How does an offspring inherit a colour?

NOTE: Prior to launching breeding, any changes will be communicated to the community.

There has been significant speculation in the ZED community around the importance of coat colour and how it is treated within the breeding process.

If you are not aware, the coat colour of each horse reflects its rarity and collectability.

Coat colour is highly valued by players and as a result, has been carefully considered in the breeding process.

This medium post covers the various aspects of breeding to maximise the coat colour outcome. The topics we will touch on include:

  1. Colour Pyramid with Colour Groups and Rarity Tiers
  2. Coat Colour Breeding Formula
  3. Defining Breeding Pairs
  4. Defining Breeding Rarity
  5. Examples of Breeding Rarity Formula

Colour Pyramid with Colour Groups and Rarity Tiers

The Colour Pyramid is a table which classifies each of the coat colours into Colour Groups and Rarity Tiers. By classifying the coat colours this way it allows players to easily identify its colour uniqueness.

Therefore, the Colour Groups comprise the following:

Blue “Neptune” — these horses are strong but calm, with a patient temperament. They are well-balanced, highly intelligent, gentle, docile, and eager to please.

Brown “Earth” — these horses love to run and possess great stamina and a desire to please their riders. They are sensitive to the handlers mood and are gentle, fast-learners and hard-working. Despite being easy-going and curious, they can be easily spooked.

Green “Wild” — these tough, independent, hardy, sure-footed racehorses take a little more time to learn. They are emotionally perceptive and tends to overreact when something upsets or frightens them. Their brave and gritty nature makes them great over long distances.

Within each colour group there is a three tier rarity scale from common, rare, and very rare.

Greyscale “Moon” — an intelligent and hard-working disposition, makes the compact versatile horses popular. A perfect balance between an attentive disposition and a healthy level of spirit.

Red/Orange “Fiery” — this spirited, bold, and quick learning horse, possesses agility and speed from its thin-skinned, slim, and long-legged physique.

Tan/Yellow “Classic” — this racehorse is quiet, conscientious and level-headed. Its passion and courage, together with its consistent energy levels, makes it perfect as a stayer.

Purple/Pink “Mystical” — this spirited horse is highly intelligent and reads race situations well. It is energetic, versatile, and is suitable for races of all conditions.

Note: Coat colour rarity is defined as the intended number of Nakamoto Z1 Genesis racehorses which have that particular Coat Colour.

For the avoidance of any doubt, we refer to a colour group as all colour types within a group. We will also refer to colour boxes, which simply means the colours within a group of a certain rarity tier. For example, if we take the Moon Colour Group, the colour boxes would be as follows:

Coat Colour Breeding Formula

Colour plays an important aspect in terms of the collectibility nature of racehorses in ZED. As a result, the colour of the offspring is complex and is determined by the following equation:

Offspring Coat Colour = Breeding Pairs (bp) x Breeding Rarity

where; Breeding Pairs (bp) and Breeding Rarity (br) are discussed in detail below.

Please note that the gender outcome for every offspring is generated randomly.


Defining Breeding Pairs

There are three (3) possible Breeding Pairs (bp):

Therefore, the three different Breeding Pairs (bp) can be represented in the following equations:

  1. S = D Exact Colour
  2. S ≠ D Exact Colour but S = D Colour Group
  3. S ≠ D Exact Colour and S≠ D Colour Group

Note: Where Dam (Mother) and Sire (Father) are different coats, a general rule that the Sire’s influence is approximately 65% whilst the Dam’s influence on the outcome of the foal is approximately 35%, is applied.

Therefore, depending on the Breeding Pair of the Dam and the Sire, three different formulas will be applied to determine the coat colour of the offspring.

1. Dam and Sire have an identical Coat Colour (S = D Exact Colour)

Where the Dam and Sire have an identical Coat Colour. This means the Dam and Sire colour comes from the same Colour Group and the same Colour Box. Therefore, the following breeding outcome of the offsprings Coat Colour will be applied at random:

  • 40% chance: identical Coat Colour as parents
  • 25% chance: identical Colour Box as parents
  • 15% chance: any adjacent Colour Box as parents
  • 15% chance: less rare Coat Colour in same Colour Group to parents
  • 4% chance: any Coat Colour below parents Colour Box (if any)
  • 1% chance: any Coat Colour in the same Colour Group above the parents Colour Box (if any)

2. Dam and Sire do not have an identical Coat Colour but are in the same Colour Group (S ≠ D Exact Colour but S= D Colour Group)

