User blog comment:BonesMcGee/Brainstorm: Potential savings in using the hurry hatch trick/@comment-5116140-20120803001445/@comment-5116140-20120803165059

How many tries does it take to get a premium egg using the Hurray Hatch Trick and what is the average cost per egg? To answer this question, we need to use the Geometric Probability Distribution.

Many villagers have been frustrated trying the hurry hatch trick to get a premium egg. This is because the probability p of success on a single try is quite low, so it can take quite a few tries.

Geometric Distribution

Let's assume all tries have the same probability p and that there is no memory. That is, if you fail 10 times in a row this does not change the probability of getting a premium egg on the next attempt. Under these assumptions, we have what is known as a geometric probability distribution.

The probability of success on the nth attempt is: P(n) = (1-p)^(n-1) * p.

This formula is easy to understand. On each try, the chance of success is p, so the chance of failing is (1-p). The formula simply says you must have failed on the first (n-1) tries before getting your premium egg on the nth attempt.

P(n) = (1-p)^(n-1)      *     p

n-1 failures     then one success

Coin Tossing Example

To illustrate the geometric distribution, let's play a coin toss game. Keeping tossing a fair coin until you get heads up – at which point I will give you the rare GeoMetroDon. For a coin p = 1/2 or 50%.

Since P(1) = ½, half will get the GeoMetroDon on the first shake! One quarter will get it on the second shake, one eighth will get it on the third shake and so on,

The average or mean number of shakes for a geometric distribution is:

Mean = 1/p

For the coin tossing example, the average player this takes two shakes to get the rare dino.

The Average Cost of a Premium Egg using the Hurry Hatch Trick

The HH trick is the same as tossing a coin, except the probability p of success on a single trial is much smaller. For now, let's guess p = 1/32.

Then on average, you could expect a premium egg about once every 1/p= 32 tries.

If each egg costs $250, the average cost per egg will be

Cost = $250/p =  $250*32 = $8000

In future notes, we will try to find a sharper estimate for p, the probability of success using the hurry hatch technique and explain how the variance formula Var = (1-p)/p^2 explains why so many people give up on this technique before they have had success.

PS: Bones, I hope you do not mind if these Geometric Probability Distribution notes appear here. They seem related to your original question.

ID: TinyRobinEgg