#### A Math Forum Project

 ESCOT Problem of the Week: Archive of Problems, Submissions, & Commentary

Student Version

### Rock, Paper, Scissors III - posted January 19, 2000

Try Rock, Paper, Scissors - Part I and Rock, Paper, Scissors - Part II before you do this problem. If you are working on this activity right after Part I or Part II, please make sure to quit the ESCOT runner and start it again.
This is a simulation of a three-person game of Rock, Paper, Scissors. The game rules are as follows:

1. Ed receives 1 point if all three players display the same hand arrangement.

2. Angelique receives 1 point if all three players display different hand arrangementa.

3. Vicky receives 1 point if just two players display the same hand arrangement.

Who do you think will win this game: Ed, Angelique, or Vicky?

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Students made a wide range of predictions for the outcomes. The majority correctly predicted that Vicky would win most of the games, but quite a few thought that Ed and Angelique would tie on the rest of the games. Their simulation outcomes were quite similar, of course, and most students were able to convert their own outcomes into percentages. Very few students generalized from their own particular outcomes as to whether other simulations should produce similar results or whether there could be any patterns in these results.

### Highlighted solutions:

 From: Jordan H., age 13Ryan B., age 14Mac W., age 14 School: Issaquah Middle School, Issaquah, WA

1. What is your prediction for each player's score? Why do you think it will
turn out this way? (Answer this first. Then play the simulation. Then come
back and answer the other questions.)

I think that vikcy will win and angelique will have a little more than
Ed. I put a graph out and it ended up that ed won one out of nine, angelique
won two out of nine and vicky won six out of nine.

2. How many points did each player get when you ran the simulation?

It was about on average angeleque gets about ten more than ed, vicky gets
three times as many as angelique and about four times as many as ed.

3. How do these results compare with your prediction?

they are the same as my prediction.

4. What is the winning percentage for each player?

ed gets 11.1% angelique gets 22.2% and vicky gets 66.6%.
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 From: Sarah A., age 14Jared A., age School: Issaquah Middle School, Issaquah, WA

Our prediction is that Vicky will win.  This is because there is more of a
chance of having two of the same thing than all the same or none of the same.
2. How many points did each player get when you ran the simulation?
Ed got 24 points, Angelique got 44 points, and Vicky got 132 points.
3. How do these results compare with your prediction?
They compared equally because Vicky won.
4. What is the winning percentage for each player?
For Ed's percentage, you divide 12 by 200 and get 12%.  To find Angelique's
score, you divide 44 by 200 and get 22%.  To find Vick's score you divide 132
by 200 and get 66%.  12% plus 22% plus 66% equals 100%.
------------------------------------

### 23 students received credit this week.

Jared A., age - Issaquah Middle School, Issaquah, WA
Sarah A., age 14 - Issaquah Middle School, Issaquah, WA
Megan B., age 13 - Issaquah Middle School, Issaquah, WA
Ryan B., age 14 - Issaquah Middle School, Issaquah, WA
Katharine C., age 12 - Issaquah Middle School, Issaquah, WA
Callen F., age 13 - Issaquah Middle School, Issaquah, WA
Megan G., age 13 - Issaquah Middle School, Issaquah, WA
Greg H., age 12 - Issaquah Middle School, Issaquah, WA
Jordan H., age 13 - Issaquah Middle School, Issaquah, WA
Omar H., age 13 - Issaquah Middle School, Issaquah, WA
Elizabeth J., age 12 - Issaquah Middle School, Issaquah, WA
Carly M., age 13 - Issaquah Middle School, Issaquah, WA
Leslie M., age 13 - Issaquah Middle School, Issaquah, WA
Robert M., age 13 - Issaquah Middle School, Issaquah, WA
Chris N., age 13 - Issaquah Middle School, Issaquah, WA
Lucas O., age 14 - Issaquah Middle School, Issaquah, WA
Holly S., age 14 - Issaquah Middle School, Issaquah, WA
Sei T., age 12 - Issaquah Middle School, Issaquah, WA
Jesse U., age 13 - Issaquah Middle School, Issaquah, WA
Benjamin W., age 14 - Issaquah Middle School, Issaquah, WA
Mac W., age 14 - Issaquah Middle School, Issaquah, WA
Brian Y., age 14 - Issaquah Middle School, Issaquah, WA
Devon Y., age - Issaquah Middle School, Issaquah, WA