Math Game: Six Hundred

Today I’m working on the next book in my Math You Can Play series, culling the games that don’t fit. Six Hundred is a fine game, but I can’t figure out how it landed in the prealgebra manuscript…

Math Concepts: addition, multiplication, parity (odd or even).
Players: any number.
Equipment: six regular 6-sided dice (my math club kids love this set), free printable score sheet, pen or pencil.

Click Here for the Score Sheet

Set-Up

A full game consists of eighteen rounds of play. Players may share the dice and score sheet, taking turns around the table. But for a large group you may want to have extras, so that two or more people can be rolling their dice at the same time.

How to Play

On your turn, roll all six dice up to three times. After each roll, you may set aside one or more dice to keep for scoring, if you wish. Once a die has been set aside, you may not change your mind and roll it again.

After the third roll, choose an unused category on your score sheet. Count the dice according to the rules for that section, and write down your score. If your dice do not fit anywhere, then you must take a zero in the category of your choice.

When all players have filled their score sheet and recorded any appropriate bonuses (or penalties), whoever has the highest score wins.

Scoring

Dice are scored in eighteen categories, in four sections, as follows. The maximum possible score is 600 points.

Numbers

Record the sum of only the dice showing that number. For example, if you rolled 1, 1, 3, 4, 4, 4, you could score 2 in the Ones category. Or you could score 12 in the Fours category, or zero in the Fives.

Bonus: If the combined Numbers score is 80 or more, add 35 points to your total.

Rungs (1–4)

Score the total of all six dice. Like a ladder, the score in each rung must be greater than the one before it. Rung 1 gets the lowest number, and Rung 4 the highest.

You may fill in the rungs in any order. But if you write 18 in Rung 2, then the score in Rung 1 must be 17 or less, and the score in Rung 3 must be at least 19.

Penalty: If the Rung scores don’t fit the ascending value rule, this category is worth zero.

Clusters

Score the total of all six dice, if they fit the rules for that category.

  • Four of a Kind: at least four dice show the same number.
  • Five of a Kind: at least five dice show the same number.
  • Odds: all six dice show odd numbers.
  • Evens: all six dice show even numbers.
Patterns

Score the amount shown for each pattern.

  • Series: 30 points you roll 1, 2, 3, 4, 5, 6.
  • Pairs: 30 points if you roll three pairs of matching numbers. Four dice showing the same number may be counted as two pairs.
  • Triplets: 30 points if you roll two sets of three dice with the same numbers, such as three 2s and three 5s.
  • Sextet: 36 points when all six dice show the same number.
Game Bonus

If you score at least one point in all eighteen categories, or if the only zero you take is for the sextet, then award yourself an additional 36 points.

History

Players around the world have played poker-style dice games for ages. I grew up with Yahtzee, but you may know the game by Yatzy, Yacht, Generala, or another name.

Reiner Knizia included this mathematical version in his book Dice Games Properly Explained. And I found it online at Michael Ayers’s Stick Insect blog.

John Golden posted a simpler “Mathzee” game played with five dice on his Math Hombre blog — and while you’re there, be sure to check out his amazing Math Games page.


CREDITS: Feature photo (top) by rekre89 via Flickr (CC BY 2.0).

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17 thoughts on “Math Game: Six Hundred

  1. Hi Denise,
    We have a dice collector in the family, so I am definitely going to take a look at the dice game book you mentioned.
    He also loves game theory and coming up with new games.
    I’m afraid that Yahtzee will most likely be the game of choice with my kids. We have the Dalek version and the original one, too
    The 600 game sounds like pre- algebra material to me because there’s lots of arithmetic with natural numbers.
    If I can get that many dice I might try it.
    😺Kim

      1. I did a bit of game theory with a middle school group several years back. I didn’t find a good way to present it that would hold their interest, so I’ve never done it with later groups.

        The kids were intrigued with the *idea* of game theory, that there’s a branch of mathematics for studying games. But if you try to get into it deeply, it turns into politics and economics.

  2. Middle school seems like a good age to introduce some of the newer fields of Mathematics, like game theory. I was curious about it, so I found out as much as I could by reading and watching YouTube(yikes- don’t let me get pulled into that black hole!).
    I’m not looking to teach about it, however, from what I read, logic is being applied to situations daily, as you make decisions and knowing what the outcomes could be, could help you make a more logical decisions.
    Here is the video I liked:

    It’s a science channel🙂

          1. Thank you. I will bookmark it. It might take me awhile to figure out Desmos- or I can get the kids to help.😎
            I’m having trouble getting to the factors game. It looks like fun. I hope I can get to it. 😺

  3. Since I only have 2 kids left for homeschool math, technically speaking, I just share things that I’m interested in with them on the side, not as an actual subject. It helps them see that learning math is a life-long adventure.
    I just have to figure out how to explain to my 13 yr old why logrithms are not fractals after she watched Vi Hart without me. I was so confused, but happy to see her drawing them.

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