User blog:RobinCarr/Virtual Dino Den, Explore How Baby Dinos are Born in the Dino Den

DinoGenesis and EggCount
This blog explores the amazing "Theory Of DinoGenesis", which describes the process by which baby dinos appear in the Dino Den. If your parents won't give you straight answers about where babies come from, at least you will know where baby dinos come from. The Theory of DinoGenesis has been strengthened by the recent publication of the treatise "On The Origin of DinoSpecies", by the noted prehistoric naturalist Sir Charles Darwinite, a distinguished colleague of the celebrated Professor OneStone.

Let's start with the Theory of DinoGenesis which describes only one of the four processes by which baby dino eggs can be created in your village.

The First Process of DinoGenesis: The Great Spinning Drum of Dino Eggs
The most common process to obtain a new baby dino is to first obtain a Random Egg from the dino den, at a small cost, and then wait for it to hatch. In contrast to the other mechanisms, all the various species of dinos can always be obtained as Random Eggs, provided they have been introduced. However, even the magical Dino Den cannot violate causality, you will never obtain an egg for any dino which has not yet been introduced.



Why are some dinos more likely to visit your village than others? Why are some so hard to get by Random Egg? These great questions are explored in the next section.

Dino Eggcount in the Great Dino Egg Drum
For each dino, the process of DinoGenesis is determined by a Dino Lottery. First just over 2000 eggs are chosen as suitable for your village. Each egg is given a number, starting at 1, and placed in a giant Dino Egg Drum. Until recently, the Egg Drum held exactly 2088 dino eggs.

But something wonderful happened with the introduction of the magical dino-bird, the Nemicolopterus and on August 31st or September 1st, the Giant Turtle. For each of these dinos, a single beautiful new egg was added to the Great Spinning Dino Egg Drum bringing the egg count to a grand total of TotalEggCount = 2090!

Yep, two new eggs!

Egg Counts
When you ask for an egg from the Dino Den, the Egg Drum is spinned and then one egg is chosen at random and placed in your Dino Den. An identical egg is also placed back in the Egg Drum so your Dino Den is always ready to deliver a new egg. So, some dinos appear more often simply because their species is alloted more eggs in the Great Egg Drum.

The number of eggs alloted each dino species is called its EggCount and is the single most important number determining how likely you are to get that dino! In the Giant Egg Drum, there are always exactly 500 Mammoth eggs, 500 Stego eggs, 500 Anky eggs and 500 Parasaurolophus eggs. So, exactly 2000 of the eggs are for common dinos, which is why they pop out of the Dino Den so often. In addition to the two thousand common dino eggs, the Great Dino Gods drop in a limited number of RareEggs, at the moment there are 88 rare eggs in the Great Egg Drum.

At least one additional Rare egg is added each time a new dino in introduced.

For example, if the next dino is awarded n eggs, there will then be a total of 2089 + n = (2089 + n) eggs, but all the previous eggs remain exactly as before. So far the EggCounts for rare dinos have all been either 1, 6 or 9.

No one knows why the Dino Gods choose these three numbers, but every rare dino has one of these three Egg Counts. Perhaps it is like a flower which always has the same exact number of petals.

One Egg: The rarest of the rare dinos with just one egg are the Nemicolopterus, the Mesohippus or Pony, the Minmi, the Ingridia, the Corythosaurus, the Brontornis, Pachycephalosaurus, Bambiraptor, Archaeopteryx, Lucky Mammoth, Love Stego, Sabretooth, Raptor and Brontosaurus. These 14 dinos have a total of 14 eggs amongst them.

Six Eggs: The next rarest of the rare dinos all have six eggs. These are the Giant Sloth, the Whooly Rhino, Homalocephale, Kentrosaurus, and Triceratops. These five dinos have a total of 30 eggs amongst them.

Nine Eggs: Finally the nine egg dinos are the Spinosaurus, Andrewsarchus, Pterodactyl, Dimetrodon, and Protoceratops. These five dinos have a total of 45 eggs amongst them.

You can see we now have a total of 89 rare eggs = 14 + 30 + 45

Not all the eggs inside the Dino Egg Drum are shown. Remember there are 2000 common dino eggs and only 89 rare eggs. You can see there is just one Pony egg, one Corythosaurus egg and 6 sloth eggs shown, plus quite a few common eggs illustarted near the top of the egg-drum. The Spinning Drum with 2089 Dino Eggs explains all the features of the Dino Den, once you know how many eggs there are in the drum for each kind of Dino. Fortunately Rupert and Regina were able to send a keen-eyed Archaeopteryx, to fly near the Great Egg Drum and count all the eggs. That's the EggCount Number given for each dino in the table on the Dino Den Page.

