I don't think she can either win 1v2. In her 1v1v2, two of the AIs were fighting each other, so she actually played 1v1 for a while.

We need to host our own LLM and train it to defeat @borg-.

????????????????????? And here I thought @Seleucidsactually 1v3.... can you please word it properly next time and not sound deceiving. I would like to see you actually 1v3ing those AI or is 1v2 your limit? Oh and I'm talking to seleucid here not you Ittihat.

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.