CBS Game Theory Talks

Introduction
Public summary: 

This is a series of talks from CBS 2017 and 2018 exploring games we encounter everyday and the mathematics behind them.

Talk from CBS 2017 + 2018
Useful information
Kit List: 

The Kruskal's Count Experiment (lots of duplo or bigger bloacks)
A monopoly board
Grime Dice Experiment
Evolution Games PLUS Experiment
[Large Fishtank(s)
Food Colouring
Wooden Spoons
A bath toy with a spinny thing on it]
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4 giant golden balls with Split or Steal inside
A selection of voting remotes
A large cardboard screen
2 signs with Left and Right on either side

Explanation
Explanation: 

This was given as two talks at CBS 2017 and 2018. Originally it was intended to be one talk but it turns out there's a lot of interesting things to talk about so there wasn't time to get through everything I could have spoke about.
Here follows some of the ideas in the order they appeared in the talks, as well as [some ideas that didn't make the cut]. Please email tw432@cantab.net for slides for these talks, it's one big (>100MB) power point plus videos and gifs. Slides can be skipped as appropriate and this is mostly in speaker notes.

Maths, Games and Being Nice (2017)

What is maths? - Well everything really.
Monopoly - I could win if I could buy properties everyone landed on, but it's complicated so lets play a simple game.
Volunteers for Kruskal's Count Experiment (3ish) - Volunteers use a laser pointer to move around a giant board on the screen, the audience can follow their own paths from their seats. The PowerPoint gives an animated demo of how to play. We then set a trap (buy a property) around the board, Hands up if you're caught, nearly everyone falls into it! Volunteers leave.
We then work backwards to find out where we could start, there's not many places.

[We could also look at the emergence of a steady state, if we keep going round we end up stuck in a giant loop, this isn't the case in monopoly as we have some more randomness but maybe we still have a preference for certain paths and squares]

Monopoly
We explain the similarities and the rules of the game. We explore some of the reasons why we might prefer some squares, there's lots of ways to get to jail and when rolling two dice it's more likely we'll get some numbers than others.
Simulation of Monopoly - this shows how we move, we notice no cycles but some squares get landed on more.
Allows you to value how much a property is worth but only if you play long enough.
[ How long is long enough? Take 3 2L pop bottles filled with water and get 3 volunteers down. Put a drop of black food colouring in each bottle and put the lid on firmly. Ask one child to hold it still, the other to swirl it slightly and the third to shake it quickly. We should be able to see under the visualiser the differing colours after a minute. It's very difficult to predict where the colours are until they've fully mixed which is what we're having to wait for in Monopoly. You can also do this with fish tanks, wooden spoons and bath toys. How might changing the rules affect these times or simulate it's value for Monopoly]
How might these ideas be useful, well this is how google ranks it's search results, it visits random links on a page and uses this to rank pages.

Grime dice experiment
We need one volunteer to play a dice game. We'll try and roll the highest number and you can look at the dice and pick first too. The dice display in big on the screen (Note there's actually a difference between these and the CHaOS Grime Dice as CHaOS has the expanded set of 5, image needs updating). Order is Red > Blue > Green > Red. We take a close look and see winners. But they form a cycle, so by picking second I increase my chance of winning!
We then compare this to rock paper scissors. It's the same relationship between the options.
[We can then look at pairs of dice and a 5 player game]

Lizards
Explanation of how evolution is like a game.
Talking about Side Blotched Lizards, the strengths of these kinds look like Rock, Paper, Scissors too!
This causes a cycle in the population.
Females are very important in making sure none of the tree splotches go extinct.

Who Wants To Be A Mathematician? (2018)
For this talk voting remotes need to be handed out to all audience members (including parents) small children should use there parents remote.

We repeat the introduction from last time on What maths is and what a game is.

Coordination
Explain some simple games. Firstly Coordination, we'll need two volunteers with their adults. On opposite side of a giant screen. The children should pick out Left or Right and if they match they'll get a reward, after two goes the adults can take the sign and the same question will be asked but this time we'll give some context of you driving down a road. The adults should pick left. They may return to their seats.

Golden Balls
We then move onto the Game of Split or Steal, made famous by TV Game Show Golden Balls. 2 new volunteers come to play. We can then watch the video and see why we should always steal, play once more and return.
Explain some analogues with evolution and animals playing games, we can turn this into a food fight game.
[Analyse this game]

Millionare
You may think it's just a game of knowledge, but we have some advantages, ask the audience. We'll ask some questions now and get you to vote on the remotes. If you're not 100% sure then press the answer you're most confident in.
Ask some questions of ranging difficulty targeted at kids, adults etc.
Lets say this is really difficult question that none of you know, if most of you are guessing what's going to happen. (Question like "Which month is my birthday in?")
Okay now we're going to ask if you don't know the answer don't press anything.
What's this going to do? Well if people are guessing at random they're adding on lots of random noise, if it's all equal then that's fine but when only a few people know the answer it could mask that signal.
Ask birthday question again and get CHaOS helper to vote on several remotes for correct answer. Friends in the audience then can come through.

Risk Assessment
Date risk assesment last checked: 
Tue, 02/01/2018
Risk assesment checked by: 
Tdwebster
Date risk assesment double checked: 
Fri, 12/01/2018
Risk assesment double-checked by: 
Josh Garfinkel
Risk Assessment: 
DESCRIPTION Modelling evolution via game theory.
RISKS 1. Children swallowing duplo or lego pieces

2. Tossed coins flying off and hitting someone

3. Many children trying to occupy the same card

4. Cards are slippy if stood on
5. People may trip on dice
6. Slip hazard from spilt liquids.
7. Cardboard divisor could be an obstruction to fire exit.
8. Paper cuts from signs.
9. Allergic reaction to any sweets given out.
10. Swallowing of voting remotes.
ACTION TO BE TAKEN TO MINIMISE RISKS 1. The duplo pieces should be sufficiently large to discourage swallowing. Do not use lego with very small children and keep a close eye on the box of lego.

2. Check you can flip a coin without losing control of it, otherwise just spin it on the table. It's perfectly fine to let the children toss the coin themselves, but make sure they're capable of doing it safely with a trial flip first.
3. Keep the number of children playing the game on the giant cards under a sensible limit, I would suggest 8 at a time, and discourage them from running or any form of pushing and shoving
4. Discourage people from actually stepping on the cards.
5. Keep dice on table
6. Do not use necessarily large amounts of water/food colouring. Replace lids on nearby bottles when not in use. Mop up all spills promptly. Keep visitors away from area until cleaned up.
7. Divide to be moved by presenter/CHaOS Audience member in case of fire.
8. Signs to be covered in tape so safe.
9. Use boiled sweets so limited allergens, give to parents.
10. Hand remotes to parents of small children to supervise them using if necessary.
ACTION TO BE TAKEN IN CASE OF ACCIDENT 1. Call first aider if child swallows, if choking encourage child to cough.
In all cases, call first aider in case of injury
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