Skip to main content
Engineering LibreTexts

9.12: Exercises

  • Page ID
  • \( \newcommand{\vecs}[1]{\overset { \scriptstyle \rightharpoonup} {\mathbf{#1}} } \) \( \newcommand{\vecd}[1]{\overset{-\!-\!\rightharpoonup}{\vphantom{a}\smash {#1}}} \)\(\newcommand{\id}{\mathrm{id}}\) \( \newcommand{\Span}{\mathrm{span}}\) \( \newcommand{\kernel}{\mathrm{null}\,}\) \( \newcommand{\range}{\mathrm{range}\,}\) \( \newcommand{\RealPart}{\mathrm{Re}}\) \( \newcommand{\ImaginaryPart}{\mathrm{Im}}\) \( \newcommand{\Argument}{\mathrm{Arg}}\) \( \newcommand{\norm}[1]{\| #1 \|}\) \( \newcommand{\inner}[2]{\langle #1, #2 \rangle}\) \( \newcommand{\Span}{\mathrm{span}}\) \(\newcommand{\id}{\mathrm{id}}\) \( \newcommand{\Span}{\mathrm{span}}\) \( \newcommand{\kernel}{\mathrm{null}\,}\) \( \newcommand{\range}{\mathrm{range}\,}\) \( \newcommand{\RealPart}{\mathrm{Re}}\) \( \newcommand{\ImaginaryPart}{\mathrm{Im}}\) \( \newcommand{\Argument}{\mathrm{Arg}}\) \( \newcommand{\norm}[1]{\| #1 \|}\) \( \newcommand{\inner}[2]{\langle #1, #2 \rangle}\) \( \newcommand{\Span}{\mathrm{span}}\)\(\newcommand{\AA}{\unicode[.8,0]{x212B}}\)

    Exercise \(\PageIndex{1}\)

    The following are the possible hands in poker, in increasing order of value (and decreasing order of probability):

    two cards with the same rank
    two pair:
    two pairs of cards with the same rank
    three of a kind:
    three cards with the same rank
    five cards with ranks in sequence (aces can be high or low, so Ace-2-3-4-5 is a straight and so is 10-Jack-Queen-King-Ace, but Queen-King-Ace-2-3 is not.)
    five cards with the same suit
    full house:
    three cards with one rank, two cards with another
    four of a kind:
    four cards with the same rank
    straight flush:
    five cards in sequence (as defined above) and with the same suit

    The goal of these exercises is to estimate the probability of drawing these various hands.

    1. Download the following files from
      : A complete version of the Card, Deck and Hand classes in this chapter.
      : An incomplete implementation of a class that represents a poker hand, and some code that tests it.
    2. If you run, it deals seven 7-card poker hands and checks to see if any of them contains a flush. Read this code carefully before you go on.
    3. Add methods to named has_pair, has_twopair, etc. that return True or False according to whether or not the hand meets the relevant criteria. Your code should work correctly for “hands” that contain any number of cards (although 5 and 7 are the most common sizes).
    4. Write a method named classify that figures out the highest-value classification for a hand and sets the label attribute accordingly. For example, a 7-card hand might contain a flush and a pair; it should be labeled “flush”.
    5. When you are convinced that your classification methods are working, the next step is to estimate the probabilities of the various hands. Write a function in that shuffles a deck of cards, divides it into hands, classifies the hands, and counts the number of times various classifications appear.
    6. Print a table of the classifications and their probabilities. Run your program with larger and larger numbers of hands until the output values converge to a reasonable degree of accuracy. Compare your results to the values at

    Exercise \(\PageIndex{2}\)

    This exercise uses TurtleWorld from Chapter 4. You will write code that makes Turtles play tag. If you are not familiar with the rules of tag, see

    1. Download and run it. You should see a TurtleWorld with three Turtles. If you press the Run button, the Turtles wander at random.
    2. The step method gets invoked by TurtleWorld. It invokes steer, which turns the Turtle in the desired direction, wobble, which makes a random turn in proportion to the Turtle’s clumsiness, and move, which moves forward a few pixels, depending on the Turtle’s speed.
    3. Create a file named Import everything from Wobbler, then define a class named Tagger that inherits from Wobbler. Call make_world passing the Tagger class object as an argument.
    4. Add a steer method to Tagger to override the one in Wobbler. As a starting place, write a version that always points the Turtle toward the origin. Hint: use the math function atan2 and the Turtle attributes x, y and heading.
    5. Modify steer so that the Turtles stay in bounds. For debugging, you might want to use the Step button, which invokes step once on each Turtle.
    6. Modify steer so that each Turtle points toward its nearest neighbor. Hint: Turtles have an attribute, world, that is a reference to the TurtleWorld they live in, and the TurtleWorld has an attribute, animals, that is a list of all Turtles in the world.
    7. Adjust the rules and your steer method for good quality play; for example, it should be possible for the slow Turtle to tag the faster Turtles eventually.

    This page titled 9.12: Exercises is shared under a CC BY-NC-SA 3.0 license and was authored, remixed, and/or curated by Allen B. Downey (Green Tea Press) .

    • Was this article helpful?