45  43. Practice Questions - TOPIC: loops (writing code)

QUESTION 1 - TOPICS: generating random values

# Write a function named, rollDice that simulates the rolling of one or
# more dice. 
# 
# - The function should take a single argument, numberOfDice that indicates the
#   number of dice being thrown.
#
# - numberOfDice is expected to be a positive whole number. 
#   If it is not then the function should stop and display an
#   error message.
#
# - The function should return a vector of random whole numbers.
#   The value of each number should be randomly chosen to be  1,2,3,4,5 or 6.
#   There should be as many numbers in the vector as indicated by the
#   argument numberOfDice.
#
# For example:
#   > rollDice(1)
# [1] 3
# 
# > rollDice(1)
# [1] 6
# 
# > rollDice(2)
# [1] 2 4
# 
# > rollDice(2)
# [1] 6 1
# 
# > rollDice(5)
# [1] 6 3 3 4 6
# 
# > rollDice(5)
# [1] 4 4 2 6 5
# 
#
# PART A 
#
#   Use the sample function to write rollDice.
#
#
# PART B
#
#   Instead of the sample function, use the runif function (see ?runif).
#   Set the min and max arguments of runif to 1 and 7 respectively. 
#   Then use the trunc function to remove the decimal points from the
#   values that runif returns. Using this approach it will be 
#   impossible for the code to result in anything other than
#   1,2,3,4,5 or 6. runif will NOT generate a 7 since
#   the documentation for runif says the following:
#   
#       runif will not generate either of the extreme values unless 
#       max = min or max-min is small compared to min, and in particular 
#       not for the default arguments.
# 
#   Therefore once you truncate the result that you get from runif you
#   will be left with numbers that are either 1,2,3,4,5 or 6.
#
#
# PART C (THINKING DEEPER)
#
#   If you follow the hints above, for part B, the resulting rollDice function, 
#   is not 100% "fair". Note that according to the documentation mentioned above 
#   if you specify min as 1 and max as 7, then runif will never generate 7.0000 
#   or 1.00000. Therefore, technically, the result of your rollDice function 
#   would be very slightly less likely to generate 1s than other numbers.  
#   Think about how you could theoretically fix this - One way is that you could
#   set min to 0 (zero) and max to 7 and then truncate the result with trunc. 
#   If you get a zero, you keep repeating this process until you got a 
#   number that wasn't 0. 
############.
# ANSWER
############.

rollDice <- function(numberOfDice){
  sample(1:6, numberOfDice)
}

# Examples
rollDice(1)
[1] 2
rollDice(1)
[1] 5
rollDice(2)
[1] 2 3
rollDice(2)
[1] 4 3
rollDice(5)
[1] 3 4 5 6 1
rollDice(5)
[1] 3 2 5 1 4
############.
# ANSWER
############.

rollDice <- function(numberOfDice){
  trunc(runif(numberOfDice, min=1, max=7))
}

# Examples
rollDice(1)
[1] 6
rollDice(1)
[1] 2
rollDice(2)
[1] 6 3
rollDice(2)
[1] 1 1
rollDice(5)
[1] 1 3 6 5 1
rollDice(5)
[1] 6 6 1 3 4
############.
# ANSWER
############.

rollDice <- function(numberOfDice){
  answer = numeric(0)
  
  while(numberOfDice > 0){
    # add additional rolls to the answer
    answer = c(answer, trunc(runif(numberOfDice, min=0, max=7)))
    
    # record how many dice were zeros (we will have to regenerate these) 
    numberOfDice = sum( answer == 0 )
    
    # remove the zeros 
    answer = answer [ answer > 0 ]
  }
  
  return(answer)
}

# Examples
rollDice(1)
[1] 5
rollDice(1)
[1] 2
rollDice(2)
[1] 3 1
rollDice(2)
[1] 6 6
rollDice(5)
[1] 2 5 1 6 1
rollDice(5)
[1] 2 4 3 2 6

