Phantom Roll: Knowing the Odds (long, math)

[Icemage]

Kinda off topic (please don't hurt me, moderators. >_< ), but where do I go (on web) to educate myself so I can understand the math behind this dicussion?

This is a reasonably simple explanation to the theory behind dice probability, and much of the myth and superstition behind it:

http://mathforum.org/library/drmath/view/56502.html

What Karinya and I did above was simply extend the concept of rolling dice to keep adding one die at a time until specific conditions were reached. Karinya used a statistical model, I used iterative programming, and we basically arrived at roughly the same conclusion - two paths to the same general goal.

Karinya basically took the concept of a single die roll: one value determined randomly between 1 and 6, then used a spreadsheet to create an expanded chart of the results of various additional rolls, then did some manipulation to the final results to get percentages.

My method used a program that simulates dice rolls, then sets conditions under which the rolling stops - the program then keeps rolling dice until it fulfills one of my terminating conditions, then records the result for tabulation at the end. It repeats this process one million times, then examines the frequency of each result.

Karinya's method is numerically accurate, but underlying math and conditions become increasingly complex as you start adding more conditions to the experiment. My method is less accurate, but is more tolerant of new test conditions.

To learn more about statistics, you'll probably need to take a formal course either in high school or college. It's possible to learn statistics from the web, but I don't recommend it; it's very easy to get confused and misunderstand many of the concepts behind probability and statistics.

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Now, what would be really amazing if somebody got the stat boosts for each roll and figured out which of these strategies is the best.

(IE: Penalty of bust and chance weighed with gains and chance.)

Whoever does that gets a cookie and half of mine. Chocolate Chip, I may throw in milk if the table is organized.

As I mention above, I can easily add weighting to my program, but I need some reliable numbers to generate a valid weighting scheme.


Icemage

[Karinya]

Yeah, I looked at doing something like that, but effectiveness numbers aren't known for all rolls. The ones that *are* known are consistent (I think), so you could reasonably speculate that the same pattern applies to others, I guess.

But there's still the problem of how much to discount the bust penalty since it only applies to one player while the bonuses apply to - how many players? It depends on which roll and the party setup.

Furthermore, some rolls may not have a bust penalty or it may be irrelevant (Evoker's and Healer's for CORs not subbing WHM, and Wizard's, Warlock's, Ninja, Gallant's and the pet rolls pretty much always). Aside from the interference with future rolls, which is difficult to quantify.


So basically I concluded that trying to do an "Expected Average Results" column in the analysis would require introducing too many additional unknown variables and the results wouldn't reliably represent anything useful.