Originally Posted by

**Ken Holloway** Hi,

I have been given a two pronged problem to solve at college whereby I need to calculate the percentages involved in winning a game with a weighted coin.

The game is the be the first to score 5 successes and the coin is weighted 70/30 in favour of heads.

First part is:

How would I go about calculating the possible scorelines involved and the percentage chances of either side winning this game?

I have tried using binomial distribution by drawing out a map and checking off potential scorelines but get confused when having to nullify branches of the tree that are essentially out of play (becuase the goal of 5 has already been reached).

Is there a more simple approach to working out percentages for all possible scorelines and the chances of winning the games?

The Second and more tricky part is:

How do I calculate the percentage chance of either side winning in any given scoreline?

So for example if it is 3-1 to Heads or they are drawing 4-4 , what are the chances of either side winning now?

Any help would be appreciated