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brairtrainer

Dragcave Maths

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The question about the 100th EG lineage got me wondering: How long would it take to create a 100th gen clean stairstep and how many dragons would you need? For a 100th gen inbred one?

Clean stairstep: You would need 101 CB dragons, 2 original parents and 1 more CB each generation.

It would take 600 days (without any incubates)—Since there are only two dragons per generation, egg limits don't come into play, so it's just 6 days for a dragon to grow up times 100 generations.

 

Inbred is trickier but only slightly. By inbred stairstep, I'm assuming you mean that the offspring of each generation is bred with one of the original CB parents. For this, you would only need two CBs.

As for time, it would take 700 days. Rather than waiting 6 days each generation for the egg to mature, we're now waiting 7—breeding cooldown for the CB parent with whom each offspring is repeatedly being bred. Incubate wouldn't do nothing here, because the egg has more than enough time to grow up while the CB parent is still cooling down.

 

EDIT: Ninja'd but I'll still keep this post here because it also has the times in addition to the dragons.

Edited by Engiype

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Wow, it's actually possible to get a gold trophy in significantly less than a year. I never realised that.

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I love math! And someone thought to combine it with Dragon Cave. This is cool.

 

I remember the first time I calculated the number of CBs needed for an even gen lineage. I did 10 just on a whim and thought "aw man" when I got the number. Most of these I never even thought of trying to calculate. I love the square root of the purple dragon.

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Just to sort of revive this thread, here's a question I thought of myself. I've been wanting to do something about Thuweds on here for a while, too.

 

If I go to the Thuweds page, how likely is it for there to be an open breeding slot?  How much time do I have to grab it?

 

Good question, me!

 

First let's compile what we know. There are 48 official Thuwed pairs. There are 57,662 users (as of 4:22 PM Cave time on February 28) on the forums. Breeding cooldown is 7 days. TJ has said the breeding lists are a fixed length, so we can infer that whenever someone is bred an egg, a spot should immediately open up on the list for that pair.

 

Now let's move into randomly guessing estimating some of our unknowns, regarding DC's users. Not everyone on DC has a forum account, so let's say 2/3 of them do. Not everyone is active, either. Let's go with 2/3 once again. And not everyone knows about the Thuweds page, although since we've already counted out the people who aren't very active, most of the people who are left probably do. 2/3 has been serving me well so far, so let's use it again. Last, let's just say that the users that are left check the Thuweds page once per day.

 

We're done making up extrapolating data about the users, so now let's move on to the Thuweds themselves. I think it's pretty reasonable to assume that the Thuweds breed eggs as soon as breeding cooldown wears off, in order to satisfy the users on the lists as soon as possible. Let's also assume that there are no rejections or anything like that (seeing as these are, after all, official pairs that have been around a while). Okay, I think we're done inventing inferring our data now.

 

So 57,662 users divided by 2/3 (or multiplied by 3/2) gives us 86493 total DC users. 2/3 are active, so that brings us back down to 57,662. 2/3 of them know about the Thuweds page, so now we have 38441 and 1/3 (we'll just round that to 38441) users, each checking the Thuweds page once per day. I know they're not, but if those views are perfectly evenly distributed throughout the day, then that means someone checks the Thuweds page once every 2.2476002185166879113446580473973 seconds.

 

Now the Thuweds themselves. A 7-day breeding cooldown divided by 48 pairs breeding ASAP means a slot on one of the lists opens up once every 3.5 hours (again, evenly spaced). That's 6.8571428571428571428571428571429 times a day, so if you go to the Thuweds page at any given minute, there's a 0.0047619047619047619047619047619% chance that a slot will be open.

 

So long story short, if you happen to be lucky enough to find an open slot on a Thuwed list, it would behoove you to take it while you can, and be quick about it.

Edited by Engiype

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6-7 Months is easily doable if you grab hatchies from trades or departure threads.

And from the AP. You'd be surprised how many hatches I've grabbed out of there. And there are more that I missed, too. I always wonder why you'd abandon a hatchie. Oh well.

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If it's a Black or Vine, you'd abandon it because it didn't hatch Alt. Not sure about any other breed.

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I always wonder why you'd abandon a hatchie. Oh well.

Presumably chiefly because of the creature limit. Sometimes, people reach it. I know, I know, it sounds crazy, but it's actually happened to me once! laugh.gif

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Just to sort of revive this thread, here's a question I thought of myself. I've been wanting to do something about Thuweds on here for a while, too.

 

If I go to the Thuweds page, how likely is it for there to be an open breeding slot?  How much time do I have to grab it?