QUESTION 2 - TOPICS: loops, cat vs return

# NOTE: You must answer the previous question before doing this one.
#
# Write a function named keepRollingUntilSnakeEyes. 
#
# - The function should not take ANY parameters. 
#
# - The function should keep calling rollDice(2) inside of a loop to 
#   simulate multiple rolls of two dice. 
#
# - The loop should stop when the roll is two ones (i.e. "snake eyes"). 
#
# - The function should display the values each roll as shown below. 
#
# - The function should return the total number of rolls that were made. 
#
# - See the examples below. 
#
# HINTS: 
#   a.  Use the cat function to display the messages.
#   b.  Use a variable to keep track of how many rolls took place
#   c.  keep looping until you get a 1 and a 1
# 
# EXAMPLES: 
# 
#   Note that in the first two examples below, the last value displayed is the 
#   value that is "returned".  
#   In the third example below, the return value is captured in a variable 
#   and is displayed in a separate command.  (also see the next question). 
#
#   > keepRollingUntilSnakeEyes() # return value appears after all the messages
#   roll #1 was: 2 and 1
#   roll #2 was: 3 and 5
#   roll #3 was: 6 and 5
#   roll #4 was: 4 and 1
#   roll #5 was: 5 and 5
#   roll #6 was: 6 and 1
#   roll #7 was: 2 and 3
#   roll #8 was: 6 and 3
#   roll #9 was: 5 and 4
#   roll #10 was: 6 and 3
#   roll #11 was: 6 and 3
#   roll #12 was: 4 and 5
#   roll #13 was: 4 and 1
#   roll #14 was: 4 and 2
#   roll #15 was: 1 and 1
#   [1] 15
#   
#   > keepRollingUntilSnakeEyes()  # return value appears after all messages
#   roll #1 was: 1 and 1
#   [1] 1
#   
#   > numRolls <- keepRollingUntilSnakeEyes() # return value captured in numRolls
#   roll #1 was: 2 and 1
#   roll #2 was: 4 and 3
#   roll #3 was: 3 and 6
#   roll #4 was: 3 and 6
#   roll #5 was: 4 and 3
#   roll #6 was: 6 and 4
#   roll #7 was: 6 and 2
#   roll #8 was: 3 and 2
#   roll #9 was: 4 and 1
#   roll #10 was: 1 and 1
#   
#   > numRolls  # This is the value that was returned from the function
#   [1] 10
############.
# ANSWER
############.

# WHAT TYPE OF LOOP SHOULD I USE?
#
#   You can always use a while loop to solve a looping problem.
#   However, sometimes a for loop makes the code easier to read and write.
#
#   Can I use a for loop in this case? NO
#
#   You should only use a for loop when it's possible to know before the loop
#   even starts how many times it will iterate (i.e. how many times it will
#   go around). 
#
#   In this case, it's impossible to know in advance how many times it will
#   take to get snake eyes. It could happen the 1st time, the 50th time,
#   the 500th time, or never (but that's unlikely).

keepRollingUntilSnakeEyes <- function(){
  
  roll <- rollDice(2)
  rollnum <- 1
  cat("roll #", rollnum, " was: ", roll[1], " and ", roll[2], "\n", sep="")
  
  while (roll[1] != 1 || roll[2] != 1){
    roll <- rollDice(2)
    rollnum <- rollnum + 1
    cat("roll #", rollnum, " was: ", roll[1], " and ", roll[2], "\n", sep="")
  }
  
