One of my favorite encounter card designs to date. Similar to The Shadow Behind You, Hunted by Byakhee plays mind games with you. Yes, you are unlikely to pass an (6) test, but if you manage to minimize your failure, Hunted could end up whiffing. On the other hand, it's equally likely that a Byakhee is right on top, wasting any investment you made to minimize failure. Of course, you could expend resources to push yourself into ABT (Anything But Tentacles) range, but A) That would be extremely expensive, in A Phantom of Truth on Standard you might need to hit 11 depending on how much doom is in play, 2) Any resources you use to minimize failure on Hunted are resources you could have used to deal with any Byakhee it ended up spawning instead, and Γ) The is always a risk, but investing so many resources into resisting Hunted means that pulling the turns from bad to catastrophic, especially since, as we established in point 2), that means the resources you lost to the aren't available to fight the Byakhee Hunted spawns (which, given that you're digging 6 cards into the encounter deck, it's extremely likely to do).
Granted, this is mostly academic, the majority of the time I've drawn Hunted I've chosen to simply take it on the chin, but the point is it feels like a real choice. Unlike cards like Rotting Remains, you're unlikely to flat-out pass Hunted by Byakhee, turning your focus from "What are the odds expending this resource will let me pass?" to "What are the odds that expending this resource will mitigate my failure sufficiently to avoid the worst-case scenario?" Even going from 6 down to 5 down substantially reduces your chance of finding an enemy, forcing you to consider not just the chaos bag but the composition of the encounter deck. How many Byakhee are already in play or in the discard pile? If horror is a problem, how many Omen cards are left in the encounter deck?
What do you choose to do?