Breeding for stat grades question?

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ChrisOfChaos
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Breeding for stat grades question?

Post by ChrisOfChaos »

Let's say you had two adult Chao. One is a Swim type with the DBAAD stats, and has recessive stats of CCBDC. The other is a Run type with the ASDEA stats, and has recessive stats of BBCCB. If you wanted to breed them to get a ASAAA Chao, how many times would you need to breed them together?
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Mamkute
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Re: Breeding for stat grades question?

Post by Mamkute »

Since chao grade genetics are pretty complicated, and having many (5) different factors, the chance of getting the perfect combination is quite low.

For each stat, you have only one desired allele (A or S) out of 4 possible, and there are five stats, so the chance should be 1/4 multiplied for five times:

(1/4)*(1/4)*(1/4)*(1/4)*(1/4) = (1/4)^5 = 1/1024

That is not to say it would take 1024 times. It could just take one try- the chances though are just very very unlikely.
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ChrisOfChaos
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Re: Breeding for stat grades question?

Post by ChrisOfChaos »

I'm not sure that's accurate. I think your equation is showing all possible stat grade combinations disregarding which grade applies to each stat. If we remember that each stat grade is applied to a specific stat (aka four Run stat grades in a Chao's genes can only fill the Run stat grade of a newborn), I think the odds are somewhere around 1/24. Also, I'm currently trying to breed a Chao with specific stats. I've bred around 30 Chao and I've only been about one stat grade away from what I'm specifically looking for (I even bred two Chao in a row that were one stat grade apart from each other).
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Re: Breeding for stat grades question?

Post by Mamkute »

I think I am correct, but I could very easily have failed at the logic. So I will describe my thinking. Please point out where you think I went wrong.

As you said, there are four options for a stat's grade. For the Swim grade, in this case D, C, A, and B. So there is a 1/4 chance of getting an A in Swim.
There is then a 1/4 chance of getting an S in the next stat, and so on.
The odds of two statistically independent events happening together is obtained by multiplying, so that is 1/16 to get an A in Swim and an S in Fly.
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Re: Breeding for stat grades question?

Post by ChrisOfChaos »

The way I'm looking at it is that for each stat grade, a Chao has four inherited possible grades for each stat. So if it's four grades per stat, there is a 1/4 chance of a Chao having one of those stats, just like you said. If we count the five stat grades we can see, this equation is repeated for all five stats. So we would do 5*4, meaning that out of 20 Chao, one of them will probably (although it's not guaranteed) have the desired stats. I think I am correct about this because out of the 30 tries I've attempted, many of the Chao have four or three stat grades in common. I'm not sure I'm entirely correct, but if I'm getting so many Chao with very similar stat grades, I don't see how 1/1024 can be right either.
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Post by Jeffery Mewtamer »

As Mamkute says, you multiply the probabilities of independant events, but there are actually 3 alleles each parent can pass down.

In addition to an allele inherited from each parent, a Chao has an allele for it's current Stat Grade. The alleles inherited are immutable, but the one for current grade improves everytime a Chao evolves into that stat's evolution.

to give a sample punnet square for a single stat Grade:

Let's say Chao one inherited B and A grades from its parents and has since been upgraded to S. Its Alleles would b A, B, and S.

Let's say Chao two inherited D and E grades from its parents and has since been upgraded to C. Its Alleles would b C, D, and E.

The Punnet Square would be:
A B S
C AC BC SC
D AD BD SD
E AE BE SE

As you can see, this gives a 1/3 chance of the S grade being passed down, but there's only a 1/2 chance the S grade will be dominant if passed down, giving a total chance of 1/6. Multiplying this out for all five stats gives 1/7776.

Now, since Store bought chao have the same value for both inherited alleles, and the allele that corresponds to the current grade is initially equal to one of the inherited alleles, it's quite likely for a Chao to have multiple copies of an allele, increasing the chances that allele will be passed down. For example, if you took a store bought Chao with an A-grade, evolved it so that the A-grade becomes a S-grade, it would have a 2/3 chance of passing down A and a 1/3 chance of passing down S, but even though a store bought Chao that started with a S-grade is guaranteed to pass down that S, there's still only a 1/2 chance the child will display the S instead of whatever it inherits from the other parent.