  rollnum  
}

numRolls <- keepRollingUntilSnakeEyes()
roll #1 was: 1 and 2
roll #2 was: 4 and 2
roll #3 was: 5 and 5
roll #4 was: 5 and 1
roll #5 was: 5 and 3
roll #6 was: 6 and 4
roll #7 was: 2 and 1
roll #8 was: 2 and 5
roll #9 was: 4 and 5
roll #10 was: 6 and 5
roll #11 was: 1 and 2
roll #12 was: 2 and 1
roll #13 was: 3 and 3
roll #14 was: 2 and 4
roll #15 was: 4 and 6
roll #16 was: 6 and 6
roll #17 was: 4 and 6
roll #18 was: 6 and 6
roll #19 was: 3 and 3
roll #20 was: 4 and 2
roll #21 was: 5 and 5
roll #22 was: 3 and 5
roll #23 was: 5 and 1
roll #24 was: 6 and 1
roll #25 was: 2 and 6
roll #26 was: 6 and 4
roll #27 was: 1 and 3
roll #28 was: 1 and 6
roll #29 was: 1 and 1
numRolls
[1] 29

QUESTION 3 - TOPICS: loops

# Modify the function that you created in the previous question, 
# keepRollingUntilSnakeEyes. In this new version you should define a single 
# argument named, showOutput. The default value of showOutput should be FALSE. 
# If showOutput is TRUE then the messages should be displayed. 
# If showOutput is FALSE then the messages should NOT be displayed. 
# In either case, as with the last question, the function should return 
# total number of rolls.  For example:
#
# EXAMPLES: 
# 
# > keepRollingUntilSnakeEyes()        # this will not show output
# [1] 48
#
# > keepRollingUntilSnakeEyes(showOutput = FALSE)  # nor will this
# [1] 80
#
# > keepRollingUntilSnakeEyes(FALSE)               # nor will this
# [1] 1
#
# > keepRollingUntilSnakeEyes(TRUE)    # this WILL show output
# roll #1 was: 4 and 4
# roll #2 was: 4 and 6
# roll #3 was: 5 and 4
# roll #4 was: 4 and 3
# roll #5 was: 5 and 6
# roll #6 was: 5 and 5
# roll #7 was: 2 and 3
# roll #8 was: 3 and 1
# roll #9 was: 1 and 3
# roll #10 was: 3 and 4
# roll #11 was: 3 and 2
# roll #12 was: 1 and 2
# roll #13 was: 6 and 3
# roll #14 was: 1 and 1
# [1] 14
#
# > keepRollingUntilSnakeEyes(showOutput = TRUE) # this WILL show output
# roll #1 was: 2 and 4
# roll #2 was: 6 and 1
# roll #3 was: 4 and 2
# roll #4 was: 5 and 4
# roll #5 was: 5 and 6
# roll #6 was: 1 and 1
# [1] 6
############.
# ANSWER
############.

# WHAT TYPE OF LOOP SHOULD I USE?
#
#   You can always use a while loop to solve a looping problem.
#   However, sometimes a for loop makes the code easier to read and write.
#
#   Can I use a for loop in this case? NO
#
#   You should only use a for loop when it's possible to know before the loop
#   even starts how many times it will iterate (i.e. how many times it will
#   go around). 
#
#   In this case, it's impossible to know in advance how many times it will
#   take to get snake eyes. It could happen the 1st time, the 50th time,
#   the 500th time, or never (but that's unlikely).

keepRollingUntilSnakeEyes <- function(showOutput = FALSE){
  
  roll <- rollDice(2)
  rollnum <- 1
  if(showOutput){
    cat("roll #", rollnum, " was: ", roll[1], " and ", roll[2], "\n", sep="")
  }
  
  while (roll[1] != 1 || roll[2] != 1){
    roll <- rollDice(2)
    rollnum <- rollnum + 1
    if(showOutput){
      cat("roll #", rollnum, " was: ", roll[1], " and ", roll[2], "\n", sep="")
    }
  }
  
