a.k.a Infinite Candy Crush
Background:
"Candy Crush Saga" is called a match3, but it has some "special" events that will eliminate all rows, eliminate all "candies" of a particular shape, or even convert all candies of a particular shape into "special events".
When I make a match lower down in the grid, it changes all the rows above it and creates secondary matches or special events. When I trigger a special event in the lower rows, similar phenomena occurs.
For larger grids there is a higher likelihood of making a match or event. The events also have higher likelihood of making a match.
Question
Given: the rules for candy-crush matching or special events (link, link), given a uniformly randomly selected population of in the field, and given an initial move of one of
- (preferred) a horizontal match of 3 identical non-special candies
- (extra credit)an acceptable "activate special" that either matches a striped or wrapped candy by combining it with two appropriately similar non-special candies
- (extra credit)combine two adjacent specials, or
- (extra credit)combines a "sprinkle" with either an adjacent non-special or special.
Find: the size of board such that a match or special event in the bottom row sets off a cascade that - Case1: definitely goes for more than 1000 iterations of events - Case2: (extra credit) probably or definitely goes indefinitely.
I put "extra credit" because I'm being fun. I think math is fun, so I am hoping that it is allowed here.
More references: