drakizora🌙 g1
daedal ebony (#110938)
Divine
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Posted on
2019-02-09 06:19:01
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| Probability of Passing Tigon |
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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 |
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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 |
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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%
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) |
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