A Little Probability
Now we are in a position to make a lot of predictions about the Dino Den and the probability for each dino.

Here are some examples.

1. Since each of the commom dinos, such as the mammoth, has 500 eggs, the chance of getting a specific common dino is 500/TotalEggCount or a little less than 1 in 4.

2. The chance of getting the new Pony with its allotment of only one egg is 1/2089 so on average, if you hatched 2089 dino eggs, you should expect only one pony!

3. How does the Hurry Hatch Trick work?

Some villagers just purchase one egg after another until they get an egg whose hurry hatch cost is not 12 crystals. Although this throws out a lot of rare dinos, they also throw out all the common dinos. There are a total of only 52 eggs in the drum that do not have a hurry hatch of 12. This has been updated to include the new Nemicopterus Egg.

So, if you want to use this trick, you will on average need to try about TotalEggCount/52 = 40.17 times

The mathematics is governed by the Geometric Distribution. I myself tried this trick for about 10 days, but now prefer to just hatch one ordinary dino a day, and then fatten it up for fusing. Others just love the hurry hatch trick and spend hours trying for those rare eggs! You can see they really have to work quite hard at it. I think it's perfectly fine as long as they can afford to spend 250 gold coins so many times.

4. What are the rarest Dinosaurs? Why the rarest dinos are the ones that have just ONE EGG!

The rarest dinos are truly one-of-a-kind! Details are given above.

5. Post you own great questions below, and we will answer them. Good ones will move up here so others can enjoy the result.

Table of Probabilities for Hurry Hatch Tricksters
If you regularly toss out dino eggs and only keep the few that meet a certain search criterion, then you are a Hurry Hatch Trickster. You need help! Below you will find a table that helps you predict how many tries it will take to "Get The Dino Egg You Want". It seems such a table is needed because we regularly hear reports that some days the trick is working and other days it is not. It may be true that something like that happened in the remote past, but in the recent future, that is just not the case. The Spinning Dino Egg Drum is as constant as the spinning Earth. (With a few small changes when additional eggs are plopped in.)

Question: How come sometimes I get a rare egg right away. Other days no luck at all? Perhaps no other question here has so much folk lore spinning around it.

Myths: Revenge of the Dino Gods, TV is upset, TV is appeasing us for all the myriad technical problems.

But the truth is, all this variation is described and predicted by the Geometric Distribution It is simply chance.

Below is a table of quartiles and selected percentiles for those using the most common Hurry Hatch Trick. Let's call this variation of the trick, toss the dirty dozen. Here you toss out all eggs with a hurry hatch of 12, the dirty dozen, but keep all the others. So you keep any egg with a HH of 8, 10 or 13. This is your strategy for success. If you use another strategy, the numbers will be slightly different. Use the Talk section below to request the numbers for your version of the strategy. I have it all in a spreadsheet and can pump these numbers out in minutes!

Probabiity on first try using your HH-Strategy

Whichever strategy you use, we need to calclate P1, which is the probability you will get the egg you want on the very first try ! Using the Dirty-Dozen Strategy, you keep 52 eggs out of the total 2089 eggs. That means P1 = 52*100/2089 = 2.489%. Just a little less than 1 in 40. But how likely is that? Most HH Tricksters spend even hours trying to get that rare egg. The following table gives the cumulative probabilities for selected numbers of tries.

Yikes! Let's think about those numbers. A success means you keep at it until you succeed.

1. If you try this trick on 40 different days, you can expect to win only once on the very first try.

2. On average, you will have success in 12 or less attempts only about 1/4 of the time. First Quartile.

3. On average, half the time, it will take between 13 and 55 eggs. So the  fourth spread  is 43. Huge variation!

4. Half the time, you will win that special egg in 28 tries or less. This is the median.

5. On average, you will need more than 55 eggs about 1 try in 4.

6. On average, you will need more than 92 eggs or more about 1 try in 10. So you see, the Geometric Distribution P(n) = p*(1-p)^(n-1) has an enormous variation when p is small.

In fact for this distribution when p <<1, both the standard deviation and the fourth spread are quite close to 1/p or about 40. It is this huge variation that is causing all these claims about good luck one day and no eggs at all the next day. Just chance! No need for any myths!

Virtual Dino Den
Using just the known EggCount for each dino, we have built a Virtual Dino Den in Excel. You can tap away at it and get a new dino every time you tap. The dinos will appear in a statistical way which is identical to the Dino Den.

A link will to the Virtual Dino Den will appear here in the future.