Probability of winning the game with multiple variables
I am trying to solve a complicated problem at least too complicated for me to solve.
Lets say I have a game
- 100 players play the game in the same time
- Players are asked one question every day
- Every questions have 3 possible answers and only 1 correct answer - every correct answer worth 1 point)
- Every answer has same probability to be correct (Probability of the answer being correct is 0.33333 and wrong is 0.66667)
- Player gets 10 correct answers (10 points) win the game and all statistics get reset and game starts again
- If a player answers 5 consecutive correct answer then the player win prize but no reset so game carries on
- If a player answers 3 consecutive questions wrongly then his statistics get reset and he starts win 0 points.
- The game is played for 1 year (365 days)
All above are variable
How frequently a player win the game by answering 10 questions correctly
How frequently a player gets a prize by answering 5 consecutive questions correctly.
I need the formulas to use in Excel..
Anyone can help as I need this urgently.