User blog:Heg Oiu/An exact definition of level difficulty


 * An optimal move is a move that maximizes the average probability of success of the possible resulting boards, assuming subsequent optimal moves; the probability of success for a board is the probability of success of an optimal move.
 * The probability of success with 0 moves left is 0 if you failed and 1 if you succeeded.

The probability of success for a level is the average probability of success of all possible boards (with optimal moves).

The "hardness" or "difficulty" of a level is the number of tries that is needed to succeed with a level with a probability of at least 0.5 (with optimal moves).

Let the number of tries required to virtually guarantee success on a level be the number of tries needed to have at least a 0.95 chance of succeeding with the level.

Then the difficulty and the "guarantee" numbers are ln(0.5)/ln(1-p) and ln(0.05)/ln(1-p) respectively, where p is the probability of success. The guarantee number is ln(0.05)/ln(0.5) = 4.3 times larger than the difficulty number.

The difficulties of all current Candy Crush levels (without boosters) are less than 100, since, surely, you are likely to succeed on any current level in less than 100 tries with very deliberate play.[1]

[1] Some evidence for this claim is needed. However aren't there videos of all levels (without boosters) that at least indicate this? Anyway, this is my experience, FWIW.