  rollnum
}


keepRollingUntilSnakeEyes()        # this will not show output
[1] 27
keepRollingUntilSnakeEyes(showOutput = FALSE)  # nor will this
[1] 7
keepRollingUntilSnakeEyes(FALSE)               # nor will this
[1] 13
keepRollingUntilSnakeEyes(TRUE)    # this WILL show output
roll #1 was: 1 and 2
roll #2 was: 6 and 6
roll #3 was: 3 and 1
roll #4 was: 4 and 4
roll #5 was: 1 and 4
roll #6 was: 5 and 6
roll #7 was: 6 and 1
roll #8 was: 6 and 3
roll #9 was: 4 and 6
roll #10 was: 5 and 1
roll #11 was: 2 and 3
roll #12 was: 4 and 4
roll #13 was: 4 and 2
roll #14 was: 3 and 6
roll #15 was: 3 and 4
roll #16 was: 4 and 5
roll #17 was: 3 and 2
roll #18 was: 2 and 6
roll #19 was: 6 and 4
roll #20 was: 1 and 6
roll #21 was: 4 and 4
roll #22 was: 6 and 4
roll #23 was: 3 and 6
roll #24 was: 6 and 6
roll #25 was: 5 and 1
roll #26 was: 3 and 5
roll #27 was: 3 and 1
roll #28 was: 5 and 6
roll #29 was: 3 and 6
roll #30 was: 2 and 3
roll #31 was: 2 and 6
roll #32 was: 5 and 3
roll #33 was: 4 and 4
roll #34 was: 4 and 1
roll #35 was: 4 and 6
roll #36 was: 6 and 5
roll #37 was: 5 and 1
roll #38 was: 4 and 4
roll #39 was: 4 and 2
roll #40 was: 3 and 3
roll #41 was: 3 and 5
roll #42 was: 1 and 3
roll #43 was: 6 and 4
roll #44 was: 4 and 4
roll #45 was: 3 and 2
roll #46 was: 3 and 6
roll #47 was: 1 and 4
roll #48 was: 2 and 2
roll #49 was: 1 and 3
roll #50 was: 2 and 1
roll #51 was: 2 and 6
roll #52 was: 4 and 1
roll #53 was: 2 and 3
roll #54 was: 1 and 1
[1] 54
keepRollingUntilSnakeEyes(showOutput = TRUE) # this WILL show output
roll #1 was: 1 and 5
roll #2 was: 5 and 6
roll #3 was: 6 and 1
roll #4 was: 2 and 4
roll #5 was: 4 and 5
roll #6 was: 1 and 6
roll #7 was: 5 and 1
roll #8 was: 4 and 2
roll #9 was: 6 and 5
roll #10 was: 2 and 5
roll #11 was: 6 and 6
roll #12 was: 1 and 2
roll #13 was: 6 and 6
roll #14 was: 2 and 5
roll #15 was: 2 and 2
roll #16 was: 3 and 5
roll #17 was: 5 and 6
roll #18 was: 5 and 6
roll #19 was: 2 and 1
roll #20 was: 4 and 4
roll #21 was: 5 and 3
roll #22 was: 6 and 5
roll #23 was: 1 and 6
roll #24 was: 3 and 4
roll #25 was: 6 and 5
roll #26 was: 6 and 1
roll #27 was: 2 and 3
roll #28 was: 5 and 4
roll #29 was: 2 and 1
roll #30 was: 3 and 4
roll #31 was: 1 and 1
[1] 31

