@ffs here is a draft, let me know if this information is enough or if more is needed (I will pitch in the other "outcomes" - i.e. runewords, later)
--------------------------------------------------------------------
General information
CL(
t) = Probability(
S,
t) = 100% - P(!S,
t) is called
Confidence Level,
where
S means success of a defined outcome and !
S means not success (in other words, fail).
CL(
t) is interpreted as the probability of succeeding in
t runs or fewer.
E is the
expected number of runs, defined as the integral over t*p(
S,
t) from
t = 0 to infinity (not the runeword
)
p(
S,
t) is the probability mass density, which is the derivative with respect to
t of 100% - P(!
S,
t).
E is the continuous case of the
average value = the sum of runs for all players to achieve
S divided by the sum of players.
The format (x,y) means P(x number of Ber runes)*P(y number of Sur runes)
it will make much more sense later on, trust me.
The number of patterns for each rune and difficulty is based on the findings by Fruit.
--------------------------------------------------------------------
Outcome:
At least one effective Ber (straight drop or cubing of 2 Sur)
P(!S,
t) = (0,0) + (0,1)
Code:
CL vs. # of Runs, for p5 and p7
CL p5 p7
----- ----- -----
25% 672 776
50% 1437 1477
65% 2008 2043
75% 2476 2584
85% 3149 3364
95% 4501 4956
E = 1846 runs for p5, corresponds to 60.5% CL
E = 1801 runs for p7, corresponds to 59.6% CL
Graph over CL vs. # of Runs:
Interpretation of the results:
For this outcome, we see that for ~1700 Runs or fewer, you have a higher chance of success at p5 than on p7.
The expected number of runs for success are in both cases ~60% at 1801 (p7) vs. 1846 runs (p5).
What is "fastest" or "best" is not easy to answer since it depends on your target probability (and other things like runes & jewels - will make a discussion on that later, and safety for HC - monsters deal around 10% less damage on p5 compared to p7).
At 95% CL, there is a ~10% difference in the number of runs needed (~4500 on p7 vs ~5000 on p5) which is around 3-3.5 hours.
Left to post:
Same as above but for Infinity (2Bers), Enigma (3Bers) and Infinity + Enigma (5Bers).
I will also do CL graphs and tables for Trav and Cows, and possibly also Arcane Sanctuary and Act 5 Super-/Sparklychests (using the results from Fruit's work).
In addition, I will discuss Jewels and Charms from LK p5 vs p7 using more of the excellent work by Fruit.
EDIT:
I will start a
new thread about these things, this post was just meant as a template / fast feedback.
By having "my" own thread, it will be easier for anyone to pull out numbers and figures for their own guides and such, plus the discussion will be more focused.
When I have more results ready and make my own thread, this post will be edited/removed.
