User blog:SmartAlyx/Breeding THEORY & Algorithm Analysis

Breeding THEORY,  Alyx's Algorithm  &  Analysis of Valentine Type Breeding Pairs...''' '''

My Breeding THEORY (based on observations & research) is that every time you hit "Breed" there is a slot machine style random generator that has:

CONSTANTS: [60% chance of landing in the (C)ommon slot] [30% (R)are] [9% Super Rare (SR)] [1% Ultra Rare (UR)].

Once it lands on say C's slot it then randomly selects one of the C dragons possible which I call VARIABLES. Because C is statistically the most likely, you want C Fails to have as low an incubation Length (iL) as possible.

If you are unable to avoid certain really Bad Fails, then the trick is to find a Breeding Pair (BP) that introduces more Fails in that bad Fails Rarity  -  UNLESS it is the same Rarity as the dragon you want to Breed. In that case you want as few dragons competing in the Rarity of the dragon you want to Breed to increase chances of Breeding it.

NOTE:  I would LOVE someone who works for Storm8 to tell me if my Breeding THEORY is correct. It would help IMMENSELY if they could let me know if there is a different statistical breakdown of the likelihood of each Rarity being Breed. My 60% = C / 30% = R / 9% = SR / 1% = UR is my best GUESS based on logical probability. But if I do not have it exactly right I believe, based on observational Data from my own Breeding attempts, that I am close enough for government work. :)  (I do not have the patience, time, nor energy to keep records on Breeding attempts - but if anyone has & they want to pass along their Data I'm interested in results. I have a public DS email I Post.)

What I try to do is find a Breeding Pair (BP) with the fewest Fails of 12h or more but it doesn't guarantee your dragon, especially when it's UR.

NOTE:  I arbitrarily chose 12h as the cut off for what makes a bad Fail, figuring that anything over 12h has me frustrated, but under 12h I am somewhat mollified.

Example... Breed:  (DIAMOND & FOREST) = C, FOREST 20 seconds & UR, QUETZAL 32h. Some may get really lucky & breed Quetzal w/ in 3 attempts. Others must wade through over 300 FOREST Fails. Fails HAPPEN, but having Fails w/ as low an incubation Length (iL) will get you past them faster. I try to keep Breeding the same pair until successful, in a war of attrition against Storm8's code, until it cries "Uncle" & gives me what I want. You can try "resetting" by Breeding something else then returning. Folks have their own theories, preferences, & superstitions when Breeding.

NOTE:  When Breeding Level ONLY matters in that dragons MUST be @ least L4 to Breed & both parent dragons MUST be L15 to Breed any PRIME dragons.

If you want an UR dragon & 1 pair = 10 dragons w/ 3 C all well over 12h iL & 2nd BP is the same except there are an additional 5 C, all w/ iL well under 12h, the 2nd BP is better.

There is a bit more involved in assessing the quality of a BP. That there be as few Fails as possible in the Rarity of the dragon you want. (Only 1 UR = DIAMOND, is excellent).

I created an Algorithm to obtain a single % for mutiple Constant % of multiple Variable %... It is easy to use once explained... My Algorithm accounts for all the dragons iL in each Rarity obtaining a % of Breeding a Fail of 12h or longer, then a % chance for Breeding 12h or longer Fails for all dragons & then compiles those w/ % chance of Breeding each Rarity to give an accurate, single % of Breeding a Fail of 12h or more.

Summary of what makes a good BP:

1)  Lowest number of C Fails w/ iL of 12h or more. 2)  Lowest iL possible for all Fails. 3)  Fewest number of Fails possible in Rarity of dragon you want. 4)  Algorithm = accurate % chance of breeding Fail of 12h or more that is hopefully (30%) or less.

. ..