QUESTION 4 - TOPICS - loops

# NOTE: You must answer the previous questions before doing this one.
#
# Do all of the following steps:
#
# PART A
# 
#   Write a function named playManyTimes that calls the function 
#   keepRollingUntilSnakeEyes in a loop.
#   The function playManyTimes should take an argument, n, that indicates the
#   number of times the game should be played. playManyTimes should return a
#   vector that contains the number of rolls it took each time the
#   keepRollingUntilSnakesEyes function was called. For example:
#
#   > playManyTimes(3)
#       [1] 66  1 22
#
#   > playManyTimes(10)
#   [1]   6  27  35 106  38  51 100   1   1  26
#
#
# PART B
# 
#   Run the command:     results <- playManyTimes(10000)
#   to capture the results of playing the game ten thousand times. 
#
# PART C
#
#   Create a histogram of the results with the command:   h <- hist(results)    
#   The histogram should look similar to the example shown below. You can see
#   from this histogram that the function keepRollingUntilSnakeEyes  
#   is much more likely to return smaller numbers than to return larger 
#   numbers:
#
#
# PART D
#
#   In the previous step the command:        h <- hist(results) 
#   displayed a histogram. However, the function also returned an R "list"
#   that was captured in the variable h. The value of the list wasn't 
#   displayed since hist returns an "invisible" value (see ?invisible)
#   In any case, even though the return value is "invisible" you can still
#   display the contents of this variable to examine details about 
#   the histogram (see the output below). 
#
#   For example, the counts entry in h contains the number of values in the 
#   results variable that fell into each "bar" of the histogram. 
#   The sum of all these counts are 10,000,as should be expected.
#
#   Examine the value of the counts entry in the list.
#   Then use the sum function to check to make sure that the
#   counts sum to a total of 10,000 (as they should).
############.
# ANSWER
############.

##################.
# PARTS A and B
##################.

# WHAT TYPE OF LOOP SHOULD I USE?
#
#   You can always use a while loop to solve a looping problem.
#   However, sometimes a for loop makes the code easier to read and write.
#
#   Can I use a for loop in this case? YES
#
#   You should only use a for loop when it's possible to know before the loop
#   even starts how many times it will iterate (i.e. how many times it will
#   go around). 
#
#   In this case, since the value of n (i.e. the number of times to loop)
#   is known before we even start the loop, we can use a for loop (as well 
#   as a while loop).

#------------------------------.
# This version uses a for loop
#------------------------------.
playManyTimes <- function(n) {
  answer <- numeric()
  
  # From just the following line you can see that we will loop n times. 
  # Each time through the loop, one of the values in the vector 1:n is
  # placed into the variable num. In this simple loop we don't need 
  # to use the variable num inside the body of the loop, however, we
  # still need to specify a variable name in the first line of the for loop.
  
  for(num in 1:n){    
    answer <- c(answer, keepRollingUntilSnakeEyes())
  }
  answer
}

playManyTimes(3)
[1] 122  89  59
playManyTimes(10)
 [1] 103  43   8  17  64  17   4   5   1  12
#--------------------------------.
# This version uses a while loop
#--------------------------------.
playManyTimes <- function(n) {
  answer <- numeric()
  
  # With a while loop, it's not as easy to know how many times the loop
  # will iterate (go around) as it is with a for loop. With a while loop
  # to understand how many times the loop will iterate (go around)
  # you must analyze all of the code for the loop and understand it.
  
  while(n > 0){
    answer <- c(answer, keepRollingUntilSnakeEyes())
    
    # This line is only in the while loop version.
    #
    # You should NEVER change the value of the "loop variable"
    # in the body of a for loop. That would defeat the whole purpose
    # of a for loop.
    
    n = n-1  
  }
  answer
}

playManyTimes(3)
[1] 10 63  8
playManyTimes(10)
 [1]  9 54 35 39 35 30 82  6 21 26
##########.
# PART C
##########.
results <- playManyTimes(10000)
h <- hist(results)

##########.
# PART D
##########.

# show the structure of the h variable
str(h)
List of 6
 $ breaks  : num [1:22] 0 20 40 60 80 100 120 140 160 180 ...
 $ counts  : int [1:21] 4307 2449 1418 771 444 254 160 89 55 25 ...
 $ density : num [1:21] 0.02153 0.01225 0.00709 0.00385 0.00222 ...
 $ mids    : num [1:21] 10 30 50 70 90 110 130 150 170 190 ...
 $ xname   : chr "results"
 $ equidist: logi TRUE
 - attr(*, "class")= chr "histogram"
# show the complete contents of h
h
$breaks
 [1]   0  20  40  60  80 100 120 140 160 180 200 220 240 260 280 300 320 340 360
[20] 380 400 420

