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Coin Tossing Games

You and I play a game involving successive throws of a fair coin. Suppose I pick HH and you pick TH. The coin is thrown repeatedly until we see either two heads in a row (I win) or a tail followed by a head (you win). What is the probability that you win?

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Win or Lose?

A gambler bets half the money in his pocket on the toss of a coin, winning an equal amount for a head and losing his money if the result is a tail. After 2n plays he has won exactly n times. Has he more money than he started with?

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Thank Your Lucky Stars

A counter is placed in the bottom right hand corner of a grid. You toss a coin and move the star according to the following rules: ... What is the probability that you end up in the top left-hand corner of the grid?

Mathsland National Lottery

Stage: 3 and 4 Challenge Level: Challenge Level:1
Use the +/- buttons in the top left hand corner to increase or decrease the number of balls in the Number Tumbler. For example, to simulate the UK National Lottery, increase the number of balls to 49.
 
Use the +/- buttons by 'Your Ticket' to increase or decrease the number of spaces on your lottery ticket. For example, to simulate the UK National Lottery, increase the number of spaces to 6.
 
Then click on the numbers in the Number Tumbler to select which numbers you would like on your lottery ticket. 
 
At the bottom of the screen, use the +/- buttons to choose how many draws will be simulated.
 
Once the simulator is set up, click the 'Simulate lottery draws' button to run the lottery your desired number of times.
 
The 'Matches black' button marks every time one of the numbers from your ticket was drawn.
The 'Sort matches' button rearranges the draws with all your winning tickets together.