Posted by Probability of Passing Tigon

drakizora🌙 g1
daedal ebony (#110938)

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Posted on
2019-02-09 06:19:01
Probability of Passing Tigon

Hi everyone! 

Tigon heats are being sold like mad, so I thought I would share the statistics of tigon (and by extension, leopon) passes. From what I've seen in some chats, people have tried to calculate the probability but have done it wrong. I'll be including my calculations and an extremely brief skim of basic probability below for anyone who is interested in seeing and or wants to follow my work. If you don't care for it (which is perfectly fine), you're free to scroll past it and see what you came for.

Keep in mind that these are purely off the rates of tigon naturally passing through its rate. Items such as GMO cows and lion meats are not considered because those do not and cannot affect a tigon mother's chances of passing the mutation to her cubs.

The Math

So, a common misconception is that people think with a 10% pass rate, a litter of three cubs would offer a 30% chance of getting a tigon. That sounds like it would make sense, 10% + 10% + 10% for three cubs, but this is not a correct calculation.

That type of calculation of simply adding up the probabilities is reserved for mutually exclusive events. That basically means that it is impossible for the events to occur at the same time, with the events being having multiple tigons. While that is definitely unlikely (one tigon is rare enough), it is possible because cub mutations are rolled per cub, not per litter. They are independent events, meaning that they do not effect each other. In a litter of cubs, all cubs have the same 10% chance to be a tigon. If one of the cubs is a tigon, the chance for the other cubs does not change at all. The general rule is that if you're going to add probabilities up, the description of the probability will involve "or" in it.

If you still don't get why you can't just add up the probabilities, here's a less-mathy debunk of it: A coin has a 50% chance of landing on tails. But if you have two coins, the chance doesn't increase to 100% tails. Replace two coins with 50% for tails with three cubs with 10% for a tigon and that's what people have been trying to do.

Now let's move on to how to actually calculate. Imagine this is our litter of three cubs below, with one slot for each cub.

[ ] [ ] [ ]

Now let's say the first cub will be a tigon, and the rest will be not-tigon cubs.

[T] [N] [N]

To calculate the probability, we replace the slots with their respective probabilities and multiply! It's 10% for a tigon, and 90% for not a tigon. We use multiplication here because we're searching for the probability of all of these events happening at once. The key word for multiplication is "and". We're calculating the probability of one tigon and two non-tigons.

[.10] * [.90] * [.90] = .081 = 8.1%

But it doesn't stop just there. We want all the chances to get a tigon. So we'll calculate two tigons and three tigons. This is where we use addition. Another way of phrasing it is that we're looking for the probability of getting one tigon or two tigons or three tigons. These outcomes can't happen at the same time, but we're happy to get any of them. ("But if you have three tigons, you technically have two at the same time!" No. The result is three. 3 =/= 2)

We'll briefly go back to the coin explanation, and discuss it in terms of "and" and "or". What's the probability of getting tails and tails when I flip two coins? Here we multiply the probability of getting tails and tails together. What's the probability of getting heads or tails? Here is where we add the probabilities.

Back to business. The thing is that there's multiple variants for one and two tigons. As shown above, we calculated for if the first cub is the only tigon. But what if the second cub is the only tigon? Or the third?

Honestly I don't really remember the exact explanation to how you calculate the the number of ways to get a specific option (such as the number for all the ways you can get only one tigon in a litter). I could hand calculate every single option, but that's like eight equations... Plus when you have a statistics calculator to do the work for you, you don't really need to know the specifics by heart.


The Results

For the moment we've all been waiting for...

The probability of getting at least one tigon cub from a litter of three from a first generation tigon is...

27.1%

For a litter of four, the odds are

34.39%

When breeding from a tigon that isn't a first generation, the odds of passing become 5%. For a litter of three from next generation tigons, the odds are:

14.2625%

A litter of four is

18.5494%

Lionesses can have a total of 6, 7, or 8 heats in their lifetime. If you're breeding a first generation tigon at every heat (and using buffalo balls each heat), the probability of getting a tigon from 6 heats is:

84.9905% - 92.0234%

7 heats is

89.0581% - 94.7665%

And 8 heats is

92.0234% - 96.5663%

For non-first generation, the probability with 6, 7, and 8 heats respectively is:

60.2786% - 70.8012%
65.9438% - 76.2174%
70.8011% - 80.6289%

unknown.png

There you go! Those are the probabilities for tigons passing! If you read through my math, I hope you might have learned something today.

