In my last post I wrote about a Probability Activity created by Stone Librande. In this post I will adapt what he has created, but the credit goes to him.

Give each student a blank die (or stickers on a regular die that they could write on). Each student can write any number they want on each of the sides, but they still need to have a sum of 21. Also, the students cannot use the number combination 1, 2, 3, 4, 5, 6. Game play is that two students each roll their die, the player with the bigger number gets a point. This is repeated until one of the students has 10 points. The students keep switching partners to see how many times they can win.

After the students have used experimentation to determine the best die, take a look at why.

Suppose Player one used the numbers 3, 3, 3, 4, 4, 4 on his die, and player 2 used the numbers 0, 2, 2, 4, 5, and 8 on his. Below is a chart of the different outcomes. Gray is a tie, blue is a win for player 1, and red is a win for player 2. You can see out of 36 outcomes player 1 would win 18 times, player 2 would win 15 times, and they would tie 3 times. The corresponding probabilities: 50%, 42%, and 8%.

#### Activity #1: Create the Best Die

Give each student a blank die (or stickers on a regular die that they could write on). Each student can write any number they want on each of the sides, but they still need to have a sum of 21. Also, the students cannot use the number combination 1, 2, 3, 4, 5, 6. Game play is that two students each roll their die, the player with the bigger number gets a point. This is repeated until one of the students has 10 points. The students keep switching partners to see how many times they can win.

After the students have used experimentation to determine the best die, take a look at why.

Suppose Player one used the numbers 3, 3, 3, 4, 4, 4 on his die, and player 2 used the numbers 0, 2, 2, 4, 5, and 8 on his. Below is a chart of the different outcomes. Gray is a tie, blue is a win for player 1, and red is a win for player 2. You can see out of 36 outcomes player 1 would win 18 times, player 2 would win 15 times, and they would tie 3 times. The corresponding probabilities: 50%, 42%, and 8%.

At this point you could challenge the students to create a die that would always win. I'm not sure that this is possible, but see where the students take you.

#### Activity #2: Create the Best Space Ship

You can find some information for this on Stone Librande's website. Use this link, scroll down to 7) and click on

*Squoddron Odds Chart (Excel file)*. This will lead you to all the possible outcomes but there are no directions. That's where I will*try*to fill in.
I decided to play against my son to make sure everything made sense. So here goes nothing...

First you are going to need a 4-sided, 6-sided, 8-sided, and 10-sided die for each student.

Each student should draw a spaceship that has one engine, two weapons, and one shield. Here is my spaceship:

And here is my son's spaceship:

Once you have your ships, place one die on the engine, one on the shield, and the other two on each weapon. Which die on which part you ask. That's the magic of this activity. Each person gets to decide for themselves. A person who thinks that the engine (or speed) is the most important will put the 10-sided die on that. A player who things that offense is the most important will put the 10-sided die on a weapon. You get the idea.

Now you are ready to play. You start this by decided who is going to attack first (you will take turns attacking each other). Then both players roll their engine die at the same time.

We started with my son attacking me. He used his 10-sided die for his engine and I used my 4-sided die for my engine. He rolled a 7 and I rolled a 2. Since he rolled a higher number than I did, his engine is faster than mine and he was able to attack me.

Next he rolled both of his weapon dice (6-sides and 8-sided) while I rolled my shield die (10-sided). He rolled a 4 and a 3; I rolled a 6. Since my shield was a greater number than both of weapon numbers, I deflected both of his shots and he did not win the battle.

Next we switched rolls. We continued this back and forth until one of us won 5 battles. At this point, the students would find another person to battle with, preferably winners vs. winners to have a class winner.

Notes:

If the person attacking rolls a number lower than the defender, there is no battle because the attacker wasn't able to go fast enough to get to the other spaceship.

If the engines roll the same number an attack will take place.

If a weapon and a shield roll the same number, the shot is deflected.

After playing a few rounds, I wanted to switch the position of my dice as I imagine my students might want to do. This would be a good time to have discussions with them as to why they would want to change things around.

BTW my son won.

As a gamer, this is amazing. My guess is that I'd want the die with the highest average roll for my engine, because that's the first gate for both attacking and defending. I think I'd put the next two on weapons, based on the idea that I will already be defending less frequently due to my engine....but I know that sometimes in the real world, things have quirky ways of working out.

ReplyDeleteYou definitely drew me in. I'm going to be thinking about this all day! :D

Regarding activity #1, there is no single best die. It is possible to create 3 dice so that A beats B more than 50% of the time, B beats C, and C beats A. Love this problem.

ReplyDeleteDefinitely using at least #2 this spring - thanks!

ReplyDeleteFor #2, why isn't 1,4,4,4,4,4 the best die? Don't you just want to have as many faces exceed 3.5 as possible?

I can beat your die with 1, 1, 4, 5, 5, 5. You would win 10 out of 36 or 28% of the time. We would tie 7 out of 36 or 19% of the time. And I would win 19 out of 36 or 53% of the time.

DeleteCould this be done with a 6 position spinner? That might be easier to make than stickers on a dice.

ReplyDeleteAbsolutely!

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