# Yahtzee

Players: 2 and up
Ages: 5 and up
Which dice do you want to re-roll? Why?
What are the odds that you will roll a 5 with that die?
Which boxes can you fill in with the dice that you just rolled?
Who is winning? How do you know?

Can a three-year-old play Yahtzee? Well, no, not exactly. The rules are simply too complex.

But can a three-year-old have a rich mathematical experience while playing a modified version of Yahtzee, or by helping their parent or sibling play? Of course!

You may have noticed that I am pretty liberal with my age recommendations for games. This is intentional; I believe that kids can gain mathematical ideas and insights from a game, even if they don't have the attention or skill to complete the game in its original form.

Once you know how to play a game, you can modify it to meet the needs of your children. To illustrate what I mean, let's talk about Yahtzee.

## How to Play

Yahtzee is a classic for a reason. The setup is a breeze, the rules are comprehensible, and the strategy is deep.

Each player rolls five dice and then chooses whether to re-roll any of those dice. The best roll is a yahtzee, where all five dice have the same value.

After three total rolls, the player then determines which scores she qualifies for with her roll. Did she roll four 5s and a 1? Then she can claim a four-of-a-kind for 21 points (the sum of all five dice). She has other options, though. She could add up all the 5s and get 20 points, or she could add up the 1 and get 1 point.

Each player has thirteen rounds, during which they are trying to fill in their thirteen boxes on the score card. The only complication is that once a box has been filled, you can't fill it again. If you already scored a four-of-a-kind and roll another four-of-a-kind, you have to find a different box to fill.

At the end of the game, players add up their points. The player with the highest total wins!

(By the way, I have never completed a full thirteen-round game with any of my kids. It's fine! They learned plenty before they started throwing couch cushions at me during round seven)

## Where's the Math?

Yahtzee is a great game because it has accessible math for young kids, older kids, and adults.

For pre-school children, the dice provide a great opportunity to work on matching, counting, and subitizing. What's that last one?

Subitizing is the process of seeing a quantity without having to count by ones. Think of the way that five dots are arranged on a die. Do you have to count them one by one, or do you just know it's five? That's what it feels like to subitize.

Young kids get a chance to practice this skill over and over with dice, counting the pips until they internalize the way that six, five, four, and so on are represented on dice. Then they can match them on subsequent rolls. Even a three year old can tell if they've rolled a yahtzee!

Older kids get to practice addition in ways that encourage them to find shortcuts and patterns. Imagine your first grader rolls three 5s, a 6 and a 4. Do they really want to sit there and add those up by counting every pip one-by-one? No way. They're going to look for ways to make this problem easier. Maybe they add 5 and 5 to get 10, then add a third 5 to get 15, and then start counting by ones. Or maybe they realize that 6 and 4 also make 10, which further shortens the time they spend counting.

Your child might cringe at a worksheet that gave them thirteen problems that look like 5+5+5+6+4. But put those same problems in the context of a game of Yahtzee, and suddenly it's exciting! After all, they gotta find out how many points they scored!

For example, when should you break up a full house to go for a Yahtzee? What are the odds of rolling a 3 on the next turn? If you roll three of a kind on the first roll, what is your likelihood of ending the round with a yahtzee?

The math in these questions is challenging enough to occupy any middle or high school student who is interested in probability. If you really want to nerd out about the math of Yahtzee, here are some problems you could occupy yourself with...

The questions you ask your child depend on the way you've modified the game.

For your youngest kids, you can simply play with the dice, in a modified version of the game Tenzi. Your child can simply roll as many times as she wants until she gets a yahtzee. As she rolls, you pepper her with questions such as "Which dice match each other? How many dots on on each dice? Is this die a five or a four?"

With early elementary kids, I would keep track of the score, but I would definitely focus less on the strategy of the game and more on adding and skip-counting. Skip-counting, by the way, is counting by some interval other than one. If you roll four 3s, you might count up 3, 6, 9, 12 rather than counting by ones all the way to 12. This skill is a prerequisite for multiplication, so it's a great one to get kids working on whenever they seem ready. After all, once they get the hang of it, they'll be much faster at counting and getting to their next roll!

For older elementary kids, I would focus my questions on the bigger strategy of the game. For example, which boxes can you fill in with this set of five dice? Finding all possible scores, even the suboptimal ones, is a mathematical skill in and of itself.

You can also inquire about the strategy of choosing to re-roll the dice. For example, if you roll four 5s and a 1, should you take the extra point and fill in the four-in-a-row box, or should you bank those 20 points in your 5s box and try to roll an even higher score for four-in-a-row? What other information should you consider when making this decision?

No matter how you play the game, you're sure to encounter some interesting math along the way. If you have a strategic question yourself, ask it out loud! Turn it into a debate.