Directions: A new futuristic casino just opened in town, “Casino Mathematico”. As part of a grand-opening promotion, you are being given $2000 (play money) with which to play several games in this new establishment. Your job is to keep a tally of the earnings you win and lose by calculating the expected values of each game.

PART 1: INVESTIGATION

Armed with your math expertise, your first job is to determine the expected value of each of the four different games offered at the casino. Use the information providedfor each game and your knowledge of expected value to answer the questions.

GAME #1: CARDS - SIMPLE

This game costs $2 to play.

You draw one card.

If it is a heart, you win $4. Otherwise, if it is not a heart, you lose.

Question 1: What is the expected value of this game?

Question 2: If you played this game 1000 times (spent all your $2000),how much would you expect to win/lose?

GAME #2: CARDS - COMPLEX

This game costs $5 to play.

You draw two cards.

If both are the same suit, you win $22. Otherwise, if they are not the same suit, you lose.

(Hint: you can think of the probability of getting two of same suit as equivalent to the probability of getting two clubs + probability of getting two hearts + probability of getting two spades + probability of getting two diamonds)

Question 1: What is the expected value of this game?

Question 2:If you played this game 400 times (spent all your $2000), how much would you expect to win/lose?

GAME #3: THE WHEEL

This game costs $10 to play.

You spin the spinner.

If your spin lands on a black segment you win $100. Otherwise, if the spinner lands on a grey segment, you lose.

Question 1: What is the expected value of this game?

Question 2:If you played this game 200 times (spent all your $2000), how much would you expect to win/lose?

GAME #4: DICE

This game costs $1 to play.

You roll two dice.

If either die is a 5 or 6, you win $2. Otherwise, if both dice are below a 5, you lose.

Question 1: What is the expected value of this game?

Question 2:If you played this game 2000 times (spent all your $2000), how much would you expect to win/lose?

PART 2: PLAYTIME

Now that you have calculated the expected value for each game above, you can make informed choices. Though, sometimes it is just fun to play a game for the sake of entertainment.J Take your $2000 and get started playing!

Notes about play:

• You choose which games you want to play and the number of times you play each game.
• You must play at least two different games, though you do not need to play them all.
• Any money that you win along the way will automatically be put set aside into an account and given to you at the end of your playing. This means that all games must be played with the original $2000 you are being given and not any winnings.
• Each time you play a game, you will earn the Expected Value for each play. So, for example, let’s say one of the games has an Expected Value of . Then, if you play it one time, this is counted as a loss of $2. When you play the game 50 times, this is counted as a loss of $100.
• Your total spending cannot exceed $2000, since that is the maximum amount you have to play with.
• You must spend your entire $2000.

Fill in the chart below.

Casino Mathematico

	$ amount you spend on game	number of times you play	expected value of each play (use negative to denote loss)	game winnings or losings (use negative number to denote loss)
Game 1
Game 2
Game 3
Game 4
Totals (add up above rows)	$2000

Your total winnings or losings at Casino Mathematico: _______________________________________

(denote loss with negative number)

Transcribed Image Text:

A standard deck of 52 playing cards is commonly used when calculating probabilities. Please note the following. There are four suits: hearts, spades, diamonds and clubs. Their symbols are ♡ Spades and clubs are black while hearts and diamonds are red. ♣ Each suit contains 13 cards, each has cards numbered 2 through 10, a Jack, a Queen, a King, and an Ace (usually counted as one or eleven). AKQJ 10 9 8 7 6 5 4 3 AKQJ 10 9 8 7 6 5 4 3 AKQJ 10 9 8 7 6 5 4 3 2 10 9 8 7 6 5 4 3 AKQ -$2 -$2 Money Wheel ● . ● e ● • • ● D • ♥ ● . · · ● ● ● € . • ● . • .. -$2 A standard deck of 52 playing cards is commonly used when calculating probabilities. Please note the following. There are four suits: hearts, spades, diamonds and clubs. Their symbols are ♡ Spades and clubs are black while hearts and diamonds are red. ♣ Each suit contains 13 cards, each has cards numbered 2 through 10, a Jack, a Queen, a King, and an Ace (usually counted as one or eleven). AKQJ 10 9 8 7 6 5 4 3 AKQJ 10 9 8 7 6 5 4 3 AKQJ 10 9 8 7 6 5 4 3 2 10 9 8 7 6 5 4 3 AKQ -$2 -$2 Money Wheel ● . ● e ● • • ● D • ♥ ● . · · ● ● ● € . • ● . • .. -$2

Answer rating: 100% (QA)

Directions A new futuristic casino just opened in town Casino Mathematico As part of a grandopening promotion you are being given 2000 play money with which to play several games in this new establish... View the full answer