This only works if the game is fair and uses true randomness (or close to) as if the dices are rigged, this means nothing
100 total hits, with each being 4-7, an average of 5,5.
100*5,5 = 550, so less then the goal, so you have less then a 50% chance to get it, more precisly:
we will firstly simplify it:
total amount of hits * lowest hit = 100*4 = 400.
goal is 600, so I will remove the lowest amount of the 600, so we have 200 left, with 0-3 per hit, with 100 hits, this is easier to see, as we don't have a wierd starting point, we have 4 options, that each have a 25% chance to happen
200 is goal, 0 is lowest, 300 is highest amount we can get
so 200/301 doesn't gain the goal (0 is an option, so we add that to the total amount as well as the amount that doesn't gain us anything), that is the chance of it not happening, but we want the chance of it happening so we do 1-200/301, (as 1 is all options, and 200/301 fail) so my answer is 101/301 options win, or 33.5548172757% chance of winning with this strategy, so no, you don't need that mutch luck, as you have a 50% or more chance on the second try (55.72), close to 70% on your thirth try, and so on, after only 13 tries you have more than 99% chance of it happening, so no, only on your very first roll is it "special"
also sorry for this kinda necro post? (i don't know when it is necroposting)