Yes, the calculations mentioned are basically flight archery: arrows falling vertically to a target, which is, by far, not the way it was done. For "flat" archery, the simplest way to fix the approximate calculation is to evaluate the y (named z in the code, doesn't matter) CDF between -1.5 and infinite (meaning it never goes above the target but hits instead, it should actually be some big number, but far away from the target the probability density is low anyway, and all considers the distributions are the same as before, thus ignores physics, other methods could be considered), and get 86.67%, which multiplied by 73.35% from x gives a total of 63.57%. If one wants to apply the circular correction, the infinite part has to be ignored, thus only a half-square (73.35%*73.35%/2) is semi-circularised (the factor pi*1.5*1.5/(3*3) is still valid, since it should be half of both, which cancels out), giving: (63.57%-(73.35%*73.35%/2))+((73.35%*73.35%/2)*pi*1.5*1.5/(3*3))=57.8%. I got the probabilities numerically (counting points falling on those shapes, which could be readdressed if wanted), and got 63.6% and 59.7%, which confirms the calculations. For just the square and circle from before I get 53.8% (which indeed is (73.35%)^2) and 46.1% (which was calculated as 42.26%, the approximation of circularisation gives then a 4% difference, which is 2% for semi-circularisation).

The X and Y values are for a horizontal circle where the arrow will land, right? My thinking is that a much bigger range of different Y landing points would still hit the target because of the low, high velocity trajectory followed by the arrows. I suppose as a result the variation in X landing positions probably contributes a lot more to overall accuracy than the Y variations. I did a test: basic carthaginian archer at 60m with 0 techs versus hero (infantry hero): 1:42 to 3:47, duration of 100 shots according to unit fire rate. 87 damage dealt at 2.016 damage per hit gives us 43/100 shots hitting the hero. metadata.jsoncommands.txt I think if archers need a buff, we could boost their accuracy some and maybe their move speed slightly.     

Petra has some pretty obvious flaws. For example, if I take one of Petra towers, it's basically the beginning of the end for Petra. It doesn’t think like “There’s a tower here, I shouldn’t pass until I have enough units.” If there’s a tower (or fortress) in the way, their units will just walk right by it.. and die. Most of the new units it produces end up behaving suicidal because of that. Sometimes I even send all my resources just to keep Petra alive. Now plays better than the previous version, but what it really needs now isn’t stat boosts: it’s improvements in behavioral intelligence. Petra needs to be able to analyze the map and adapt to the situation. Also whenever I play against a random very hard Petra, it almost always launches an attack around the minute 10. This typical behavior doesn’t feel random to me at all, it seems like a very specific play style. Petra could behave in more diverse ways. Petra never harasses with cavalry or sneaks rams around for a surprise attack. Its predictability is, in my opinion, its biggest disadvantage, even in "random" mode.   Btw I checked the replay and this is 1v1v2. Green and Yellow had already weakened each other before you attacked them.  I’m sure you can handle a 1v3 as well. It’d be great if you shared the replay of it too.

Or better pathfinding, or larger bodies of water.   So is depth somehow taken into account already? Maybe, haven't played many water scenarios.

An amazing piece of advice: recommending a blacksmith in phase 1.  ChatGPT just scrapes a chaotic mess off the internet (95% from this forum) and regurgitates it like it’s been filtered through a drunken brain. It has zero real understanding of the game. Even if it somehow managed to play, it’d still be stuck at a singleplayer level.  Multiplayer strategies, as mentioned in the topic, are a completely different thing. Real opponents can instantly ruin whatever plans you come up with. You’re racing both against other minds and the clock. You usually don’t even get to trade at all (depends on the map and your opponents). And if you’re playing against Petra, you don’t really need any serious strategy anyway. Just produce a solid number of units and it will do. When would you ever actually need a strategy with Petra? Only if you’re playing 1v2+ on very hard.