You will ruin this game with Personal Loot

Loot drops are random. In an 8 player game setting over time, the average likelihood that an A item drops and B-item drops will be equally likely for each player with the knowledge that their is binomial variance.

You could get cases where what you say happens; however over time the relative variance/standard deviation with respect to the average of the binomial distribution decreases as the number of drops increases. Mathematically, what I say is true over the long haul and not for a small sample set of n events.