Where the Dam and Sire do not have an identical Coat Colour but the Coat Colours are in the same Colour Group, the following breeding outcome of the offsprings Coat Colour will be applied at random:

  • 30% chance: same Coat Colour as Sire (Father)
  • 15% chance: same Coat Colour as Dam (Mother)
  • 13% chance: any Coat Colour from the same Colour Box as Sire (Father)
  • 7% chance: any Coat Colour from the same Colour Box as Dam (Mother)
  • 15% chance: any adjacent Colour Box
  • 19% chance: any other Coat Colour below the parents more common Colour Box (if any)
  • 1% chance: any Coat Colour in the same Colour Group above the parents Colour Box (if any)

3. Dam and Sire do not have an identical Coat Colour and are not in the same Colour Group (S ≠ D Exact Colour and S≠ D Colour Group)

Where the Dam and Sire do not have an identical Coat Colour and their coat colours are not in the same Colour Group (and therefore also not in the same Colour Box), the following breeding outcomes of the foals Coat Colour will be applied at random.

  • 40% chance: { [Dam Coat Colour Rarity x 0.35] + [Sire Coat Colour Rarity x 0.65] } and randomly select any Coat Colour, from that Rarity Tier (figures are always rounded up)
  • 30% chance: same Colour Box as Sire (Father)
  • 20% chance: same Colour Box as Dam (Mother)
  • 6.5% chance: same colour as Sire (Father)
  • 3.5% chance: same colour as Dam (Mother)

Defining Breeding Rarity

Breeding Rarity (br), factors in the difficulty in breeding rare Coat Colours. Breeding Rarity is always factored in after the Breeding Pair (bp) equation has been applied. Rarity (r) represents the number next to each coat colour in the Colour Pyramid.

Subsequently, this results in rare Coat Colours being more difficult to breed as it is proven by the following Breeding Rarity (br) formula:

br = [r³] / 1000


Examples of Breeding Rarity Formula

There are many colour variances that are possible with breeding, however, we have compiled the following two examples to illustrate some possible outcomes:

Example A — Sire and Dam are Peach Puff (Red/Orange — Rarity 5). These two horses are identical colours.

Now, we apply the first part of the logic:

  • 40% chance: identical Coat Colour as parents
  • 25% chance: identical Colour Box as parents
  • 15% chance: any adjacent Colour Box as parents
  • 15% chance: less rare Coat Colour in same Colour Group to parents
  • 4% chance: any Coat Colour below parents Colour Box (if any)
  • 1% chance: any Coat Colour in the same Colour Group above the parents Colour Box (if any)

Therefore let us assume the Breeding Pair formula determines the colour selected is from the adjacent colour box of the parent (15% chance of happening), being Cornsilk (rarity is also 5). Once the breeding pair determines the colour is Cornsilk, we then apply the rarity check.

Breeding rarity (br) = [r³] / 1000

= (5 x 5 x 5) / 1000 = 0.125 = 12.5%

Therefore, there is a 12.5% chance that the offspring will be given a Cornsilk colour and an 87.5% chance that it will drop to the lower rarity level of the same colour pyramid.


Example B — Sire is a Rosy Brown (brown rarity 7) and Dam is Antique White (greyscale rarity 9).

These two horses are not the same colours, nor in the same Colour Group.

To begin, we apply the first part of the logic:

  • 40% chance: { [Dam Coat Colour Rarity x 0.35] + [Sire Coat Colour Rarity x 0.65] } and randomly select any Coat Colour, from that Rarity Tier (figures are always rounded up)
  • 30% chance: same Colour Box as Sire (Father)
  • 20% chance: same Colour Box as Dam (Mother)
  • 6.5% chance: same Coat Colour as Sire (Father)
  • 3.5% chance: same Coat Colour as Dam (Mother)

Now let us assume that randomly, the first part of the logic is selected being:

= { [Dam Breeding Rarity x 0.35) + (Sire Breeding Rarity x .65] }

= { [9 x 0.35] + [7 x .65)] } = x (round up)

= [3.15 + 4.55]

= 7.70

= 8 (round up)

Therefore, there is a 40% chance that the offsprings Coat Colour will be randomly selected from the Rarity Tier titled “Rare”. For this example, we will assume the colour Burlywood (rarity is 8) is selected. Therefore, we will now apply the rarity check formula being:

Breeding Rarity (br) = [r³] / 1000

= (8 x 8 x 8) / 1000 = 0.512 = 51.2%

Therefore, there is a 51.2% chance that the offspring will be given a Burlywood colour and a 48.8% chance that it will drop to the lower rarity level of the same colour pyramid and a new colour is selected at random.


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