**What are the chances that a big litter of puppies will be all girls or all boys? We did the math for you and and put it in this easy-to-use puppy probability calculator!**

**Puppy Probability Predictor**

**X and Y Chromosomes**

In dogs, each cell nucleus contains **39 pairs of chromosomes**, a total of 78 chromosomes.

The first 38 pairs are called **autosomes**.

**Autosomes **are homologous chromosomes. The two chromosomes of each pair are built the same and **contain the same genes in the same order **along their chromosomal arms.

However, the 39th pair of chromosomes are called **allosomes** or **sex chromosomes**. These consist of** two X chromosomes in females**, and** an X chromosome and a Y chromosome in males**.

**Females are XX**, they can pass along **either of their Xs **to their puppies.

However, **males are XY**, they will pass along **either an X or a Y**.

It is the **presence or absence of the Y chromosome** that determines the sex of each puppy. So it’s **up to the sire **to produce either female (X**X**) or male (X**Y**) offspring.

**Puppy Probability**

Each new puppy can be either** a boy **or **a girl**.

So there are **two potential outcomes **for each puppy.

**Probability** measures **the likelihood that an event will occur**.

The chances that any new puppy will be male *or* female is **50%** or **1/2 **which equals **0.5**.

Each new puppy is **an independent event**, it does not matter how many of his siblings are boys or girls.

**The 50 % chance stays the same for each new puppy.**

In this **litter of 2**, we have** 4 possible outcomes:**

**Boy, BoyBoy, GirlGirl, BoyGirl, Girl**

These different outcomes are also called **permutations**.

**Permutation:***“Any of several possible ways in which a set of things can be ordered or arranged.”*

The number of all possible permutations in a litter equals **2 ^{(number of puppies)}**.

For a litter of 2, you have a list of only **2 ^{2}** or

**2*2**=

**4**permutations.

For a litter of 4, you have a list of only **2 ^{4}** or

**2*2*2*2**=

**16**permutations.

*Permutations take into account in which order puppies are born. We will come back to this later.*

The **number of permutations** doubles with each additional puppy:

Litter Size | Number of Permutations |
---|---|

1 | 2^{1} = 2 |

2 | 2^{2} = 4 |

3 | 2^{3} = 8 |

4 | 2^{4} = 16 |

5 | 2^{5} = 32 |

6 | 2^{6} = 64 |

7 | 2^{7} = 128 |

8 | 2^{8}= 256 |

9 | 2^{9} = 512 |

10 | 2^{10} = 1.024 |

11 | 2^{11} = 2.048 |

12 | 2^{12} = 4.096 |

13 | 2^{13} = 8.192 |

14 | 2^{14} = 16.384 |

15 | 2^{15} = 32.768 |

16 | 2^{16} = 65.536 |

17 | 2^{17} = 131.072 |

18 | 2^{18} = 262.144 |

19 | 2^{19} = 524.288 |

20 | 2^{20} = 1.048.576 |

If you know** the number of possible outcomes**, you know that **each permutation** in a **litter of 4** has a chance of **1/16 **because there are a total of **16 possible permutations**.

Another way **to calculate the chance for any single permutation** is simply to **multiply the probability of 0.5 **by **the number of puppies in your litter**.

It does not matter which path you follow from start to end. Each permutation is equally likely:

In **a litter of 4**, each outcome has a chance of **1/16** = **0.5 ^{4}** =

**0.5*0.5*0.5*0.5**=

**0.0625**.

Next, multiply with 100 and you get the probability in percent: **0.0625 * 100 = 6.25 %**.

For a litter with **either all boys or all girls**, that’s all you need! Because **no matter how many puppies you have**, there will **only ever be one order** that can produce an **all-male or all-female litter**.

But **for the other ratios** of boys to girls, we still often have several outcomes that **can lead to the same result**. That is because each permutation **takes into account the order in which puppies are born**.

Each permutation **represents exactly one order of events**.

This means, getting **boy-boy-boy-boy **is just as likely as getting **girl-boy-boy-boy**!

Both have a chance of **0.5*****0.5*****0.5*****0.5** or **6.25 %**.

However, breeders do not care **in which order their boys and girls are born**.

If we ignore the order, we can **sort our outcomes by their final number of boys and girls**.

For example:

There is **only one permutation that will produce 4 girls**.

However, **four permutations meet the criteria of 3 boys and 1 girl**!

If we summarize the** unique end results**, it looks like this:

Boys/Girls | Permutations | Chance | Sum |
---|---|---|---|

4/0 | BBBB | 6.25 % | 6.25 % |

3/1 | BBBG BBGB BGBB GBBB | 6.25 % 6.25 % 6.25 % 6.25 % | 25 % |

2/2 | BBGG GGBB GBGB BGBG BGGB GBBG | 6.25 % 6.25 % 6.25 % 6.25 % 6.25 % 6.25 % | 37.5% |

1/3 | GGGB GGBG GBGG BGGG | 6.25 % 6.25 % 6.25 % 6.25 % | 25 % |

0/4 | GGGG | 6.25 % | 6.25 % |

**B**= Boy,

**G**= Girl

To calculate the probability of **events that can be achieved in several ways**, simply **add up the odds**.