ALGORITHM TO ANALYZE BREEDING PAIRS...

$${[C(c1)] + [R(r1)] + [SR(sr1)] + [UR(ur1)]}$$

CONSTANTS:

C    =  60% R    =  30% SR  =  9% UR  =  1%

VARIABLES:

c1   =  # of C w/ iL of 12h or more divided by total # of C possible

r1    =  # of R w/ iL of 12h or more divided by total # of R possible

sr1  =  # of SR w/ iL of 12h or more divided by total # of SR possible

ur1  =  # of UR w/ iL of 12h or more divided by total # of UR possible

Finding Variables:

1)  Count the # of dragons w/ iL of 12h or more for each Rarity as well as the total dragon Fails in each Rarity.  2)  Divide those numbers by each of the total dragons in each rarity. Say there are 5 C dragons w/ an iL of 12h or more. & there are a total of 10 C dragons possible. 5 ÷ 10 = .5 or a 50% chance of breeding a C Fail of 12h or more. That is not enough Data though because we must account for the chances of breeding a Fail of iL of 12h or more for each rarity.

Example:  DIAMOND, 44h. Breed: (([SCARECROW or PIÑATA] & MYTHIC)) = 22 dragons. Minus Prime Life if 1 parent not = L15.

(C: Life 3h / Fruitful 10h / Firestorm 12h)  =  1/3  =  .6  =  c1

(R: Loch Ness 4h / Druid 6h / Wild 6h / Explorer 8h / Fairy 8h / Tree Frog 8h / Firemane 9h / Cactus 10h / Pinata 10h / Butterfly 11h / Wooden 15h)  =  1/11  =  .09  =  r1

(SR: Parakeet 5h / Landworm 6h / Honeybee 10h / Clockwork 13h / Fireflower 16h / Nymph 18h)  =  3/6  =  .5  = sr1

(UR:  DIAMOND 44h) = not a Fail so zero for UR

Constants: C    =  60%  =  .6 R    =  30%  =  .3 SR  =  9%    =  .09

Variables: c1:   1/3  =    .33 r1:    1/11  =  .09 sr1:  3/6  =    .50

ALGORITHM:  {[C(c1)] + [R(r1)] + [SR(sr1)]}

{[.6(.33)]  +  [.3(.09)]  +  [.09(.5)]} {[.198]  +  [.027]  +  [.045]} {.27} {27%}

DIAMOND, 44h. Breed: (([SCARECROW or PIÑATA] & MYTHIC))  =  22 dragons with the Chances of breeding 12h or longer Fail = [27%].

..

PASSION BREEDING...

PASSION, SR (valentine) 16h. Breed:  (LEFT HEART & RIGHT HEART) = 7 dragons:  (C:  Magic 20h)  (R:  [11h:  Athletic, Tropic], [12h:  Leftheart, Rightheart], Lunar Ram 16h)  (SR:  PASSION 16h). Passion Pit Habitat holds 3, costs 50,000 Coins, & takes 14h to Build. Highly recommend Breeding PASSION & raise to L15 (352,575 Apples) as it's an ((A DIPPS &8)) & is an excellent single type champion fighter.

ALGORITHM ANALYSIS:

Constants: C    =  60%  =  .6 R    =  30%  =  .3 SR  =  9%    =  .09

Variables: c1    =  Commons:  1/1  =  1 r1    =  Rares:  3/5  =  .6

ALGORITHM:  {[C(c1)] + [R(r1)] + [SR(sr1)]}

{[.6(1)] + [.3(.6)]} {[.6] + [.18]} [.78]  =  [78%]

PASSION is a TERRIBLE dragon to Breed because we have no choice about parents. When Breeding (LEFTHEART & RIGHTHEART) for PASSION there is a [78%] chance of Breeding 12h or longer Fails.

1BP:  LEFTHEART & RIGHTHEART dragons:  R, (valentine, red, blue) 12h. 1{Breed:  (FIRE & WATER)  =  6 dragons.

(C:  Magic 20h)  =  1/1  =  1 x .6  =  .6

(R:  Athletic 11h, Tropic 11h, [12h:  LEFTHEART & RIGHTHEART], Lunar Ram 16h)}

NOTE:  When you 1st start Breeding neither LEFTHEART nor RIGHTHEART are Fails. But once you get 1, it becomes a Fail when you repeat the BP to Breed the other. When 1st Breeding there are only 3 Rare Fails w/ only 1 being 12h or more. After you get 1 valentine type that you want = 2/4. So there is a range that must be tallied.

