You may also like

problem icon

Stop or Dare

All you need for this game is a pack of cards. While you play the game, think about strategies that will increase your chances of winning.

problem icon

Snail Trails

This is a game for two players. You will need some small-square grid paper, a die and two felt-tip pens or highlighters. Players take turns to roll the die, then move that number of squares in a straight line. Move only vertically (up/down) or horizontally (across), never diagonally. You can cross over the other player's trails. You can trace over the top of the other player's trails. You can cross over a single trail of your own, but can never cross a pair of your trails (side-by-side) or trace over your own trail. To win, you must roll the exact number needed to finish in the target square. You can never pass through the target square. The game ends when a player ends his/her trail in the target square, OR when a player cannot move without breaking any of the rules.

problem icon

Game of PIG - Sixes

Can you beat Piggy in this simple dice game? Can you figure out Piggy's strategy, and is there a better one?

What Does Random Look Like?

Stage: 3 Challenge Level: Challenge Level:1

Ed from St Peter's College started off by experimenting and gave an initial insight into the problem:
 
I flipped a coin 20 times and got the following results: 13 heads and 7 tails. The best way to analyse if the coin is real or not is whether it has a significant number more of one side over the other.

Krystof from Uhelny Trh, Prague gave examples of some of his runs:
 
I made three runs
1) THHTTTHTHHHTTHHTTTHT
2) THTHTHTHTHTHTHTHTHTH
3) HHTHHTHHTHHTHHTHHTHH
Number 1 is real, there are not exactly the same number of heads and tails, but nearly. There are also lots of different length runs, but mostly 2s and 3s.
Numbers 2 and 3 are made up. They have regular patterns. There is a very small probability of these occuring randomly.
 
There are many interesting principles of probability and statistics revealed in this simple activity. Connor from Gladesmore gave some very good points:
 
For a total random coin the number of "runs" of heads/ tails should be more weighted toward the smaller runs. Also a table where the result alternates e.g. h, t, h, t will be more likely the fake one as although the total number of heads and tails should be almost the same the order should be random. Finally when there are only a small number of coins flipped then you would expect that the total will not be completely identical.  
 
Good job everyone! Can anyone add more? What about the probability of different length runs occuring?