$counts
 [1] 4307 2449 1418  771  444  254  160   89   55   25   12    4    4    3    2
[16]    1    0    1    0    0    1

$density
 [1] 0.021535 0.012245 0.007090 0.003855 0.002220 0.001270 0.000800 0.000445
 [9] 0.000275 0.000125 0.000060 0.000020 0.000020 0.000015 0.000010 0.000005
[17] 0.000000 0.000005 0.000000 0.000000 0.000005

$mids
 [1]  10  30  50  70  90 110 130 150 170 190 210 230 250 270 290 310 330 350 370
[20] 390 410

$xname
[1] "results"

$equidist
[1] TRUE

attr(,"class")
[1] "histogram"
# show the contents of just the counts entry in h
h$counts
 [1] 4307 2449 1418  771  444  254  160   89   55   25   12    4    4    3    2
[16]    1    0    1    0    0    1
# make sure that the sum of the counts is in fact 10,000 as it should be
sum(h$counts)
[1] 10000

QUESTION 5 - TOPICS: loops, if/elseif/else, cat vs return

# The game of "craps" involves a player rolling a pair of dice repeatedly
# according to the rules shown below. 
#
#   a. The first roll:
#     i.   If the player rolls 7 or 11 he/she wins
#     ii.  If the player rolls 2, 3 or 12, he/she loses
#     iii. if the player rolls any other number, that number becomes the "point"
#
#   b. All other rolls
#     i.   If the player hasn't won or lost on the first roll, then the
#          player keeps rolling until either he rolls a 7 or 
#          the "point" (i.e. the same value as the very first roll). 
#          If the player rolls a 7 he loses. 
#          If the player rolls the "point" he wins.
#
# Write a function named, playCraps, that simulates the computer 
# playing a single game of craps. The function should return TRUE if 
# the player wins the simulated game and FALSE if the player loses the game. 
#
# Define a single argument named, showOutput. The default value of showOutput 
# should be FALSE. If showOutput is TRUE then the messages should be displayed. 
# If showOutput is FALSE then the messages should NOT be displayed. 
# In either case, the function, playCraps, should return TRUE if the player
# wins and FALSE if the player loses. For example:
#
# EXAMPLE 1 (showOutput is FALSE): 
#
#     > playCraps(showOutput = FALSE)
#     [1] FALSE
#
#     > playCraps(showOutput = FALSE)
#     [1] TRUE
#
#     > playCraps(showOutput = FALSE)
#     [1] FALSE
#
#     > playCraps(showOutput = FALSE)
#     [1] TRUE
#
# EXAMPLE 2 (showOutput is TRUE): 
#   
#     > playCraps(showOutput = TRUE)
#     roll #1: 7
#     WIN
#     [1] TRUE
#
#     > playCraps(showOutput = TRUE)
#     roll #1: 12
#     LOSE
#     [1] FALSE
#   
#     > playCraps(showOutput = TRUE)
#     roll #1: 6
#     roll #2: 11
#     roll #3: 5
#     roll #4: 5
#     roll #5: 6
#     WIN
#     [1] TRUE
#
#     > playCraps(showOutput = TRUE)
#     roll #1: 6
#     roll #2: 9
#     roll #3: 5
#     roll #4: 9
#     roll #5: 4
#     roll #6: 4
#     roll #7: 9
#     roll #8: 3
#     roll #9: 3
#     roll #10: 2
#     roll #11: 4
#     roll #12: 8
#     roll #13: 10
#     roll #14: 7
#     LOSE
# WHAT TYPE OF LOOP SHOULD I USE?
#
#   You can always use a while loop to solve a looping problem.
#   However, sometimes a for loop makes the code easier to read and write.
#
#   Can I use a for loop in this case? NO
#
#   You should only use a for loop when it's possible to know before the loop
#   even starts how many times it will iterate (i.e. how many times it will
#   go around). 
#
#   In this case, it's impossible to know in advance how many times the dice
#   will need to be rolled before the game ends. The game could end on the 
#   first roll, the 50th roll, the 500th time, or never (but that's unlikely).

