}

##### Questions #####

# What is the mean number of rolls?
rollList
mean(rollList)


# What proportion of the time do you get Yahtzee in three or fewer rolls?
rollList <= 3
sum(rollList <= 3)/length(rollList)
mean(rollList <= 3)

# Make a histogram of the number of rolls.
# Do this with the built-in hist() function, and then with ggplot2.
# You might need to use Google or ask a friend about how to use ggplot2.
hist(rollList)

#make a data frame
df <- data.frame(rollList, dieList)

#make a ggplot and add a plot
ggplot(df, aes(x=rollList)) +
  geom_histogram(color="purple", fill="white", binwidth=3)

#try a dotplot
ggplot(df, aes(x=rollList)) +
  geom_dotplot(color="purple", fill="white", binwidth=3)

#try a density plot
ggplot(df, aes(x=rollList)) +
  geom_density(color="purple", fill="white")


# Add a vertical line at the mean value to your histogram
ggplot(df, aes(x=rollList)) +
  geom_histogram(color="purple", fill="white", binwidth=3) +
  geom_vline(aes(xintercept = mean(rollList)), 
             color="blue", linetype="dashed") +
  ggtitle("Number of Rolls")



##### Extension: Count the number of rolls of individual dice #####
# We previously counted each round of the game as 1 roll, regardless of how many dice were rolled simultaneously.
# Now, modify the simulation so that it counts the total number of dice that are rolled.




# What is the man number of rolls of individual dice to get Yahtzee?




# Make a histogram of the number of rolls until you get Yahtzee




# Display both histograms (total rolls and total rolls of individual dice) simultaneously (they should overlap).
ggplot(df) + 
  geom_histogram(aes(rollList), color="#333333", fill="blue", alpha=0.3, binwidth=3) + 
  geom_histogram(aes(dieList), color="#333333", fill="orange", alpha=0.3, binwidth=3)

ggplot(df) + 
  geom_histogram(aes(rollList), binwidth=5, color="black", fill="green", alpha=0.3) +
  geom_histogram(aes(dieList), binwidth=5, color="black", fill="blue", alpha=0.3)





# Make a scatterplot of total rolls vs. total rolls of individual dice
ggplot(df, aes(x=rollList, y=dieList)) +
  geom_point(color="purple", alpha=0.2)

ggplot(df, aes(x=rollList, y=dieList)) +
  geom_point(color="blue", alpha=0.1) + 
  geom_smooth(method=lm, color="green")

ggplot(df, aes(x=rollList, y=dieList)) +
  geom_jitter(color="blue")



##### Another Extension: Frequencies of outcomes #####
# How often does each number 1,2,...,6 appear as the matched number? 
# The proportions won't be 1/6, because sometimes there is a tie for matches, and one number (the smaller one?) is chosen.




# What sort of plots could you make to visualize this?