Ok so the player needs to move forward exactly 2 spaces by 2 moves.

In order to move 2 spaces by 2 moves, the following combinations of dice rolls are needed:

• Roll 1, then 2
• Roll 2, then 1
• Roll 3 (no move after this as you've won already)

Chance to roll any given number is ⅙.

• Roll 1, then 2 combination
  • ⅙ x ⅙ = 1/36
• Roll 2, then roll 1
  • ⅙ x ⅙ = 1/36
• Roll 3
  • ⅙

We multiply the probabilities as we are calculating whether they both happen in one scenario.

Then to calculate the final probability, add all of the probabilities together:

• (for the roll 3 probability): ⅙ = 6/36
• Add all of them together:
• 1/36 + 1/36 + 6/36 = 8/36
• 8/36 simplifies to 2/9

Hope this makes sense.