We can all learn a few things from the Ball python mutation breeders. There are far too many breeders in Australia that think that hitting the odds are a definite. The below post was made by Tomrhargreaves on Captive Bred Reptile Forums. It is the follow up to Hitting the odds part one; that we shared the link for earlier.
Probability, chance and hitting the odds, in my opinion it’s a very important part of ball python breeding.
Even for those that have no interest in morphs and combos, if you’re breeding one normal to another there’s still the 1/2 chance of each hatchling either being male or female. When you start looking at base morphs, and designer combos of those morphs, the numbers start getting bigger and the odds longer.
What I’d like to do in this post is to examine and explain the probability of hitting a certain combo, but go beyond the odds of just 1 specific egg, or the Punnet Square and look at the probability for a whole clutch (as long as you’ve been graced by more than one egg in that clutch!). It’s come up on the forum before but I don’t think I made my point very well so here’s the long version, because it makes a BIG DIFFERENCE!
An example of single egg probability, or the output of a Punnet Square being:
I have paired my Pastel to my Spider, what are the odds of hitting a Bumblebee?
The answer is 1:4 for each egg but I won’t be properly explaining why here or how to calculate it for other pairings, so suggest that if you are unsure about why this is the case and do want to know more, check out the following links to valuable, free online resources – the first link being why I’ve titled this thread as ‘Part 2’.
Hitting the odds! (how hard can it be?)
Markus Jayne, Ball pythons | Genetics
World of Ball Pythons – Genetics – Co-dominant
World of Ball Pythons – Genetic Wizard
At this stage I should do some housekeeping. As you can probably tell, this is going to be a lengthily post, I apologise for that in advance but I’d like anyone who’s interested in the topic to understand and benefit, which will mean going into some detail. I’m also going to try to stick to generic terms used in the hobby e.g. ‘Super’ rather than ‘Homozygous’, again to try and avoiding adding to confusion. Having said that, this is still going to be a geeky, maths based post and I do understand that’s not everyone’s cup of tea. Hopefully at least one other person also finds this interesting.
So, why does clutch size make any difference to whether or not you hit that combo you’re looking for? Each egg will still carry the same probability regardless of how many are laid…?
What’s crucial is that each egg represents another opportunity for you to hit that combo. When you want to hit at least one from a number of eggs that you’re given, the more eggs, the greater the probability is that you’ll do it. But don’t take my word for it. Here’s the maths, calculators at the ready…
Keeping with the Pastel x Spider pairing mentioned above: There’s a 1/4 chance per egg that you’ll hit a Bumblebee. That’s because there’s 4 possible outcomes of that pairing per egg: Normal, Pastel, Spider or Bumblebee. Each one has the same chance of appearing as any of the others so it’s 1 in 4 or 25%.
If you happen to have been given 2 eggs by your female then you can apply the same theory as above. Work out the total number of possible outcomes from those 2 eggs and the number of those outcomes that include at least 1 Bumblebee. That’s how probable it is that you’ll get at least 1 Bumblebee from those 2 eggs. I’ll give you a spoiler now; it’s not the same as 1:4!
The table below gives all 16 outcomes that you can possibly get from those 2 eggs, ranging from 2 normals, to 2 Bumblebees and everything in-between. The figure that we’re looking for is those 7 out of 16 that include 1 or more Bumblebee. That 7/16 chance is a lot better than 1/4 and more precisely 43.75%
So what if you’re clutches are bigger, much bigger? What’s the probability of getting at least 1 Bumblebee then?
Same pairing:
5 eggs – 76.27%
8 eggs – 89.99%
12 eggs – 96.83%
16 eggs! – 99.0%
When you get up to 16 eggs the numbers are crazy, upwards of 4 billion opportunities with just close to that including at least one Bumblebee, hence the 99% result.
Hopefully that makes some sense; so let’s move on to calculating it yourself, preferably without having to draw a table that has a billion or more boxes, we all have things to be getting on with, right?
As with everything these days there’s two ways to do this:
1. You calculate it yourself, which isn’t as tough as it sounds.
2. Use the Internet to do it for you, which is just as easy as it sounds.
Let’s use a different pairing this time though and pick one from another thread on the forum. Off to the forum to find a recent clutch post, pairing and number of eggs…
Ok, so I’ve avoided a few recent posts to make this more interesting and settled on Darren from CPR, who got 4 eggs, details below.
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Originally Posted by smileyculture
 Clutch # 4 Pastel Calico x Lemon Pastel 4 Eggs , 2 slugs
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Method 1 – Calculate it yourself.
Pastel Calico x Lemon Pastel = 1/8 chance per egg of hitting the Super Pastel Calico. That’s 12.5%
But what about for 4 eggs.?
Total number of possible outcomes is 8 x 8 x 8 x 8 because you have 4 eggs each with a 1/8 chance.
= 4096
Total number of those that DON’T include a Super Pastel Calico is 7 x 7 x 7 x 7 and that’s because you have 7 out of 8 that won’t include the 3 gener per egg.
= 2401
Subtract those that don’t include a Super Pastel Calico from the total to get the number of outcomes that DO include at least one Super Pastel Calico
4096 – 2401 = 1695
So that gives 1695 possible outcomes out of 4096 in total that do include at least one Super Pastel Calico.
(1695/4096) x 100 = 41.38%
That’s not too bad at all and in fact if it had been 6 healthy eggs the probability would be 55.12%, so not a huge leap. Which is all down to it being 1:8 rather than the 1:4 that was given earlier with the bumblebee example.
Method 2 – Use the Internet.
I’m yet to find another method that is as easy as this but this one does require you to think of the situation in terms of throwing dice. Unfortunately, as clever as Wolfram Alpha is, it’s not familiar with Royal Python genetics (yet).
For the example above go here:
Wolfram|Alpha – It’s not cheating if I still press some buttons
The number of eggs = number of dice
Chance per egg = sides per die
Outcome that you’re looking for = anything really but in this case ‘at least one 8’
What we looked at above was hitting one specific outcome, at least once. Which is why it’s ‘at least one 8’. For reference, this is better than calculating ‘exactly one 8’ because more than 1 Super Pastel Calico e.g. 2/3/4 of them is also a desirable outcome!
It doesn’t matter what number on the dice you pick because they all have the same chance as each other. So any number can represent the Super Pastel Calico, in the same way that any number can represent a Normal.
Here’s one last example that I think’s pertinent based on the long odds from one egg and the number of people shooting for it in some form.
Double het x Double het = 1/16
4 eggs = 22.75%
8 eggs = 40.33%
12 eggs = 53.9%
16 eggs = 64.4%
11 eggs is actually the tipping point that turns the odds in your favour i.e. above 50%. Getting a visual Double Recessive from any less than 11 eggs and you’ve smashed the odds, more than 11 eggs…well you still have your visual double recessive so I’ll pipe down!
That’s it, that’s all. Hopefully, for those that are interested, you now have a better idea of the how achievable that dream combo is, although it appears none of it matters because death is coming. 
Link to full thread: http://www.captivebredreptileforums.co.uk/ball-royal-pythons/55044-hitting-odds-part-ii-going-beyond-punnet-square.html
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