If you have some specific questions, feel free to ask me!




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Edited on 30/05/20 @ 17:37:28 by drakizora🌙 2x rosette ebony (#110938)

Kahvi ☕ (#48874)

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Posted on
2019-02-09 12:51:41
Wow, didn't expect to learn math today but here we are :D This is really helpful, thanks



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sal (#116987)


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Posted on
2019-02-09 13:01:41
bookmarked!! super helpful post



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AimPyre | G2
Jellyfish Preon (#98461)


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Posted on
2019-02-09 13:20:54
Bookmarked! Thanks!



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JurisCat (Cats) (#126652)

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Posted on
2019-02-22 11:31:44
I'm glad you did those calculations, although its interesting that theyre all pretty close to just saying 5% + 5% + 5% .



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Jassy {Cln Astral
Dawn MR/ESR} (#56647)

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Posted on
2019-02-24 00:06:59
So just out of curiosity since I actually saw this happen today, what's the probability of getting four tigons in a litter of four cubs from a first gen mama?



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Fading Angel (G2 2k)
[Frozen] (#81854)

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Posted on
2019-02-24 00:13:30
Wait, you saw a 4 Tigon litter? :0 thats insane.



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drakizora🌙 g1
daedal ebony (#110938)

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Posted on
2019-02-24 05:49:19
Four tigons, god that's nuts. The probability of a first gen producing four tigons would be .01%. But if the odds of getting a litter of four in the first place was also calculated (which is currently not known), the resulting probability would be even lower.

I could use some luck like that smh



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Jassy {Cln Astral
Dawn MR/ESR} (#56647)

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Posted on
2019-02-24 18:05:51
Ah, I was mistaken. The person had two sets of twins in a row, not one litter of four. BUT STILL!!!! Insane luck!!



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Shu .Gaggle™
Clean.G4 [5K] (#42)

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Posted on
2019-02-24 18:08:18
Oh I have a thread very similar to this one xD



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Vox (G2 Prismatic
2xRosette) (#180186)

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Posted on
2020-01-18 19:40:39
This makes my nerdy heart happy!



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Moonz (#164180)

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Posted on
2020-01-26 00:36:42
Guys, I dont think they say a litter with 4 tigon Cubs. I'm assuming the more cubs, the higher chance for ONE of them to have the mutation.



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drakizora🌙 g1
daedal ebony (#110938)

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Posted on
2020-01-27 11:23:44
The number of cubs doesn't influence the chance of one specific cub, they all have the same odds. If there are more cubs, that's more rolls (because there are more cubs) that could possibly be a tigon.



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Arctictea (#347)

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Posted on
2020-02-06 10:12:09
You probably already know this (or don't care to know it) but a quick way of calculating chances with multiple "win" conditions (one or two or three or four tigons) is to calculate the chance for failure (zero tigons) and then take 1-chance for failure.

So chance for tigons = 1 - chance for no tigons
Chance for no tigons is easy to calculate: 0,9^n, where n is # of cubs.
So chance for tigons = 1 - 0,9^n

Quick and simple. Using n=3 gives the same chances as stated above.

What I find is interesting is the fact that if bred only on "natural" heats the probability to get a follow-up tigon is less than one. So tigon-lineages are pretty much doomed to die out sooner or later unless barked.



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survivor (#183270)

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Posted on
2020-02-06 10:13:20
Love this, thank you!



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Jassy {Cln Astral
Dawn MR/ESR} (#56647)

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Posted on
2020-02-06 10:42:15
I'm not sure just how doomed they are to die out without barking, honestly. I was gifted a 2nd Gen 5yo tigon girl way back when from my sister Sonia, and her tigon lineage has continued fairly strongly with only ONE 7-barked heat used on her granddaughter, Arunika. No other barks have ever been used, and no additional breeding items aside from each heat being buffy balled and IBFed. I'm up to Gen 6 with little Aida and her sister, Phoenix! There have also been two others born along the way that I ended up gifting to my sisters.

So in total, I've been lucky enough to produce 8 further tigons down the line from my 2nd Gen girl, Roshani.



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Edited on 06/02/20 @ 10:53:52 by Jassy {G2 Clean Bast Striped} (#56647)







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