In our example, the chance for 3 boys and 1 girl is **6.25% + 6.25% + 6.25% + 6.25% = 25%** because there are four ways to get there (BBBG, BBGB, BGBB, GBBB).

By the way…

You can think of puppy gender as a **coin-flip experiment**, the math is the same.

You can use this calculator for any scenario with **two possible outcomes** and a **50/50 chance**.

- What are the chances for only
**merle**puppies in a**M/m x m/m**litter with 6 puppies? About**1.6 %** - How likely is it to have 5
**tan point**and 5**sable**puppies in an**A**litter? About^{y}/a^{t}x a^{t}/a^{t}**24.6 %** - What are the odds of getting only
**black**puppies in a**B/b x b/b**litter of 8? About**0.4 %**.

**The 50/50 Chance**

The **50/50 chance** for boys and girls **does not predict the ratio of puppies in a litter**.

Rather, **each puppy has a 50% chance** of being a boy or a girl.

From this, we can calculate how likely it was that **your litter happened as it did**.

However, **probabilities **will never reliably** predict single events**, just their **average distribution in a large number of repeated trials**. They provide **the likelihood of different outcomes** over the long run.

Even with **even odds for a boy or girl**, the outcome of a whole litter of puppies **is random**.

Anecdotally, breeders will tell stories about **sires or dams **with a tendency to produce mostly boys or mostly girls. But keep in mind that **individual dogs and their offspring count** are **really small samples**.

You can’t read that much into these small numbers.

All humans tend** to see patterns where there are none**, this makes us prone to superstitious beliefs.

Based on “* anecdotal data*“, it is not possible to prove whether an observed ratio of boy/girl puppies

**is just random**or whether

**the supposed 50/50 chance really is skewed**.

So, is there a true **50/50 chance** for every puppy to be born **a boy or a girl**?

Well, if you look at large enough sample sizes, the **boy-to-girl ratio** should be very close to **50/50**.

In reality, there might be **a slight bias towards male puppies**.

But **the more litters you look at**, the higher the chance of reaching 50%.

A study that looked at only 436 litters found about **52%** of puppies to be boys^{[5]}. Another study that analyzed 37.946 litters found a proportion of male puppies of **51.2 %**^{[6]}.

Just as, let’s say, **litter size** is determined by a number of things, there seem to be just as many **factors that can tweak the 50/50 chance** for boys or girls.

Think of variables such as the **breed of dog**, the **ratio of X to Y sperm cells** a sire can produce, **vaginal pH** during fertile days, the **timing of mating**, or the **age gap between a breeding pair**^{[1-4]}.

There seem to be **a fair amount of factors **that can **slightly skew the odds** for specific dogs or pairings to produce an **off ratio**. However, these findings are** not necessarily consistent across breeds**.

Even the **coin flip**, a classic example of 50/50 probabilities, **turned out to be slightly off** in real life. To get to this conclusion, they tossed the coin a whopping 350.757 times.

Can you confirm these results by tossing a coin 100 times at home? Of course not.

So again, you can’t reliably prove a skewed ratio **based on small samples**!

Even if your stud dog really had a 60% or 70% chance of producing boys and was the most popular of sires, there is no way to confirm this **based on his comparatively small number of puppies**.

In summary, even **with an undeniable amount of variation** in real-life scenarios, the probability of getting heads or tails, or in our case **boys or girls**, still **does not stray too far off from a 50/50 chance**.

**So for the purpose of our calculator, I think it’s ok to assume an even 50 % chance.**

**Learn More**

**Links**

[1] Anna Carolina Lopes Martins et al. (2019). **Maternal age, paternal age, and litter size interact to affect the offspring sex ratio of German Shepherd dogs**. Theriogenology 135. *https://doi.org/10.1016/j.theriogenology.2019.06.022*

[2] Schrack et al (2017). **Factors influencing litter size and puppy losses in the Entlebucher Mountain Dog**. Theriogenology 95. *https://doi.org/10.1016/j.theriogenology.2017.03.004*

[3] Groppetti et al. (2023). **An exploratory study on the sperm ratio in dogs: repeatability over time and some reproductive effects**. Archives of Veterinary Science 28.2.

[4] Antonov et al. (2014). **Dynamics of Vaginal pH in the Bitch during Proestrus and Estrus**. Animal and Veterinary Sciences. *https://doi.org/10.11648/j.avs.20140204.13*

[5] Kania-Gierdziewicz (2019): **Effect of inbreeding on fertility traits in five dog breeds**. Czech J. Anim. Sci. *https://doi.org/10.17221/104/2017-CJAS*

[6] Chastant-Maillard et al. (2016). **Reproductive performance and pre-weaning mortality: Preliminary analysis of 27.221 purebred female dogs and 204.537 puppies in France**. Reprod Dom Anim. *https://doi.org/10.1111/rda.12845*

[7] Lindblad-Toh et al. (2005). **Genome sequence, comparative analysis and haplotype structure of the domestic dog**. Nature 438. *https://doi.org/10.1038/nature04338*

Hi! I’m Steffi. I am a biologist and a big time dog nerd. You are curious about coat color genetics? You’ve come to the right place! Read more.