Also, the 1/6 of the above punnet square is the worst case scenario and requires that both parents have 3 different alleles each and no alleles in common. If an allele appears twice in the headings of the punnet square, it would have a 1/3 chance of being displayed by the child, 3 times 1/2, and so on. (1/3)^5 is 1/243, (1/2)^5 is 1/32, (2/3)^5 is 32/243 which is between 1/7 and 1/8, and to give a more complicated example:

(5/6)*(4/6)*(3/6)*(2/6)*(1/6) =
(5*4*3*2*1)/(6^5) //Product of fractions is product of numerators over product of denominators.
(5*4)/(6^4) // 2*3 in numerator cancel out factor of 6 in denominator and factor of 1 is redundant.
(5*4)/(36^2) //Partial evaluation of denominator
5/(36*9) // reduce 4/36 to 1/9.
5/324 //Evaluate denominator. result is 1 in 64.8.

Even if you had a Purebred All-S Chao and bred it with an S-free Chao, you'd only have a 1/32 chance of the child being an impure All-S chao.

You'd be better off mating until you get a Chao with better stats than one of the parents and then swapping out the weaker parent for the child than trying to breed the same pair until you get the optimal outcome. That said, if you want to save scum for optimal or near optimal results, I believe the child's stats are set at the moment the parents mate, so you're best bet would be to save after feeding the parents heart fruit but before placing them near each other and resetting if the hatchling has a bad combination.
ChrisOfChaos
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Re: Breeding for stat grades question?

Post by ChrisOfChaos »

I see. This is still pretty confusing, but I think I'm going to keep at it anyway. I am trying to breed for an all-S Chao (actually a Chao with only S and A stats, which I DID get after about five attempts but lost it due to my computer updating without giving me a chance to save), and I've gotten close, so I think it's worth keeping at it. Thanks for the info, it's very helpful. I'll update once I get the Chao I am looking for.
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Re: Breeding for stat grades question?

Post by Mamkute »

Thank you Mewtamer, for bringing up what I failed to recall (and would have failed to calculate properly.) This is a problem even more convoluted than a lot of real world genetics.
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Re: Breeding for stat grades question?

Post by Jeffery Mewtamer »

The closest real world analogue I can think of to the "Inherit two, display one at random" bit is how human females have two X-chromosomes, but one X-chromosome stays coiled up too tightly to ever be used for building proteins, but that's a coin flip that's performed on a cell-by-cell basis rather than at the organism level(also has the interesting side effect that some women who are carriers for X-linked color blindness actually have Tetrachromatic vision instead of the usual trichromatic vision due to some cone cells using the X-chromosome with the faulty gene and some with the normal gene).

The whole improving the parent's stat grades improves the best grade they can pass down part can only be explained by epigenetics, of which I know very little and to my knowledge is a field that is still in its relevant infancy. Chao, as portrayed in the adventure games, are simpler than pretty much any real-life organism of comparable size, but they still display a level of complexity hard to understand with only highschool biology level knowledge of genetics.

If the parents' alleles for a single stat were truly random, than they would be equivalent to rolling six dice. If I'm not mistaken, the 5!/6^5 =5/324 calculation I did above are the chances of rolling a straight of six dice in a single roll, meaning you have a 319/324 chance of at least 1 pair.

But the parents' alleles aren't random. Store bought chao have inherited alleles equal and a Chao that has never evolved into a given evolution has its displayed allele for that stat equal to one of its inherited alleles. So, the allele most likely to be displayed by the child would, on average, be expected to have at least a 1/3 chance, and the non-randomness present in how the games are implemented raises the chances further and if you started with store bought Chao that got a good roll of the dice to begin with, the optimal allele for each stat probably isn't the rarest allele.

Even if I had the full information of the parents, I suspect the exact probability of an optimal breeding would be more than I could calculate by hand, but I could probably write a program to do it, and if I knew how to read binary files, it could even extract the data from the chao garden save.

Anyways, I'm now convinced this is a problem worth consulting the greater minds over at the Twisty Puzzles Forum.
ChrisOfChaos
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Re: Breeding for stat grades question?

Post by ChrisOfChaos »

Gotta say it sounds like we'll never get a concrete answer on this. It's amazing that way back then when home gaming was still young SEGA managed to create something so complex and intricate.

As for my Chao, I settled for one that is SADSS (and is now an adult SACSS). It's going to take a long time to get his Run stat to an S but I think it will be worth the wait.
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