I'll even do them more. I wrote a very simple R script so they can visualize the instability of their RNG system for a given r and p.

=========

#Number of required successes

r = 5

#Probability of success

p = 1/3000

#Number of players (or some large amount to calculate the proportion of players accurately)

b <- 1000

#Used to store the results

S <- double(b)

for(i in 1:b){

#a will track the number of successes within an attempt

a <- 0

#n is the number of trials within an attempt

n <-0

while(a < r){

#For every iteration, increase the number of trials by 1

n <- n + 1

#was a success or not

y <- rbinom(1,1,p)

if(y==1){a = a+1}

}

#record the number of attempts

S[i] <- n

#print every 100 iterations

if(i%%100 == 0){print(i)}

}

#histogram

hist(S,freq=F,xlab="n",,main=paste("Proportion of people and their required number of trials for p = ",round(p,6), "and r = ", r))

#plot mean

abline(v = r*((1-p)/p) +1, col = "red",lwd = 2)

#plot 2.5% and 97.5% quantiles for the 95% middle

abline(v=quantile(S,c(0.025,0.975)),col="purple", lwd = 2)

=====

From this image, it is very clear that if p = 1/3000 and r = 5, 95% of the players will fall between getting those 5 fragments either within 5000 trials or 30000 trials. Some unlucky players will take excess of 50000 trials. We don't need to be guinea pigs when it takes a couple minutes to do a valid simulation. They don't even need to know any formulas.