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When asking questions about particular genes or horses it’s always best to include a link so we can really help you to understand on something your looking at

Personally I breed for KP (a hidden gene) and only mark (with a prefix or at the end of their name) my Homo KP horses and their het offspring (only inherited one copy) their grand foals don’t get marked unless they are guaranteed to have at least 1 KP from the other parent or are themselves showing KP.

Ah, ha! okies, that makes sense. so if the allele is there in one parent in a previous generation, and doesn't show up at all in a more recent generation, then that foal will not have that gene unless it's hidden and the only want to know the hidden allele was even there, is to have one pop up on a foal.

That answers that! Thank you!

Another question. In the auctions, I look for certain traits, and a list comes up with foals that obviously do not have the trait listed at all, and it should be a showable trait. So what about those as carriers?

If both parents are carriers of a gene (heterozygous), hidden or otherwise, then the foal will have a 25% chance of inheriting a copy from both parents and being homozygous for the gene. It's all modeled after real life genetics. I'll give you an example, using a hidden gene. If I'm going way too simple, which I might be now that I see your above response, I apologize. BUT now I've gotten this far so I'm going to finish. This is Aristo:

Aristo
Aristo is homozygous snowflake, that's why he's all white now in his old age. When he was younger he had those little snowflake spots. Snowflake is recessive, so a horse needs to be homozygous to show it (and have a copy of appaloosa).
These are two of Aristo's foals, Seelie and Gisele.

Seelie

Gisele
They are both heterozygous for snowflake because they got one copy from Aristo (as all his foals do since he's hom) and neither of their mothers had snowflake.
Then I bred the two of them together (inbreeding has no negative effects in game) and got this girl:

Myrtha
Myrtha is homozygous snowflake. Each parent had a 50-50 chance of passing on their copy, and she got both, which maths to a 25% chance.

Then I bred her to this guy, before I gelded him, who has the same story- both his parents are Aristo's foals, both are het, and he's hom

Jen the Gelfling
and got this pretty girl, who is young enough that you can actually still see the snowflake, lol. She has to be hom snowflake, because both of her parents are.

Aughra
Now, for an added bonus, Aughra is also hom satin, another recessive gene. That's why she's got that pretty shiny coat. Satin is not a hidden gene, so if you look at the genetic test results of the horses on her pedigree, you can follow it. Aristo is homozygous satin. All his foals, which means all four of Aughra's grandparents, are at least het satin. Both of her parents, Jen and Myrtha, inherited a copy from one parent but not the other. Myrtha, for instance, inherited Gisele's copy but missed Seelie's. (There's a 50% chance of that happening when both parents are het like that.) Then Aughra got both. So we have Aristo, who's satin, then two generations with no visible satin, but all carriers, and then Aughra, who's all shiny!

Okay, I hope this helps and was neither too confusing nor too basic! =))
I second PPN, I'd love links to the horses and/or search you're referencing so we can figure it out, I'm curious now!

What traits are you looking for?

The more specific you are the better we can help.

The search is very powerful and can be used to really narrow down the list shown but other times you may be asking it for contradictory genes that are not possible to show what your actually looking for