We are trying to find the average number of moves of a game. The game is big enough that we can approximate the probabilities with a bell curve. We could also use a simulation. Both give an accurate enough result. We do not need the exact answer. The average roll moves you 3.5 spaces. The probability that you land on the star on any given pass is thus 2/7, and miss it, 5/7. So the average number of passes you make is 5/(7-5) = 5/2 = 2.5 passes. 2.5*24 equals 60 squares. The average number of rolls will then be 60/3.5 equals 17 and a seventh rolls. The standard deviation for this is calculated by the formula below, and it gives about 7.071. What we do next is surprisingly simple: subtract the average number of turns it takes to move standard deviation from the average. In equation form, 17.143-7.071/3=Our answer is that the game takes an average of about 14.79 turns.
D=\sqrt{\frac{qty\times(s^2-1)}{12}}\\[8pt] D=5\sqrt2\approx7.071