playCraps <- function(showOutput = FALSE){
  rollNumber <- 1
  point <- sum(rollDice(2))
  
  if(showOutput){
    cat("roll #", rollNumber, ": ", point, "\n", sep="")
  } 
  
  if(point == 7 || point == 12){
    if(showOutput)  cat("WIN\n\n")
    
    return(TRUE)
    
  } else if (point %in% c(2,3,12)){
    if(showOutput)  cat("LOSE\n\n")
    return(FALSE)
    
  } else {
    
    while(TRUE) {
      roll <- sum(rollDice(2))
      rollNumber <- rollNumber + 1
      if(showOutput){
        cat("roll #", rollNumber, ": ", roll, "\n", sep="")
      } 
      
      if(roll == 7){
      
        if(showOutput){
           cat("LOSE\n\n")
        } 
      
        return(FALSE)
      
      } else if ( roll == point) {
      
        if(showOutput){
          cat("WIN\n\n")
        }
        return(TRUE)
      }
    }    
  }
}

playCraps(TRUE)
roll #1: 3
LOSE
[1] FALSE
playCraps(TRUE)
roll #1: 3
LOSE
[1] FALSE
playCraps(TRUE)
roll #1: 8
roll #2: 4
roll #3: 8
WIN
[1] TRUE
playCraps(TRUE)
roll #1: 8
roll #2: 8
WIN
[1] TRUE
playCraps()
[1] TRUE

QUESTION 6 - TOPICS: loops

###########.
# PART A
###########.
# We can simulate playing craps many, many times. This can be done to 
# generate an estimate the probability of winning a game of craps.
# 
# Do the following:
#
# a. Create a function, playCrapsManyTimes, that takes a single argument, n. 
#
# b. The function should return a vector that contains the results of calling
#    the playCraps command n times. 
#
# c. Use the function to simulate playing craps ten thousand times
#
# d. Calculate the percent of times that the player won the game 
#    (i.e. total TRUEs divided by total number of games played). 
#    Since TRUE is treated as 1 and FALSE as zero, it is possible to use 
#    the mean function to calculate this.
#
# e. For example the following shows that there is only 
#    approximately a 47.9% chance of winning the game of craps.:
#
#      > results <- playCrapsManyTimes(10000)
#      > mean(results)
#      [1] 0.47915
#
#    The more times we play, the more accurate our estimate of the
#    probablily of winning will be.
# WHAT TYPE OF LOOP SHOULD I USE?
#
#   You can always use a while loop to solve a looping problem.
#   However, sometimes a for loop makes the code easier to read and write.
#
#   Can I use a for loop in this case? YES
#
#   You should only use a for loop when it's possible to know before the loop
#   even starts how many times it will iterate (i.e. how many times it will
#   go around). 
#
#   In this case, since the value of n (i.e. the number of times to loop)
#   is known before we even start the loop, we can use a for loop (as well 
#   as a while loop).

#------------------------------.
# This version uses a for loop
#------------------------------.

playCrapsManyTimes <- function(n) {
  answer <- logical()
  for (num in 1:n){
    answer <- c(answer, playCraps(FALSE))
  }
  answer
}
results <- playCrapsManyTimes(100000)
mean(results)
[1] 0.47788
#--------------------------------.
# This version uses a while loop
#--------------------------------.

playCrapsManyTimes <- function(n) {
  answer <- logical()
  while (n > 0){
    answer <- c(answer, playCraps(FALSE))
    n = n - 1
  }
  answer
}
results <- playCrapsManyTimes(100000)
mean(results)
[1] 0.47864