Math 103 - CooleyStatistics for Teachers OCC

Classroom Activity #11 – Red Dog

In this lesson, students learn one version of the card game of Red Dog.Students calculate conditional probabilities based off several hands of cards being dealt in sequence.

Learning Objectives

Students will:

  • Have a basic understanding of the gameof Red Dog.
  • Calculate conditional probabilities based off the cards played.

Materials

  • Red Dog Activity Sheet
  • A standard deck of cards (optional).

Instructional Plan

Red Dog, also known as Red Dog Poker or Yablon, is a game of chance played with a deck of cards. It is a variation of the card games Acey-Deucey or In-Between. Red Dog was first introduced to Nevada casinos in the 1980’s, but since then its popularity has declined despite being featured in many online casinos. There are several card games all called Red Dog that have different rules, the following is the version of Red Dog we will using in this activity.

Red Dog is played with a standard 52-card deck. This game may be played with up to eight decks; however, as the number of decks increases the house’s edge decreases. The house's advantage begins at 3.155% with one deck, and then falls to 2.751% when eight decks are used. This is in contrast with some other casino card games, such as Blackjack, where as the number of decks increases the house’s edge increases as well.

Red Dog uses 3 cards dealt in a single hand. Red Dog cards are ranked as in poker, with aces high, and suit is irrelevant. A wager is made, two cards are dealt face up on the table in the outside positions, and then the third card is dealt face down on the inside. Refer to the picture above. After the two cards are dealt face up three possible outcomes occur:

  • If the two outside cards are consecutive in number (for example, a four and a five, or a jack and a queen), the all three cards arere-dealt using the original wager. The third (or middle) card was not used.
  • If the two outside cards are of equal value, then the third (or middle) card is turned over. If this third (or middle) card is of the same value, then the payout for the player is 11:1; otherwise all three cards are

re-dealt using the original wager.

  • If the two outside cards dealt have at least one card in sequence between them (for example, a three and an eight), then a spread is announced which determines the payoff (a 4-card spread, in this example), and the third (or middle) card will be turned over. Before turning over the third card, the player has the option to double his bet. If the third card's value falls between the first two (exclusive), the player will receive a payoff according to the spread; otherwise if the third card’s value falls outside of the first two, then the house wins.

Spread Between First and Last Card / Payout if Middle Card Falls in the Spread
1 card / 5 to 1
2 cards / 4 to 1
3 cards / 2 to 1
4 to 11 cards / 1 to 1 (even money)

Distribute the Red Dog Activity Sheet.

Explain to students how the game of Red Dog is played.

For advanced students, explain the spread table, otherwise, just stick to the basic concept of the game.

Students can work in groups to answer the questions

Extensions

  1. Teachers could come up with their own creative questions.
  2. Extend the lesson by actually playing several games of Red Dog with the students.

NCTM Standards and Expectations

Data Analysis and Probability Standards for Grades 6–8

1.Use proportionality and a basic understanding of probability to make and test conjectures about the results of experiments and simulations.

References

This lesson was created by TopCatMath.com.

Red DogActivity SheetNAME ______

Red Dog, also known as Red Dog Poker or Yablon, is a game of chance played with a deck of cards. It is a variation of the card games Acey-Deucey or In-Between. Red Dog was first introduced to Nevada casinos in the 1980’s, but since then its popularity has declined despite being featured in many online casinos. There are several card games all called Red Dog that have different rules, the following is the version of Red Dog we will using in this activity.

Red Dog is played with a standard 52-card deck. This game may be played with up to eight decks; however, as the number of decks increases the house’s edge decreases. The house's advantage begins at 3.155% with one deck, and then falls to 2.751% when eight decks are used. This is in contrast with some other casino card games, such as Blackjack, where as the number of decks increases the house’s edge increases as well.

Red Dog uses 3 cards dealt in a single hand. Red Dog cards are ranked as in poker, with aces high, and suit is irrelevant. A wager is made, two cards are dealt face up on the table in the outside positions, and then the third card is dealt face down on the inside. Refer to the picture above. After the two cards are dealt face up three possible outcomes occur:

  • If the two outside cards are consecutive in number (for example, a four and a five, or a jack and a queen), the all three cards are re-dealt using the original wager. The third (or middle) card was not used.
  • If the two outside cards are of equal value, then the third (or middle) card is turned over. If this third (or middle) card is of the same value, then the payout for the player is 11:1; otherwise all three cards are

re-dealt using the original wager.

  • If the two outside cards dealt have at least one card in sequence between them (for example, a three and an eight), then a spread is announced which determines the payoff (a 4-card spread, in this example), and the third (or middle) card will be turned over. Before turning over the third card, the player has the option to double his bet. If the third card's value falls between the first two (exclusive), the player will receive a payoff according to the spread; otherwise if the third card’s value falls outside of the first two, then the house wins.

Spread Between First and Last Card / Payout if Middle Card Falls in the Spread
1 card / 5 to 1
2 cards / 4 to 1
3 cards / 2 to 1
4 to 11 cards / 1 to 1 (even money)

Answer the following questions. Only one deck is to be used. Unless otherwise stated, assume each time that the deck gets shuffled. Also, disregard any knowledge of the different payouts based on the different spreads.

  1. Look at the cards on the previous page. If these two cards were dealt, what is the probability of winning?
  1. Suppose the two cards dealt face up are a 10 and a King, what is the probability of winning?
  1. Suppose the two cards dealt face up are a Queen and a 6, what is the probability of winning?
  1. What two cards dealt face up would you need to have the lowest probability of winning? What is that probability? Are there any other pairs of cards that would also have the lowest probability of winning?
  1. What two cards dealt face up would you need to have the highest probability of winning? What is that probability?
  1. Suppose the game was played three consecutive times, however, each deal was without replacement. The first three hands were the following: First hand - Jack and 5, then a Jack. Second hand - 2 and 5, then a 6. Third Hand – 4 and King, then a Queen. Now, on the fourth deal, the two cards face up are a 2 and a 7. What is the probability of winning? Compare this probability if it was with replacement?

Answer the following question. Assume that three decks are to be used. Unless otherwise stated, assume each time that the deck gets shuffled. Also, disregard any knowledge of the different payouts based on the different spreads.

  1. Repeat questions #1 through #6 under these new conditions.