- Jan 24, 2004

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**GG's Tip-o-the-Week (11-28)**

The great Meph project is finished, thanks to all who gave their input.

All drops calculated at /players 3 with 500 MF.

First, I assumed mututally exclusive drops. This essentially means that Meph is only capable of dropping 1 Set/Unique per kill. Of course, he drops more often. But the independent probability of any two specific S/U items dropping at a given time is exponentially UN-likely, therefore, I am going to assume it to be zero.

Example:

Odds of Stormlash = 1: 36,321

Odds of Stormlash AND Occulus = 1: 36,248,358

Next, let's try what I believe is a Dynkin system. Let C be a collection of subsets of X. In this example, C would be the entire exceptional grail, and X would be each individual item within C. If D is a Dynkin system containing C, then D also contains each item X within C.

Example:

If Stormlash = 1: 36,321

Then every item that SHOULD drop within 36,321 runs, WILL drop.

Therefore, if Stormlash is the rarest item at 36,321 runs, the minimum number of runs to get every item that Meph can drop is 36,321.

How many Meph runs should I run before it's just not worth it anymore???

To answer that question, I tabulated the individual odds for all the elite uniques in a spreadsheet, and graphed it. The trendline is almost flat, with a huge vertical skew at the end, representing Stormlash and Spirit Keeper.

Removing those two items created a graph definable by fourth order polynomials. I'm not too happy with that, since it still includes a great number of very unlikely drops.

Finally, I graphed 2/3 of the elites (40 of 59). This turned out to be a nice, clean linear equation.

y = 17.874x + 261.93

Therefore, if you are happy with 2/3 of the total elites, you only need to run Meph 1,000 times. Given that Meph cannot drop TC87, I believe this is the most reasonable solution.

Conclusion:

Run Meph 1,000 times, then move on.

GG