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You are right. Roman "August 2" (a.d. IV Non. Sex.) wasn't August 2 in actual solar time because the pre-Julian Republican calendar was infamously uncalibrated at the time. The pontiffs had been delaying their civil dates by roughly six to eight weeks in order to avoid intercalary months. The war actually occurred in mid-June or early July 216 BC according to astronomical study that matched the equinoxes and the time of Apulia's grain harvest. The leap-year problem under Augustus is the only small error in your remark; it occurred much later and had no bearing on 216 BC.
My unsolicited two cents on the date (anniversary) of August 2, 216 BC.
The Gregorian calendar (current) has been in effect since 1582, but not all Western countries adopted it that year.
The Julian calendar was in effect from 45 BCE, but initially the priests incorrectly calculated the leap year (every three years, not every four). This error was not noticed until the reign of Augustus Octavian (probably 5 CE). So, this is where you need to be careful.
The date August 2, 216 BC is therefore a proleptic date for both calendars.
Of course, before Caesar's reform, there was the Roman calendar.
The problem is that it was terribly confusing.
Partly because of the structure of this calendar (the unusual length of the year) and partly because of the changes being introduced.
Then there is politics – the priests interference to lengthen or shorten the year – which influenced the election of two consuls.
In summary.
If a Roman chronicler wrote the date: August 2, 216 BC, we don't actually know when it was.
In the solar calendar, "when?" is interpreted in relation to the vernal equinox (today is March 20).
If a historian were to write that the spring equinox occurred on (and then provided the date) and that the battle took place on August 2, 216 BC, we could refer to that.
And so the disputes between historians and astronomers continue.
Researchers check to see if a chronicler might have mentioned what phase the Moon was in at the time.
They try to find other chroniclers who recorded that moment in their calendars.
In short:
The anniversary of this battle cannot be celebrated today, in the year 2026, on August 2.
What should be done?
Establish a Julian Day (JD) for this battle.
Next, determine the Julian Day (JD) for the vernal equinox and try to match it to today's date.
Best regards.
Postscript
Some historians believe it should be assumed that this occurred in June, not August.
I think there is already a random map generator, it's the random maps category
I think there is already a macedonian campaign someone made floating out there. I know @Vantha has been getting all the coding stuff in place for a new tutorial that would be exactly this except I think it'll have four scenarios.
I think all the features you requested @lilypoppy are in the works, but if you wanted to get started on your own campaign it wouldn't be too difficult to start, write out your story, start making the maps. When the rest of the features get added there may be some light scripting to do but then it'll be ready!
The battle of Cannae is 2241 years old! The anniversary passed three days ago on August 2, 2026.
To mark the occasion, I wanted to share an excellent recent documentary on the battle by the channel Invicta, featuring the brilliant Dr. Adrian Goldsworthy as a guest.