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Medicine Hats in real life are Toveros, a combination of Tobiano and Overo, with a "hat" of color on the ears and a "shield" patch on the chest. The War Bonnet pattern is similar, with a larger patch on the head, sometimes covering the entire face(War Bonnet doesn't have to have the shield). HaJ has Tobiano, but there isn't an Overo gene to breed for(closest is frame, but it's not necessary for this pattern). The in-game horses I've seen with a Medicine Hat pattern typically have Tobiano with extensive white factor. Some also have SW1 or Frame in addition to the Tobiano.
Here are some examples from a horse search:

8265786


WGH Shining Native Lp


8997524


WGH 9198468 e


9197552


9191764

Unfortunately, the specific pattern doesn't have it's own gene, in-game or IRL. You can definitely try breeding for it, but there's no real guarantee that you'll get that exact pattern every time.

@MackZ overo just means any pinto gene that is not tobiano. There is no "overo" gene in real life either. Lethal White Overo is another name for frame. :)

I absolutely love Medicine Hats and breed them frequently. Most of mine are Tobiano + Frame


Px3 All the Stars


Px4 Sun in my Eyes


Px4 All Pretty Eyes


Px2 Tiny Spice

I occasionally have some that are Tobiano Frame and Splash, but I find I personally don’t prefer that expression as much


xPx2 Pop Quiz Hotshot

Tobiano Frame and Sabino is another way I get patterning similar to Medicine Hat. I personally like that more than Tobi/Frame/Splash even though it’s not as clearly Medicine Hat


Px4 Pretty Navigator


Px5 All Talk

I just got a 7th gen SUP to mare Medicine Hat Filly : Mom was also a Medicine Hat but more heavily marked, mine seem to be Tobiano / Splash

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