The Alpha Game - School Project
This is a probability game I created for school.
How to Play
This game is about spelling words with a spinner. The spinner has all 26 letters of the alphabet. As you spin the spinner, you will generate a combination of letters. If they spell a word, you win! If there are no words that start with that combination, you lose. If you could still win, you simply keep spinning the spinner until you win or lose. It costs 1 ticket to play. If you win, you get 3 tickets plus a ticket per letter in your word.
About the Mathematics
I used a computer to calculate the winning probability. It tried every possible combination of letters you can spin until they all won or lost.
First, it calculated the case where you spin an 'A' first. This has a 1/26 chance. If that chance occurs, there is a 1/26 chance that the next letter is another 'A'; this would mean you win because 'AA' is a word. The computer kept calculating and found that if you roll an 'A' first, there is a 63% chance that you will win.
However, that assumes you have already rolled an 'A'. The computer multiplied that chance by 1/26 to take into account that you may not roll an 'A' first. Then, it calculated the chance that you will win starting with any other letter and added the probabilities.
The chance that you will win a given match is (theoretically) 17.167772426522662%, and the expected number of tickets you will gain each round is 0.0625202045397612.