Sunday, 21 June 2015

Rock-Paper-Scissors: Is it maths or psychology?


I stumbled across this fascinating theory of how to win Rock Paper Scissors and thought it was another good example of how we use probability in our daily lives.

Article Link: How to Win at Rock-Paper-Scissors

YouTube Link: How to Win at Rock-Paper-Scissors

I shared these both with my class on a Google doc and suggested they read / watch at home and to start an online chat about the theory.  

This generated a really interesting discussion with children posing questions to each other or sharing their own theories as they tried to work out whether this strategy was maths or was it psychology or a mixture of both.

Google Doc Link: Our Online Discussion at Home

During the online discussion, a few children suggested we should test the theory out at school to see if it really does work or not.  It always excites me when children in my class start take ownership of our learning by making suggestions of what we should do. 

Example of some of the online discussions happening at home:

That's weird... I thought that we need a pattern, not to do it randomly.
John O’Neil
17:18 17 Jun
Well if you think about if you always did a pattern then if you played against someone 5 times in arow then they know what to do... so that is why we can do it randomly
Graeme Anshaw
17:18 17 Jun
I usually play with a pattern in mind too. Is this why I lose at games so much? Hmmmm.....
John O’Neil
17:19 17 Jun
Could be true. Could be false
Graeme Anshaw
17:21 17 Jun
You're right Jack. It DID say it is a 'theory'. Thanks for reminding me of that. Phew! Maybe I haven't been playing games incorrectly all these years

The next day:
A lot came in playing Rock-Paper-Scissors with each other and buzzing about the theory.  

Listening in, some shared how they had tested the theory out at home and found it really did work, a few were still a bit confused by it and so their classmates were explaining it to them and some were passionately debating whether it was mathematical probability, a random win or just psychology. 

Our maths learning had already begun for the day and I hadn't even said a word. Love it! They were hooked in.

Our Mathematical Experiments:

We looked at our line of inquiry we have been focusing upon and discussed what we had already found out.  

FUNCTION: Ways we can measure probability visually

I also posed our main enquiry focus for the day:

Is this theory maths or psychology?

I explained that at the end, we will be discussing this question, so we should focus on this during our activity.

As a think-pair-share, we had some time exploring different ways we could visually show the possible outcomes when we play Rock-Paper-Scissors. 

These were some of our ideas:

We initially felt this student's idea was confusing, but when we examined it a bit longer it began to make a lot more sense to us:


                                       Another idea:


A few experimented with the tree diagram we had looked at the day before:


Remembering that maths is a science, I asked what we could do with this theory.

- We should test it out!

- Let's do an experiment!

- We should write a hypothesis and test it!


So that's what we did.

We each wrote a hypothesis based upon this theory of winning Rock-Paper-Scissors.   Some children chose to write a hypothesis based upon whether you win a round, what you should do next to win again.

Some of our hypotheses we created and tested:

-When someone wins a round of Rock-Paper-Scissors, if they don't repeat what they just won at, they have a higher probability of winning again.

- If a person loses a round, they should next play whatever will beat the winners' choice as it is likely the winner will repeat the winning choice.

- There is a higher probability that a winner will repeat the same choice in the next round.

- For a loser to win the next round, they should choose whatever the winner just played as it is a high chance the winner will repeat their winning play.

- When a person wins and the other player knows the theory, they should go backwards because there is a high probability the loser will go forward.

Conducting our experiments:

When conducting our experiments we needed to design an effective way to record the results.  Rather than feeding them with a set table to follow, I think it's important to give children the opportunity to problem solve in these situations.  As they were testing out their hypotheses with each other, I chatted with some students about the way they were recording their results and finding out if they thought it was an effective way and if not, what could they do maybe to improve it.



Drawing conclusions:
After gathering our evidence, we wrote our conclusions of whether our hypotheses were proven or disproven and discussed why.  We remembered that from our previous UOI looking at scientific thinking that even when an experiment does not prove a hypothesis, it is still successful.  

Finally, we had some time thinking about our focus question:

 Is this theory maths or psychology?

After writing our thoughts, we discussed with our table partners and then as a whole class.   

We all felt that it was a mixture of maths and psychology.

Most of us felt it was more psychological than mathematical.

A few of us felt it was slightly more mathematical.

We all agreed though, that understanding this theory of how to win has given us a competitive edge in life.  :)

The Ultimate Rock-Paper-Scissors Tournament:

A suggestion shot up that we should have an 'Ultimate Rock-Paper-Scissors 2015 Tournament' to find out what happens when people know the strategy play against each other.

How could I say no?   

So, that's what we did.  We shared different ways we could design the tournament so that everyone could compete fairly.  We eventually agreed upon one idea and played it out.

We found it really interesting to play against others who knew the winning strategy.   As one student explained:

- When you play against someone who knows the winning strategy, you have to out-strategise the strategy by going against firstly what your instinct tells you to do and then to go backwards rather than forwards.  

Sounds complicated?  

 It does to me too a bit, but in the minds of the 10 / 11 year olds it all made perfect sense what they were formulating and testing out. 

I think it is brilliant when the children in my class understand something better than me!! :)

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