Some plots of binomial distribution using the best estimate of the parameter (book drop chance) and varying BK encounters may be more helpful. We need to understand that we are part of the distribution, so weird things do happen (getting book drop on first BK encounter, not getting a book after few hundred BK encounter.)

Example: Using book drop chance = 1% and no. of black kat encounter (n=298)

http://keisan.casio.com/keisan/lib/virtual/tmp/5483484773.png

x Binomial distribution
0 0.05003662287
1 0.1506153
2 0.22592293
3 0.2251623
4 0.1677345
5 0.0996241
6 0.0491412
7 0.02070596
8 0.007607871
9 0.002476187
10 7.228465E-4
11 1.9116602E-4
12 4.6182363E-5

1st column: no. of book obtained after killing 298 BKs
2nd column: the corresponding probability.

Why pick n=298? Because P(298,n>=1) ~= 0.95. We are 95% you will get at least one book after killing 298 black kats.

Take away message: Statistics are incredibly useful to understand any large scale phenomena, but you are only one of the data point making up the distribution. stop complaining when things dont work in your favor, because by principle there has to be those really unlucky and lucky ones such that the distribution holds.

Using the best estimate of book drop chance, you can also get to simulate the process and obtain (basically) the same distribution as given in my earlier post:

Put this in R and you will see the same distribution, which comes purely from computer simulation of the book drop process:

n_length = 10000 #sample size = 10000
n_trial = 298 #for each sample, try killing BK 298 times.
v_1 <- vector(length=n_length)

for (i in 1:n_length)
{
for (j in 1:n_trial)
{
if (runif(1) <= 0.01) #generating a random number on [0,1]. A book is found when the number is less than or equals to 0.01
v_1[i] = v_1[i] + 1
}
}

hist(v_1, freq=F, breaks=40)

The distribution on n (no. of BK encounter) for first success (getting a book) to occur is given by geometric distribution / exponential distribution(continuous version of geometric distribution):

Do this in R to simulate the process and get the distribution:
n_length = 10000
v_1 <- vector(length=n_length)

for (i in 1:n_length)
{
n_success = 0
n_tilsuccess = 0
while (n_success == 0)
{
n_tilsuccess = n_tilsuccess + 1
if (runif(1) <= 0.01)
n_success = 1
}
v_1[i] <- n_tilsuccess
}

hist(v_1, freq=F, xlim=c(0,298))

message: statistics are real.

Here.

I hear you like pudding, Cheshireccat.

I wonder if the difficulty level (i.e. Normal / Advanced / Elite) has any bearing on the drop ratio. It would be nice to have data on this as well, or something to confirm or disprove its bearing or lack thereof.