 

Good question, me!

 

First let's compile what we know. There are 48 official Thuwed pairs. There are 57,662 users (as of 4:22 PM Cave time on February 28) on the forums. Breeding cooldown is 7 days. TJ has said the breeding lists are a fixed length, so we can infer that whenever someone is bred an egg, a spot should immediately open up on the list for that pair.

 

Now let's move into randomly guessing estimating some of our unknowns, regarding DC's users. Not everyone on DC has a forum account, so let's say 2/3 of them do. Not everyone is active, either. Let's go with 2/3 once again. And not everyone knows about the Thuweds page, although since we've already counted out the people who aren't very active, most of the people who are left probably do. 2/3 has been serving me well so far, so let's use it again. Last, let's just say that the users that are left check the Thuweds page once per day.

 

We're done making up extrapolating data about the users, so now let's move on to the Thuweds themselves. I think it's pretty reasonable to assume that the Thuweds breed eggs as soon as breeding cooldown wears off, in order to satisfy the users on the lists as soon as possible. Let's also assume that there are no rejections or anything like that (seeing as these are, after all, official pairs that have been around a while). Okay, I think we're done inventing inferring our data now.

 

So 57,662 users divided by 2/3 (or multiplied by 3/2) gives us 86493 total DC users. 2/3 are active, so that brings us back down to 57,662. 2/3 of them know about the Thuweds page, so now we have 38441 and 1/3 (we'll just round that to 38441) users, each checking the Thuweds page once per day. I know they're not, but if those views are perfectly evenly distributed throughout the day, then that means someone checks the Thuweds page once every 2.2476002185166879113446580473973 seconds.

 

Now the Thuweds themselves. A 7-day breeding cooldown divided by 48 pairs breeding ASAP means a slot on one of the lists opens up once every 3.5 hours (again, evenly spaced). That's 6.8571428571428571428571428571429 times a day, so if you go to the Thuweds page at any given minute, there's a 0.0047619047619047619047619047619% chance that a slot will be open.

 

So long story short, if you happen to be lucky enough to find an open slot on a Thuwed list, it would behoove you to take it while you can, and be quick about it.

Very interesting. Thanks for doing all the calculations.

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Oh this is fun!

 

For each trophy level how many Red dragons do you need to never be out of Incubates if you always filled all of your egg slots and incubated each one?

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So the general formula here is this:

 

x egg slots * (14 day cooldown / 2 days for an incubated egg to grow up)

 

No trophy: 28 Reds

Bronze: 35 Reds

Silver: 42 Reds

Gold: 49 Reds

Edited by Engiype

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I did some updates and added answers to the trivia area. Answers that were more involved (meaning needing a long explaination) I left out or cut pieces out of. Keep the questions coming people.

Edited by brairtrainer

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To breed a 7th gen checkerboard, I need 32 cb males of breed A and 32 cb females of breed B is this correct?

 

Whoa, and to breed a reverse chequer of the same breed (A as female and B as male this time) would require 64 CB dragons of A and 64 CB dragons of B wacko.gifwacko.gif

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How many Pinks would you need to Influence every egg (for each trophy level)? How many if you Incubated all of them?

 

(I guess it would be best to assume you want them all one gender. Then you'd just need the same number of the opposite gender to make sure you could always have the Influence you needed available, right?)

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To not run out of pinks you'd need 25 for one gender (24.5 rounded up, taken from the need to have 49 reds since incubate is 2 weeks)

 

So to not run you you'd need 50 of pink dragons if you aren't picking up low time eggs.

Edited by brairtrainer

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Brairtrainer, can you help me check if I've drawn this 7th gen tan ridgewing x blusang project right?

 

https://i.imgur.com/V3IhiTw.jpg

 

According to the pic, I need 64 2nd gens to make a 7th gen which seems to be double the original estimate wacko.gif

 

Is this the correct chart?

 

https://i.imgur.com/yQCzs2L.jpg

Edited by SnowSherry

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The chart seems to go to 7 gens but I'm wondering if you paired up the dragons correctly.

 

To make a 2nd gen you need 2 cb dragons. To get to third gen you need to add to more cb dragons to breed the next second gen, equaling 4 cb dragons. To get to fourth gen you must double the dragons again, 8 cb dragons in total. For fifth gen you must add 8 more cbs so that you are breeding another foruth gen even gen bringing you to 16. You double those again for 6th giving you 32, and for seventh gen you double again giving you 64.

