Wild horses could run away from the player unless they sneak up on it and capture it with a lead. If approached too fast then the herd runs away (and might even kick the player).

Once captured the horse would require daily interaction (proximity and maybe feeding) for a few days to become familiarized. Before being fully tamed, the horse would have a dropping chance of running away, kicking the player and throwing them off it mounted. Being scared (nearby hostile mobs), injury or hunger could revert some of the taming.

Fowls born to tamed horses would have a shorter taming time.

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