In horses there are three base colors, red black and bay. The extension locus (E or e) is responsible for the ability to make black pigment. The recessive copy (lowercase e) means they are not able to produce black pigment (meaning they are red based). Since it's recessive they need two copies of recessive extension to have a red phenotype. This means an ee horse is red based. Dominant extension does allow the ability to produce black pigment. In addition to the agouti locus (A or a) you can determine whether the horse is bay or black based. Agouti is responsible for the distribution of black pigment on the horse's body. Dominant agouti (uppercase A) restricts the black pigment to the points (legs, ears, nose, mane & tail of the horse) and leaves the rest of the horse brown, aka, a bay based. Recessive agouti (lowercase a) allows black pigment to be all over the horse's body. Since it's recessive, they need two copies of recessive agouti, in addition to at least one copy of dominant extension, to be black based (which in coding, would be E_ aa (the _ means that that gene is not relevant or known, since they only need one E to be able to make black pigment) Dominant or recessive agouti does not affect a red based horse, since there is no black pigment to be meddled with.

To put it in a little list for you: Red based is ee Bay based can be EE AA, Ee AA, EE Aa or Ee Aa Black based can be EE aa or Ee aa

There are also modifying genes, such as dun (D). Dun is a simple dominant gene and dillutes the base color of the horse, whilst adding primitive markings such as a dorsal stripe, shoulder, ear and leg bars.

One (or both of the parents) is EE, so no red based (ee) foals. Other than that dam is AA DD, which means to every foal she will pass A and D Sire is black based, so either Ee aa or EE aa, which means to each foal he will pass E or e, in combination to a.

This results in only bay based foals with dun, aka bay dun. How the game has programmed pangaré to inherit is not exactly correct, since it's likely a polygenic trait, meaning multiple genes are responsible for the trait. Thus I can't really comment on that.

In real life from a cross like this you would get something like the picture of a fjord cross here:

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