You don't understand what's going on. As I said, in order to compare setup1={PlayerA: 450, PlayerB : 528} where Player A has 450 delay and player B has 528 delay to Setup2={Player A : 450 , Player B : 528*0.99=522}, you have to examine all possible sequences (of any length) of randomly generated numbers that can be 1 with probability 95% and 0 with probability 5%. Yes I'm taking 95% accuracy, the actual number doesn't really matter, the only thing is that it is not 100% or 0%. So let's take a sequence :
seq={1,0,0,0,1,0,1,1,1,1,0,0,0,0,1,0,1,1,1,0,1,1,0 ,0,0,1,1,1,0,1,1} for instance
This represents the sequence of hits and misses as they appear chronologically (in the log). Of course, any sequence can happen, even the sequence with 56 '0' or a sequence with 17 '1'.
For each sequence, you need to calculate the time of death, which, in our case, is the first instant where 12 '1' have appeared. Now, and I know from your earlier posts that you agree with this, for a given sequence, the first time to reach 12 '1' for setup1 (call it T1) is always greater or equal to the one of setup2 (=T2). Since any sequence can theoretically happen (hi2u non capped accuracy), all you have to do to prove that on average T1 > T2, which means probabilistically that the expectation value of T1 is > the one of T2, is that T1>T2 for just one sequence :
This is fairly easy and many sequences will happen. Of course a lot of those have low probability, depending on how close the 1st and 2nd delay are, but they still exist.
very trivial way to see it :
all the sequences where player A misses his first 20 hits and player B hits his first 20 hits will have T1>T2 obviously ! Of course they have low probability, but they exist. In your case however, all of the sequences with 3 misses will work :
Let's take seq={1,1,1,1,1,0,0,0,1,1,1,1,1,1,1} for instance. The probability that exactly 3 miss happen in the first 15 hits is 3% . So when does the mob die ?
setup1 : 450 [528] 900 [1056] 1350 [miss@1584] miss@1800 [miss@2112] 2250 [2640] 2700 3150 [3168] 3600 [3696] -> death
setup2 : 450 [522] 900 [1044] 1350 [miss@1566] miss@1800 [miss@2088] 2250 [2610] 2700 [3132] 3150 3600 [3654] -> death
As you see the mob dies @ 3696s for setup 1 and @ 3654 for setup 2, in this case setup2 is strictly better. In case you argue that this sequence is unlikely, well, we can always consider the sequence of only consecutive '1' :
seq={1,1,1,1,1,1,1,1,1,1,1,1}. Unlikely ? nope, this has probability 54% ! When does the mob die in this case ?
setup1 : 450 [528] 900 [1056] 1350 [1584] 1800 [2112] 2250 [2640] 2700 3150-> death
setup2 : 450 [522] 900 [1044] 1350 [1566] 1800 [2088] 2250 [2610] 2700 [3132] -> death
Ding the mob is dying at 3150 for setup1 and 3132 for setup2. Guess what ? Haste is faster again.
Not satisfied ? Let's examine the setups where only one miss happens :
seq={1,1,1,1,1,1,0,1,1,1,1,1,1} probability 35%
setup1 : 450 [528] 900 [1056] 1350 [1584] miss@1800 [2112] 2250 [2640] 2700 3150 [3168] -> death
setup2 : 450 [522] 900 [1044] 1350 [1566] miss@1800 [2088] 2250 [2610] 2700 [3132] 3150 -> death
zing setup2 is faster again...
Oh and yes the setup with 2 hits gives the same time, but all others don't, proving my point : on average the second setup is faster.
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