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.

Quote:

Originally Posted by smileyculture  Clutch # 4 Pastel Calico x Lemon Pastel 4 Eggs , 2 slugs

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

We all see stunning morph combos hatching out each year and each year they get more and more complex (i.e. more genes added).

We also all see some of the high price tags that are associated with them, well here’s a breakdown of hitting some of those odds that are required to make certain combo morphs, you may be suprised just how much luck you really need 

First off, a simple one;
Single gene Co-dom x Normal - statistically you should get 1 in every 2 eggs being a visual copy of the co-dom parent, in other words if you bred a Pastel to a Normal, 50% of the babies should hatch out as pastels.

How about hitting a Super?
Single gene Co-dom x SAME (eg Pastel x Pastel etc)- not too difficult to get plenty of single gene copies of the parents, again 1 out of every 2 eggs should be a copy but what about hitting the Super, well that’s not too sad at being 1 in 4, so Pastel x Pastel will give you 50% Pastels and 25% Supers…although remember you have the SAME chance of producing a NORMAL as you do a Super .

How can you improve the number of Supers per clutch? No easy answer other than using at least one super parent, i.e.
Super Pastel x Pastel would give you 50% Pastels 50% Supers (1 in 2) and NO normals…Nice!

Now that’s all pretty straight forward and can be used for all co-dom morphs (pastels, butters, Cinnamons, Mojaves etc).

What about creating a designer morph?
Let’s say you had a Pastel and a Lesser, so;
Pastel x Lesser - the top result would be a Pastel Lesser. Again not too complex, you have a 1 in 4 of hitting each combo, so 25% should be Pastels, 25% Lessers, 25% Pastel Lessers and 25% should be normals (so remember you have just as much chance hitting a NORMAL as you do hitting the Pastel Lesser ).

How about spicing it up a bit? (double x single)
Bumble Bee x Pastel - now this is where the odds start to really get low, First off the highest odds are hitting a Pastel and a Bumble bee, with 1 in 4 eggs being either of those (25%). You then have a 1 in 8 chance of hitting all the other combos which are Normal, Spider, Super Pastel & Killer Bee, so that’s just 12.5% chance of hitting that Killer Bee, with just as much chance of it being a normal , Now do you see why there are not more Killer Bees 

Now ok, what about trying to hit some a bit more special, say 3 unique genes, like Spider, Pastel & Pinstripe? Now obviously we will need to start off with 2 genes in one snake, so lets go;
Bumble Bee x Pinstripe - now on this combo all things are equal, you have as much chance an egg being a NORMAL as you do one being a Spinner Blast (Pastel, Spider, Pin). That’s just1 in 8, or again 12.5% chance on every egg producing the mutation you want. You could still hatch out 7 different combos out of this clutch plus normal, with each and every gene combo having the same chance of being produced as each other…wow now wonder these not too many Spinner Blast 

What about a real tough cookie to crack…a Double Het project.
Let’s take the following;
Double het Clown & Caramel x Double het Clown & Caramel - now obviously the Caramel Clown is what you want to hatch but how hard is it? 1 in 16…that’s one egg in every sixteen laid has statistically a chance of being the Caramel Clown, just 6.25% chance of hatching one from a clutch, still 6.25% has been hit, so there’s always hope 

Finally for now, how about this for a long shot
You have a Pastel Calico and a Spinner Blast, so you are aiming for a Super Spinner Blast Calico (super pastel, spider, Pinstripe, Calico…wow what a snake that might be ). It’s a long shot that’s for sure…you would stand just a 3.125% chance of hitting that or basically 1 egg in every 32 

Now, when you look at it like that, you can understand the value in some of these combos and the hard work (and luck) that went into some of these projects.

Good luck and may the morph gods be on your side .

Link to full thread: http://www.captivebredreptileforums.co.uk/ball-royal-pythons/26972-hitting-odds-how-hard-can.html