Only thing I've ever found able to counter Kat-Archers (besides more Kat-Archers) is massive numbers. I mean MASSIVE. Huge, even.
Although I'm tempted to try a new strategy - Regular HA's with good, swift shock cavalry backup, with a 2-1 ratio in numbers. That is, 1 HA plus 1 Shock Cav for every 1 Kat-Archer. I figure the HA's could engage and confuse the Kat-Archer while the shock cav engages and withdraws, with HA's firing to cover their retreat. It would require a lot of microing, but I think it might be doable. If it is, it would be cheaper than a single Kat-Archer, too.
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