The Duke himself was going deep into Keisha's army and he did not manage to fabricate a trap for him. He wasn't even being sneaky, he charged in multiple times.
And if you wanna talk about the first day, it's true that both sides lost 10k. But that was because the Duke fell into a trap in a scenario where he was already outnumbered 1:3. So a draw is the best Keisha can get out of catching the Duke in a trap. That speaks for itself, really.