First lets examine "RNG". RNG stands for Random Number Generator, which is a misnomer as a RNG is anything but random. A Random Number Generator works by checking against a mathematical function to produce a number within a specific set of limits. In simple programing terms it is usually somewhere between .00 and .99. A RNG is never pure random as the math which is used to generate that number can be understood and future numbers can be predicted with 100% accuracy. Second we have no idea that that 6 items means each item has a 1/6 chance of appearing every day. It could be that there is a 1/3 chance for between helms, chest and hand exotics, with there being a 1/3, 1/2 and 1/1 respective chance for a specific item to appear in each category. If so that means that there is a 1/3 * 1/2 or by the magic of pure coincidence a 1/6 chance of Voidfang appearing in any given week, a 1/9 chance of any given helm appearing in a given week or a 1/3 chance for Sunbreakers to appear in any given week. Third you are correct, previous rolls do not affect future rolls. However the chance, over a given 4 week period, that any given item will appear each week is the chance of the item appearing in a given week raised to the power of the number of weeks, given that the chance is constant across all weeks. In other words (1/6)^4 or after the math in the OP 0.00077 and some change.