Given a particular snakes and ladders board it is necessary to find:
- The most likely number of moves needed to reach square 100
- The average number of moves needed to reach square 100
- The least number of moves needed to reach square 100.
These questions became important after I purchased a board which took so long to complete that my children got frustrated. I wrote a program that analysed all possible games that could be played and then animated it.
The animation can be thought of as a long exposure photograph of games on the board. It shows where the piece is most likely to be at any point in the game, thus giving a measure of the use each square will undergo. The probability is the value on the square divided by 100000. For this board the answers were:
- Most likely number of moves = 20
- Average number of moves = 80
- Least number of moves = 8, for example: 3,2,6,6,6,2,5,4