# Three-Act Math: The Royal Flush

This was the third time CAMI tried out using a 3-Act math task. This one is called Royal Flush and is organized around the probability of a poker hand in Texas Hold’em.

Facilitator(s): Eric
Date of Meeting: July 10, 2015
Problem: · url

#### Introduction

Do you play cards? What kinds of cards do you play? What do cards have to do with probability?

• Michael – I play cards, but not a lot of poker. “Serious players are card counters, especially in gin.” Which is more likely, making money on stocks or throwing dice?
• Solange – Lots of cards, only a little bit of poker. All of the choose one/pick one where you have to do factorials.
• Brian – Weekly game of Texas Hold ‘Em. Reading people is the game.
• Tyler – Used to play a lot in high school, let his friends beat themselves. Now I just lose to sit out.
• Mark – Ruled Uno game at lunch table in Middle School. Won Texas Hold ’em tourney at bookclub meeting to discuss Casino Royale. Used to watch my grandmother Pauline play – she was a big player.
• Alison – Only played poker once or twice. Interested in probability/strategy of guessing on tests, guessing down the line versus guessing randomly.
• Cynthia – Do not play cards for money with this woman. You will lose.

#### Act One: Launch

1. We’re going to start by watching a brief video. (We watched it three times – Eric kept asking, “Would anybody like to see it again?”)

2. Would you go ahead and write down the first question that comes to your mind, if any? Just one question.

3. Would you introduce yourself to your neighbor and share your question? See if it’s the same question, or a different question.

4. I’m really curious what questions are out there. Just toss one out. Who else finds that question interesting?

5. Great. Love these questions. I hope we get to all of them. Here’s one I’ll need your help with first:

**What are the odds of getting a royal flush in this situation?**

1. No calculations yet!!! Write down an answer you know is too high – the odds couldn’t be that high – and an answer you know is too low – the odds couldn’t possibly be that low. Share them with your neighbor.

2. I want you to write down on a piece of paper your best, gut-level guess for the odds. I’m curious who can guess the closest.

3. I’m curious in here who has our highest guess.

4. What’s our lowest guess in here?

#### Act Two: Problem-Solving

1. What information do you need in order to answer this question? Get into a group of two or three people to discuss.

2. Write all the requests on the board. Give information based on their requests.

*What is the poker hand hierarchy? – Poker hand rankings

*How do you play this game?

Texas hold ’em is a variation of the standard card game of poker. Two cards (hole cards) are dealt face down to each player and then five community cards are placed face-up by the dealer—a series of three cards (the flop), then an additional single card (the turn) and another additional card (the river). The best five card poker hand is obtained by taking cards from either the community and a player’s hole cards. Players have the option to check, bet, raise or fold after each deal; i.e., betting may occur prior to the flop, on the flop, on the turn, and on the river.

*What do the other players have in their hands?

*What cards were in the center? (The flop)

*What cards do we have in our 2-card hand?

#### Extension questions

– What are the odds of getting a straight?

– What are the odds of getting a flush?

– Which hand has the best chance of winning?

– expected value calculation based on Sam’s email

– Why are poker hands ranked in the way they are?