For a grid game to match items in chains of 3 or more, how can a difficulty be calculated?
I have a number of moves, and a grid with a cell count and an element type count n, e.g. 6 different elements/types. Matching elements gives 20 score per element in a chain, e.g. 60 for a 3 element chain. If additional matches occur during the same move a multiplier is applied so e.g. the second 3 element chain will give 120 points.
I would like to be able to use a formula with the variables and then apply a difficulty variable to the outcome, so e.g. there could be a minimum score, and then 3 other levels or rankings for the score they got.
How can this be calculated with the given variables and an additional difficulty variable?
The game is a one player game, which fills a grid with elements/objects. The player then gets a number of moves. When they match a sequence in the grid, new items are dropped in to replace them, which could trigger new matches.
This isn't a very mathematical answer, but I don't think there is a good mathematical approach. I would simply create a program to play completely randomly. Have it play maybe ten thousand games and look at the statistics on what kinds of scores it gets. Base your target scores on percentiles: On easy mode, you simply have to get a better score than in 70% of those random games, on normal mode better than 90%, and on hard mode better than 99%. You will have to adjust those numbers by actually testing your game out with real human players to find out if they're too high or too low.