1st Breeding  =  1/3  =  .333... x .3  =  .1 After getting 1 valentine type =  2/4  =  .5 x .3  =  .15

Adding C% & R%  =  .6 + .1  =  .7  =  [70%] .6 + .15  =  .75  =  [75%]

1BP has a [70%] to [75%] chance of Breeding a Fail of 12h or more which is TERRIBLE. Especially because the ONLY C dragon, that has the highest probability of being Bred is a 20h MAGIC. I would NOT recommend this BP to Breed LEFTHEART & RIGHTHEART.

2BP:  LEFTHEART & RIGHTHEART dragons:  R, (valentine, red, blue) 12h. 2{Breed:  (OLYMPUS & [red, blue])  or  (TROPIC & OLYMPUS)  =  7 dragons.

(C:  Hercules 6h, Olympus 7h)  =  0

(R:  Nyx 10h, Athletic 11h, [12h:  LEFTHEART & RIGHTHEART], Lunar Ram 16h)  = 1st Breeding  =  1/3  =  .333... x .3  =  .1 After getting 1 valentine type =  2/4  =  .5 x .3  =  .15

Adding C% & R%  =  .1  =   [10%] .15  =  [15%]

2BP has only a [10%] to [15%] chance of Breeding 12h or longer Fails. So I do recommend this BP, but 4BP is better yet! Plus, 2BP's is MUCH BETTER than 1BP because 20h MAGIC Fail is avoided.

3BP:  LEFTHEART & RIGHTHEART dragons:  R, (valentine, red, blue) 12h. 3{{Breed:  ((DIAMOND & [red, blue])) = 6 dragons.

(NO COMMONS!!!)

(R:  Athletic 11h, [12h:  LEFTHEART & RIGHTHEART], Lunar Ram 16h) 1st Breeding  =  1/2  =  .5 x .3  =  .15 After getting 1 valentine type =  2/3  =  .666... x .3  =  .2

(UR:  Mercury 1h, Crusader 44h)  =  1/2 = .5 x .01  =  .005

Adding C% & R%  =  .15 + .005  =  .155  =  [16%] .2 + .005  =  .205  =  [21%]

Note:  This is an acceptable Breeding Pair (BP) because by having NO Common Fails it increases the chances of Breeding a Rare dragon. That is IF you don't mind the (?slight?) risk of a 44h CRUSADER Fail.

4BP: LEFTHEART & RIGHTHEART dragons:  R, (valentine, red, blue) 12h. 2{Breed:  ([red, blue] & TROPIC)  =  4 dragons.

(C:  NO COMMONS!!!)  =  0

(R:  Athletic 11h, [12h:  LEFTHEART & RIGHTHEART], Lunar Ram 16h)  = 1st Breeding  =  1/2  =  .5 x .3  =  .15 After getting 1 valentine type =  1/3  =  .333... x .3  =  .1

Adding C% & R%  =  .15  =   [15%] .1  =  [10%]

4BP has only a [10%] to [15%] chance of Breeding 12h or longer Fails. So I do recommend this BP!

Addendum:  The results of a BP analyzed by my Algorithm DOES NOT guarantee success OR failure. It is merely a way to get a sense of what MIGHT result when Breeding. To have an "accurate" (based on my THEORIES) consistent way to analyze different BP's to find the least onerous (read less time consuming) way to Breed a dragon you want. Take for example Breeding:  (DIAMOND & FIRE)  =  C FIRE 10 seconds & UR CRUSADER 44h. Some lucky ducks may get CRUSADER on their 3rd attempt. Others (like me!) may have to sell 300 FIRE Fails before CRUSADER appears. So even w/ a BP that my Algorithm says is the "best" patience, stubbornness, & LUCK are still required.

I welcome any questions, comments, Data, dilemmas, & rebuttals.