BungieONI
Seven gremlins in a trench coat
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Considering past evidence, a martial Genius can thoroughly smash a martial Hero. See Yenyna vs the Thunder Horse Hero. More than that our Avatar of War is going to have better stats than Yenyna, (I consider average to be the limit of the semi-stable nature AN is talking about), and the stats he's better in actually make him a better general than she was. Put that together with focusing on the Forhuch and I expect this to be a solid win against them and the nomads before the next main turn.Hoping that we'll have crushed everyone around us within a single turn and having dealt with the fallout from overmartial Mass Levy and still have the wealth and actions for a Main Warships seems overly optimistic. If the reward were something amazing, or supporting the Yeomen for temp martial was actually useful, then committing to this even while we are unsure if we'll have time to do it makes sense, but +1 Navy is simply a nice bonus, not mind blowing.
It's important to divorce More Warships from the quest bonus when discussing this. Even assuming we Goomba Stomp everyone around us immediately and still decide to More Warships, all ending this quest will have cost us is 1 Navy, and we'd have gained other benefits in its place. I just don't see the point in constraining our potential actions further for that.
The HK with no hero are boned. It will probably take the mid turn after that to beat them. By this point we get to the next main turn, the one where we should have to take the trader action of warships. In the case that it turns out we don't have two main turns and instead must take warships on the next main turn we do have guild actions, actually finding an action slot is not an issue.
Now, the fallout from the mass levy is a problem. Something we can do though is to move the mercy out of main budget and start paying them again. That leaves us with 66 martial, further from that I expect the levies to die by the cartload. 10 or so martial is the ball park I am thinking of. Puts us at 56 by the time next main turn rolls around. It's a lot over, enough that there is going to be some kind of affect, but I don't expect it to take more than half our wealth cap.
Looking at our wealth income at that point and that tech is being converted to wealth, I am confident we can pay for it. And well, it eats martial which is a nice bonus.