Given a particular snakes and ladders board it is necessary to find:

  1. The most likely number of moves needed to reach square 100
  2. The average number of moves needed to reach square 100
  3. 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
. 1 2 3 4 5 6 7 8 9 10 20 19 18 17 16 15 14 13 12 11 21 22 23 24 25 26 27 28 29 30 40 39 38 37 36 35 34 33 32 31 41 42 43 44 45 46 47 48 49 50 60 59 58 57 56 55 54 53 52 51 61 62 63 64 65 66 67 68 69 70 80 79 78 77 76 75 74 73 72 71 81 82 83 84 85 86 87 88 89 90 100 99 98 97 96 95 94 93 92 91 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 Move = 0 Pause Step Least Number of Moves = ? Probability of reaching 100 at move N .02 .01 8 20 100 200 Probability of finishing in less than N moves 1 .5 MOVE 80 100 200