 

I don't know why your chart is off :/

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Ok, I have a question: Assuming we have the number of dragon races we currently have that are capable of breeding with each other and that everyone can access caveborns of (excluding holidays, discontinued, Ultraviolet, Blunas, geode, shallow water, prize dragons, pygmies and drakes).

We then have 124 dragon types capable of breeding with each other (counting Sunset/sunrise and seasons as one and including Silver, Gold and trios. Ignoring rarexrare-breeding).

 

How long would it take to breed a lineage with a CB pair of each and how long would it be?

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First off if you did try to breed a dragon using pairs of cb's from every breed you'd start out with 248 dragons.

 

The highest you can get with those dragons is 8th gen which requires 128 dragons. You'd end up with several even gens left over: 1 7th gen (64 dragons), 1 6th gen dragon (32) 1 5th gen dragon (16), and 1 4th gen(8) left over.

 

As to how long it would take, lets assume you started breeding for the 8th gen and you were gold trophy, there were no new releases and you started breeding completely unlocked. It would take 9 breedings with 1 pair left over. If you don't use incubate you become free every 3 days for more breedings, so after 27 days you have most of the second gens for your eighth gen.

 

Assuming you breed the last pair with the push of the third gens the next set of breedings would be pushed back, and would take 4 breedings over all. Without incubates those eggs become hatchies in 3 days and leave 5 pairs left over. This batch would take 12 days to raise (counting the left over 2nd gens).

 

Following this trend you'd finish off breeding the second gens and breed the third gens to get forth gens. Since there are five pairs left over this once again inhibits the starting breeding. This will get you 3 breedings with 1 pair left over. The amount of days it would take to raise the eggs to hatiches (counting left over 3rd gens) would be 9 days.

 

Continueing this pattern we then then prepare to breed fifth gens. This is still pushed back by the one third gen pair needing to breed so I factor that in by noting the egg spot. It would take you 2 breedings to get mostly through the 5th gens but you'd get a left over of 2 pairs. These eggs would take 6 days to unlock you.

 

We then breed the left over 2 pairs as we breed the 6th gens. This breeding will take two breeding cycles and leave a pair left over, causing you to be egg locked for 6 days.

 

Now to get the seventh gens things start to get trickier. As one of the pairs is a new egg that has yet to be hatched. So you breed one pair of 6th gens, and you breed and wait for the hatchling to mature. An egg can become an adult dragon in 6 days without incubate so that is the number I'm using. 3 (days to unlock you from the first 7th gen egg) + 6 (days for the final one of the final pair to grow up)+3 days(to be unegglocked) gives you 12 days

 

So to get to the eighth gen you'd add up 27+12+9+6+6+12=72 days. This is the closest you'd get. You could breed the rest but you'd never breed them into the lineage without messing it up. I'll work out the remainder later if someone asks.

 

 

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Brairtrainer, can you help me check if I've drawn this 7th gen tan ridgewing x blusang project right?

 

https://i.imgur.com/V3IhiTw.jpg

 

According to the pic, I need 64 2nd gens to make a 7th gen which seems to be double the original estimate wacko.gif

 

Is this the correct chart?

 

https://i.imgur.com/yQCzs2L.jpg

In the first picture you have a pair of 7th gens, and it doesn't show the 8th gen you could breed from them. That's why it looks off. smile.gif The second pic is correct.

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Wow, it's actually possible to get a gold trophy in significantly less than a year. I never realised that.

I was able to do it. I did it about a week or a couple of days before my one-year anniversary last year. Just thought I'd say so. ;3

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I'm gonna guess that I'll get my Gold in August... maybe earlier.

Got my first dragon November 4th of last year.

I know have about 300 dragons.

 

EDIT: Ok... I have no idea when I'll get my Gold. 100 percent sure before my 1 year anniversary, though

Edited by MaggieXawesomeness

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If I joined July 24th 2012, and I have 262 dragons now, assuming I catch and raise all my own eggs, can I hit Gold before my join anniversary? Or do I have to trade for hatchlings? If I have to trade for hatchies (let's assume trading hatchies for eggs), then how many hatchies do I need to trade for? And how many eggs would I need as trade fodder? (assume 2 hatchies per egg.)

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back to even gen questions:

 

If i want to breed a 5/6/7/8 EG lineage adult all on my scroll.

how long would it take me assuming a gold trophy, able to catch any cbs i want, full incubates, perfect breeding and gendering. and: can this in any way be optimised.

 

for 2g: 10 days. catch 2 cb, incuhatch, breed, incuhatch.

for 3g: 15 days. catch 4 cb, incuhatch, breed, incuhatch, breed, incuhatch

 

starting with 4g it gets complicated.

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