Here’s the thing: I recently came across a comment on a forum on how much Pound Cake looked like a little Dr Whooves, and it got me thinking. “What if Dr Whooves was Pound Cake’s biological father? But what about Pumpkin Cake? She’s the spitting image of Carrot Cake… well, neither of them look like their mum. What if they had two separate fathers?”

The basic scenarios I worked out in my head is 1) Mr Cake is the father of both twins and 2) Mr and Mrs Cake had a threesome with Dr Whooves which resulted in twins, each with a different father.

So I decided to work out the probability of these scenarios happening. Why not? I love genetics and I’ve got to study for statistics at some point, might as well make it fun!

Now, I see the Cakes as a happily married couple with a normal sex life, so I don’t think Mrs Cake would cheat on her husband. But no matter how much two people love each other they can get into a rut with their sex life and become bored of the same old thing all the time. I imagine they have very vanilla tastes, so I would imagine them trying a threesome before trying BDSM to achieve this as, in human society, a threesome is more socially acceptable than leather and chains.

I also think (probably due to the way she’s drawn) that Mrs Cake is a bit older than Mr Cake. I’m not afraid to admit that I thought Mr Cake was just a freckly teen who worked at Sugar Cube Corner when he first appeared (worse, I thought he was her son! My bad). This is significant as older mares are more likely to hyper-ovulate than younger ones. Since I did this for fun I couldn’t be bothered calculating how much this would affect the probability of twins being born, especially since we don’t know how old Mrs Cake actually is, so this fact is not figured into my calculations.

In my calculations I am using Pegasus Dr Whooves as 1) I like him better, and 2) if we assume he is the MLP version of a Timelord (as some fans like to believe) than both versions are the same pony during different incarnations, travelling through history at parallel times but never appearing at the same point in time/space. So Pegasus Dr Whooves’ genotype would be ppUU (or ppUu, but that is just knit picking).

I also assumed in my calculations that Mrs Cake’s genotype is PpUu as it would be impossible for her to have mothered Pumpkin if she had no unicorns in her family background (Mr Cake, after all, only mentioned a loose relationship to a pegasus).

But enough of my musings on pony sex and society. On to the actual statistics.

Probability of Twins:

Twinning is actually a major factor in mid- to late-abortion rates of horses, as the foals compete for resources in utero. This competition usually results in the death of one or both twins, and can even put the mother at serious risk if something goes wrong.

In the end only 9% of pregnancies that go to term result in twins being born. Out of these births 64.5% result in two stillborn foals, 21% result in one dead foal and one live foal, and only 14.5% result in two living foals. My source is here.

So the probability that a twin pregnancy that goes to term will result in two live foals occurring is:

0.09 * 0.145 = 0.01305

So less than 1% of twin pregnancies result in two live foals.

If we assume that Mrs Cake is descended from a unicorn and a pegasus somewhere along the line and that Npatchett's Theory of Alicorns (with one minor correction) is correct (and that horses can have twins with two different sires) we can work out the probability of the Cake twins being two different subspecies. Here are two scenarios:

Scenario 1 - Mr Cake is the father of both twins:

This is classic Mendelian genetics which is covered by Npatchett, except that his ratios are wrong. Mr Cake must have the genotype PpUu for this scenario to be possible. So given Mr and Mrs Cake are both PpUu, the phenotypic ratios should be:

9/16 Earth ponies
3/16 Unicorns
3/16 Pegasi
1/16 Alicorns

So the probability that the Cakes would produce a pegasus foal and a unicorn foal is:

3/16 * 3/16 = 9/256 = 0.03516

Therefore, the probability that they would have a pair of twins where one is a pegasus and the other was a unicorn is:

0.01305 * 0.03516 = 0.00046

This is a very low probability indeed.

Scenario 2 – Mr Cake sired one twin and Dr Whooves sired the other:

In this scenario we assume that Mr Cake is PPUu (as he only mentions his descendancy from a unicorn) and Dr Whooves is ppUU.

                      Mrs Cake
           PU     Pu    pU    pu
Mr     PU  PPUU  PPUu  PpUu  PpUu        3/4 Earth ponies
Cake   Pu  PPUu  PPuu  PpUu  Ppuu        1/4 Unicorns

                             Mrs Cake
                   PU    Pu    pU    pu           1/2 Earth ponies
Dr Whooves     pU  PpUU  PpUu  ppUU  ppUu         1/2 Pegasi

So the likelihood of Mrs Cake birthing a unicorn foal with her husband and a pegasus foal with Dr Whooves is:

1/4 * 1/2 = 1/8 = 0.125

Assuming that both foals are sired in the same pregnancy:

0.01305 * 0.125 = 0.00163

While this is still low, it is almost four times more likely, making it statistically more favourable than both twins being sired by Mr Cake alone, given the information provided in the show.

Conclusion:

Without more information on the ancestral background of the Cakes and their sexual habits I can conclude that it is statistically more favourable that Pound and Pumpkin Cake were fathered by two different stallions.

I know I'm assuming a lot in this analysis. I'm applying real world variables to a race of intelligent ponies, which I would assume would have better prenatal care, so twins would have a better chance of making it to term. I am also assuming that two stallions can sire a different twin each.

My justification for the first assumption is that, in the show, the mane six were surprised when Mr Cake revealed the twins. Pinkie lives and works with the Cakes, if they knew they were having twins they would have had a hard time keeping the fact from her (Pinkie turns up where you least expect her). This makes me assume that Mrs Cake didn't get a lot of prenatal care from a doctor as they would have told her of what her risks were, so she was just very lucky both her foals made it to term.

The second justification is that very few horses have twins and that horse studs pay very careful attention when breeding their mares, so they wouldn’t let two males service the same mare. Half-sibling twins are not unheard of in other species, however. The rate of half-sibling litters in cats and dogs is quite high, but it has also been known to happen in humans on occasion, so I can assume it could happen in horses too.

I would also like to mention another mention another piece of canon that sparked me do this. After Mr Cake tells that mane six about his and Mrs Cake’s family connections he asks “That makes sense, right?” and does the whole nervous/shifty eyes thing, like he was hiding something (Scandal?).

In the end, while this is evidence another stallion was involved I really think the twins are both Mr Cake’s. But even if they weren’t, he’d love them just the same. I did this for fun, so if there is something wrong with my working you're welcome to tell me what I did wrong in the comments.